Michelle Rose Ga1

A Thesis submitted in confomiity with

the requirements for the Degree of

MASTER OF APPLIED SCIENCE

in the University of Toronto

O Copyright by M.R. Gd, 1999

Depart ment of Mechanical Engineering

Instihite of Biomedical and Biomaterials Engineering

University of Toronto

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The development of a glaucoma drainage valve was continued firom an earlier study. The

valve featured an osmotically generated opening/closing pressure, which was expected to

provide a level of intraocular pressure control supenor to that of currently used valves. A

large sale prototype was designed, constructed, mathematically modelled, and tested.

Tests ushg a constant supply pressure revealed an unacceptably long response tirne. In

order to reduce the response time, a second large scale prototype was designed,

constructed, mathematically modeiled, and tested. Testing with a constant supply pressure

c o h e d an adequate reduction in response tirne. The dynamic response of the valve

was then tested by replacing the constant supply pressure with constant supply flows. The

valve did not wmpletely close at low flow levels, a flaw which must be corrected before

development may continue.

My sincere thanks to my advisor, Dr. C. Ross Ethier, for his guidance and incredible

patience during the past two years. There are no adequate words to express my

appreciation.

Thanks to MIE technicians David Esdaile, Paul Kovar, and Jeff Sansorne for a n s w e ~ g

rnany questions and doing a wonderhl job mnstructing my prototypes. Thanks to Brenda

Fung (MIE) and Anne Mitchell (BBME) for helping me with the administrative details.

Financial support for this project was kindly provideci by the Glaucoma Research Society

of Canada and the Naturai Sciences a d Engineering Research Council of Canada.

. . Ab stract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . u

... Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ui Tableofcontents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv ListofSymbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

ListofFigures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . List of Tables xi

Chapter One: Introduction 1 . 1 Overview & Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 The Eye and Glaucoma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Glaucuma Treatment 4

1.3.1 Medication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

. . . . . . . . . . . . . . . . . . . . . . . . . . P-Adrenergic Antagonists (P-blockers) 5

. . . . . . . . . . . . . . . . . . . . . . . . . . . Carûonic Anhydrase Inhibitors (CAI) 5

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cholinergie Agonists 5 Prostagiandins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3 -2 Trabeculoplasty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3 -3 Filtration Surgery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1 .3.4 Drainage Implants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Non-Restrictive Flow Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Restrictive Flow Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1

1.4 Previous work on the Proposed Drainage Impiant . . . . . . . . . . . . . . . . . . . . . . 14 1.4.1 Osmotic Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.4.2 Proposed Valve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.4.3 Design Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

1 .4.4 Verification of Valve Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

1.4.5 Verification of Osmotic Valve Characteristics . . . . . . . . . . . . . . . . . . . . . 25

1.4.6Summ ary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Chapter Two: Project Outline

2.1 Hypothesis and Long Term Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.2 Specific Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Valve II Testing Results 80

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Dextran Retention 80

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 -2 Valve Il Response Tirne 81

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.3 Valve II Dynamic Response 84

Chapter Seven: Conclusions 7.1Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

7.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 7.3 Recomrnendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

7.3.1 Valve Design and Experimental Apparatus . . . . . . . . . . . . . . . . . . . . . . . 92

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 -2 Future Work 93

References

Appendix A . Drawings for Valve 1

Appendk B . Drawings for Valve II

Appendix C . Regession Analysis Output

Appendk D . Deformation Calculations

vii

area coliapsible tube cross sectional area

manometer tube cross sectional area tiltration surface ara virial coefficients

concentration

tube diameter modulus of elasticity

gravitational acceleration

collapsible tube wall thickness membrane permeability

tube Iaw constant

tube length

molecular weight

molecular weight cut-off

pressurtb chamber pressure

supply pressure

net potential diierence

pressure in dextran cuff

volume flow gas constant

flow resistance coliapsible tube radius

Reynolds number

temperature

tune

volume

collapsible tube volume

min

rnL

mL

manorneter tube volume flow across semipermeable membrane fluid velocity dynamic fluid viscosity kinematic fluid viscosity Poisson's ratio osmotic pressure fluid density time constant

d s

N dm2 m2/s - Pa, d g kgh?

min

Figure 1.1. Sagittal section through a human eyebd . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Figure 1.2. Major stages of filtrationsurgery 8

. . . . . . . . . . . . . . . . . . . Figure 1.3 : In situ positioning of the Ahmed Glaucoma Valve 10

Figure 1.4. Exarnples of currently existing glaucoma drainage implants . . . . . . . . . . . 12

Figure 1.5. Two-ceiied system with osmolarity gradient . . . . . . . . . . . . . . . . . . . . . . . 15

Figure 1.6. Schematic drawings of the proposed osrnotic valve . . . . . . . . . . . . . . . . . . 19

Figure 1.7. Sit's (1 996) osmotically controlled valve prototype . . . . . . . . . . . . . . . . . . 20

Figure 1.8 : Experimental apparatus used to determine how closing pressure affects flow

through the collapsible tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Figure 1.9. Collapsible tube flow characteristics (water) . . . . . . . . . . . . . . . . . . . . . . . 23

Figure 1.1 O: Coiiapsible tube flow characteristics (glycerol) . . . . . . . . . . . . . . . . . . . . 24

Figure 1.1 1 : Experimental apparatus used to detennine feasibility of using osmotic pressure as closing pressure source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Figure 1.12. Osrnostic valve flow charateristics (Sit 1996) . . . . . . . . . . . . . . . . . . . . . 26

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Figure 3.1 : Valve 1 33

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Figure 3.2. Valve 1 O dialysis membrane sed 34

Figure 3.3. ValveI-fillingportsandfillingtraas . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Figure 3.4. Valve 1 assembly 36

. . . . . . . . . . . . . . Figure 3.5. Cornparison of Sit's prototype and Valve I O water flow 40

. . . . . . . . . . . . Figure 3.6. Cornparison of Sit's prototype and Valve I w glycerol flow 41

Figure 3.7: Comparison of Sit's (1996) prototype and Valve 1 . glycerol flow. osmotic closingpressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Figure 4 . 1: Manometer configuration 46

. . . . . . . . . . . . . . . . . . . . . . Figure 4.2. Water flux across a semipenneable membrane 48

. . . . . . . . . . . . . . . . Figure 4.3 : Effect of concentration polarization on glycerol flow 49

. . . . . . . . . . . . Figure 4.4. Hypothesized pressure vs t h e relationship in pressure cuff 50

. . . . . . . . . . . . . . . . . . Figure 4.5. Water flux across 14K MWCO dialysis membrane 54

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Figure 4.6. Volume changes in the dextran c& 55

Figure 4.7. Experimental apparatus for determinhg system response tirne . . . . . . . . . 58

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Figure 4.8. Valve 1 time response data 60

. . . . . . . . . Figure 4.9. Log-linear regression curve fit for Valve I time response data 61

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Figure S . 1 : Modifications to Valve 1 66

. . . . . . . . . . . . . . . . . . . . . . . . . . . Figure 5.2. Valve 1 (modified) time response data 68

. . . . . . . . . . . . . Figure 6.1 : Valve II (a) photograph; @) labelled cross-sectional view 71

xi

Figure 6.2. Membrane support structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

Figure 6.3. Experimental apparatus for testing dynamic response of Valve Ii . . . . . . . 79

Figure 6.4. Valve II time response data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

Figure 6.5. Valve 11 dynarnic tests results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

Figure 6.6. The tube law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

. . . . . . . . Table 4.1 : Cornparison of published values for wia l coefficients of dextran 47

Table 4.2. Cornparison of system time constants for Valve 1 . . . . . . . . . . . . . . . . . . . . 62

Table 5.1 : Comparison of syaem time constants for Valve 1 and Valve 1 (modified) . . 69

. . . . . . Table 6.1 : Cornparison of system tirne constants between Valve I and Valve II 82

Neady 2% of the population over 50 years old suffers fiom glaucoma, the second leading

cause of blindness in Canada (Elolia et al., 1998). In most cases, glaucoma is

characterired by hi@ intraocular pressure (IOP). Kigh IOP Ievels develop when aqueous

humor drainage pathways become p d a l l y blocked causing an increase in resistance to

aqueous humor outfiow. Untreated glaucorna causes heparable damage to the optic

nerve.

Although there is no way of curing this disease, treatrnents have been developed to reduce

IOP and help presewe vision. They range fiom non-invasive topical medications to

drainage implants. Implants, which incorporate sorne form of flow-regulation mechanism,

provide an alternative aqueous humor drainage pathway nom the eye, and are typicaliy

2

used as a last resort in severe cases of glaucoma. Unfominately, implants currently in use

provide much coarser pressure control than is desirable. Specincally, IOP can often

becorne: (i) too high before fluid is ailowed to drain from the eye, risking further damage

to the optic nerve; or (ü) too low before outfiow is restricted, risking softening of the eye

and coliapse of the cornea. An improved Unplant would eliminate this dangerous hysteresis

between maximum and minimum IOPs, providing finer control and mahtaining a d e level

of IOP at al1 tirnes.

In the remainder of this chapter, the eye, glaucoma, glaucoma treatments, and the previous

work done on a new implant design are discussed in more detail.

1.2 THE EYE AND GLAUCOMA

The eye (figure 1.1) is essentiaily a sofbtissue sack that is divided into three chambers:

vitreous, posterior and anterior. Containing no bone or wtilage, the eye's shape is

maintained by the action of fluid pressure. The vitreous chamber is Wed with a

transparent, geClike material called the vitreous body. The posterior and antenor

chambers are fiiled with a transparent liquid called the aqueous humor. In addition to

providing structure, the aqueous humor also supplies the celis of the lens and coma with

nutrients and carries away metabolic waste products. Blood, which is normdy

responsible for this task, is not present in these tissues, since its opaque nature would

prevent light fiom passing through the eye.

3

Aqueous humor, a clear, coiourless liquid, is produced by the ciliary body at a rate of 2-

3pVmui (Guyton and Hall, 1996), and continually drains from the antenor chamber

through a duct known as Schlernrn's Canal, resulting in a relatively constant IOP. The

average valve of IOP in a healthy individual is 1 SmmHg, with a range fiom 12 to 2OrnmHg

(Guyton and Hall, 1996).

Figm 1.1: Sagittal section through a human eyeball. pavson. 19691

Most giaucomas develop when the aqueous humor drainage pathways become partially or

fuUy blocked, increasing resistance to normal outflow. IOP is related to aqueous hurnor

flow (Q) and flow resistance (R) by:

IOP = QR

4

The volume of the eye can be considered constant, therefore the tirne-averaged outflow of

aqueous humor must be equal to the amount produced by the ciliary body. Thus, when

the resistance to aqueous humor outfiow is increased, the result is an elevated IOP. This

elevated pressure causes irreparable darnage to the optic nerve, possibly by inhibithg

blood flow in capillaries of the optic nerve, thus preventing nutnents firom reaching the

individual neurons (Varma and Minckler, 1996). lf the IOP is permitted to remain above

2OmmHg for an extended period of the, vision is progressively impaired and blindness

eventuaiiy results. In extreme cases where IOP can be as high as 60 or 7OrnmH&

blindness rnay ocnir w i t h days or even hours (Guyton and Hall, 1996). in the case of

normal-tension glaucomq even 10P values of 15-2OmmHg can cause optic nerve damage

(Werner, 1 996).

Current medical therapy for al1 forms of glaucoma seeks to lower IOP. This is

accomplished by either reducing aqueous humor production, or reducing resistance to

aqueous humor oudlow. Frequently, these two strategies are combineci. Aithough

darnage to the optic nerve can not be repaired, lowering IOP can help to prevem fkther

damage. Available approaches for the treatment of glaucoma are reviewed below.

1.3.1 MEDICATION

The simplest treatment is the use of medication. Various types of dmgs can be used to

lower IOP. Some of these drug classes and the physiological mechanisms by which they

lower IOP are sumrnarked below.

P-blockers are believed to act on the P,-adrenergic receptors of the epithelid cells of the

ciliary body. Stimulation of the ciliary process is prevented, inhibiting the production of

aqueous humor, and reducing flow through the eye to a basal level.

Carbonic anhydrase catalyses the chernical reaction that fonns bicarbonate. In the ciliary

body, the formation of bicarbonate is iinked to the secretion of sodium ions, which are

required for the production of aqueous humor. CAIs reduce production (i.e. flow) of

aqueous hurnor by inhibiting the formation of biwbonate.

CHOUNERGIC AGONISTS

Cholinergie agonists, in pmiculw, pilocarpine, act on the muscarhic cholinergie receptors

of the ciliary muscle fibres, stimulating contraction. Contraction of the ciliary muscle

produces tension on the scleral spur. This tension is thought to pull open the trabmlar

6

meshwork (the tissue which separates Schlemm's Canal nom the anterior chamber),

reducing resktance to aqueous humor outflow.

PROSTAGLANDNS

Although the major aqueous humor drainage pathway is via the trabecular meshwork and

Schlemm's Canal, flow may also take the uveosclerd route. (Aqueous humor exiting the

anterior charnber by this route passes into the root of the iris, then flows between ciliary

muscle fibres, then percoiates through the sclera). The proaoglandin PGF2, dilates the

intramuscular spaces in the ciiiary body, reducing flow resistance, thus lowering IOP.

Drug therapy is a non-invasive, low risk treatment. However, in many cases, medication

does not sufficiently lower IOP and surgical intervention is required.

The least invasive surgical therapy for giaucoma is argon laser trabeculoplasty (ALT), in

which an argon laser is used to make smaii bums in the trabecular meshwork. It has been

theorized that during the healing process, contraction of the tissue causes the trabecular

meshwork to lose some of its resistance to the flow of aqueous humor.

ALT is not always successfùl and is no longer wmmonly used. In about 50% of cases,

IOP levels become dangerously high within five years of the procedure. In these

situations, a second ALT is generally performed, unless IOP levels have rernained normal

for l e s than a year, in which case filtration surgeiy is recommended.

During filtration surgery, the surgeon attempts to bypass the outfiow pathway altogether

and create an altemate route for aqueous humor outfiow. Figures 1.2 (a) and (b) illustrate

the procedure, and show a cross-sectional view of the resulting drainage pathway,

respectively. An incision is made in the conjunctiva to expose the sclera. Ushg a sharp

blade, the surgeon penetrates through haif of the scleral layer and cuts to fom a

rectangular fiap. A small block of tissue is excised from undemeath the fiap before it is

loosely sutured closed. The conjunctiva is tightly sutured back in its original position.

Aqueous humor seeps out of the chamber through the f'iap's edges. The flow rate can be

adjusted by changing the tightness of the sutures.

This procedure has a poor prognosis for certain types of gfaucoma, and also if the patient

has had surgery penormed on the sclera previously. However, even if the prognosis is

good, the formation of scar tissue may result in failure to maintain a Iow IOP. Laser

treatment to remove the scar tissue is sometixnes effkctive. If this is unsuccessfiii, the

surgeon may attempt another fltration surgery in another quadrant of the eye or

recommend the implantation of a drainage device.

(ii i)

(ii

scleral flap

. . - . . . . . . . . . . . . . . . . . . . . .

1 +excised block

. t Figure L .2(a): Major stages of filtration surgery; (i) penetrating the conjunctiva, (ii)

cutting the half-thickness sclerai flap, (fi) excising a block of scled tissue, (iv) the

sutured flap [ Ritch et al., 19961; (b): Cross-sectional schematic of the sclera after

fiitration surgery, arrows indicate aqueous humor outflow pathway.

A Nowl Glaucoma h m q c Valve

In cases where filtration surgery fails to control IOP or has a poor prognosis, implantable

devices are used. Implants are designed to provide a low-resistance drainage route for

aqueous humor, thus bypassing conventional outflow pathways. Implants direct aqueous

humor outnow frorn the anterior chamber to the space between the sclera and conjunctiva.

From there, the aqueous humor moves through intercellular spaces and is absorbed by

orbital capillaries and lymphatics (Ritch et al., 1996). A wide variety of implants have

been developed in the past 30 years, ranging fiom a simple tube to more complex syaems

involving filtration plates and valves.

Genedy speaking, these drainage systems consist of two sections: an inlet tube and an

outlet structure. The inlet tubes are fairly standard between the various systems: a piece

of silicone tubing with an outer diameter of approximately 0.6 mm and inner diameter of

about 0.3 mm. The proximal end is placed in the antenor chamber. The distai end of the

tubhg is comeaed to a variety of possible structures, such as silicone bands, round

silicone discs, or irregularly shaped plates through which the fluid exits. These structures

are oflen referred to as explants. Figure 1.3 illustrates the in situ positioning of an

implant, and its size relative to the eye.

Figure 1.3: in situ positioning of the Ahrned Glaucoma Valve New Worid Medical,

19961

If aqueous hurnor were perrnitted to flow fieely through an explant, the anterior chamber

would coliapse due to hypotony, that is, low intraocular pressure. Therefore, explants

rnust incorporate some mechanism by which outfiow is controlled. Depending on the

outflow control mechanism in the explant, drainage implants are classified as either non-

restrictive or restrictive flow devices. Current implants belonging to both classifications

are described below, and are illustrated in figure 1.4.

An object implanteci in the body will soon find itself covered with fibrous tissue (Pilliar,

1997). The Molteno drainage implant, introduced in 1969, takes advantage of this

phenornenon to limit aqueous humor outflow. Fibrous tissue foms a "filtration bleb"

around a perforated, aaylic plate explant. The filtration bleb pennits sufficient outflow to

maintain a satisfactorily low IOP (Molteno et al., 1977), yet provides enough flow

resistance to prevent hypotony .

11

The Baerveldt implant works on the same prhciple as Molteno's device, but has holes in

the centre of the acrylic plate explant. When the fiitration bleb foms, the fibrous tissue

goes through the holes, holding the explant f i d y in place.

The major disadvantage associated with these types of explants is that the filtration bleb

takes several weeks to form. This means that there must be a way to temporarily limit the

oudlow during bleb development. To achieve this, the silicone tube leading fiom the

antenor chamber to the explant is often partiaily tied or clamped at the t h e of

implantation, requiring a second surgery several weeks later to release the constriction.

R E S ~ C T T V E FLOW DEVICES

Attempting to avoid shon-term post-operative complications, particularly overdrainage

and hypo tony, implants were designed t hat incorporate flow-restrictive elements.

The Krupin Eye Disk consias of a silicone tube and plate explant. similar to Molteno's

design. However, rather than simply allowing fluid in the tube to drain into the explant,

the tube's distal end is sealed and there are severai horizontal and venicai slits. As IOP

increases, the tube elastically defoms and permits fluid to enter the explant.

The OptiMed implant regulates flow with a conductive polymethyl methacrylate matrix.

Capillary action draws fluid through the matxix as IOP increases.

In the Ahmed implant, fluid must flow between two layers of thin silicone membrane

before leavhg the explant. At low IOP, the membrane layers collapse preventing outflow;

and as IOP increases, the fluid pressure forces the membrane layers apart, openhg the

pathway.

Figure 1.4: Examples of cwrentty existing giaucoma drainage implants: Molteno (A),

Baerveldt (B), ûptimed (C), Ahmed O), Knrpin (E) [Ritch er al., 19961

13

In vivo testing of several ditferent giaucoma drainage implants was performed in rabbit

eyes by Prata et al. (1 995). Their results demonstraîed that none of the devices

maintained their nominal pressure levels when being pefised at the flow rates expected in

human eyes. The implants referred to as "valves" pedormed like fiow restrictors, not as

true valves which open and close at specific pressures. Porter et al. (1997) did an in virro

study of several implants and discovered a wide range in their penormances. The valved

implants had average ciosing pressures that ranged between O. 1 and 12.6mmHg. Only 2

out of thq8 valves tested by Porter el al. succeeded in closing before the pressure

dropped below 9rnmHg. The desired IOP in moa cases is approximately 1SmmHg. Some

surgeons rnay lower IOP to the IO- 12mmHg range, but pressures below this range put the

coma at risk of coilapshg.

The disadvantage with this class of implants is that although they offer post-operative flow

resistance, they do not behave as tnie valves with speci£ic and consistent opening and

closing pressures. This may be an improvement over non-restrictive flow devices, but the

problem of accurately controllhg post-operative IOP remains unaddressed.

A new type of drainage implant was proposed in a study by Sit (1996). This device was

expected to elimlliate the difnculties expenenced with current implants by balancing fluid

and osmotic pressure to control outfiow.

Sit's valve design took the following criteria into consideration:

the valve should have definite opening and closing pressures in order to precisely controI IOP the valve should be fiilly open at aiî pressures above the opening pressure the valve should be simply designed and durable, containing no electronic components and a minimum of moving parts the valve should be compact and biocompatible

The flow through Sit's valve is controlled using osmotic pressure. Therefore, pnor to any

further discussion on Sit's valve, a brief overview of osrnotic pressure is necessary.

Osmosis is the movement of water across a serni-permeable membrane from an area of

high osrnolarity to one of low osmolarity. Osrnolarity refers to the concentration of

dissolved cornponents. For example, a 1 millimolar solution of NaCl, which dissociates

into Na' and CI', has an osmolarity of 2 miliiosmoles.

15

In a twoceiied system such as the one show in figure 1.5, water moves across the serni-

permeable membrane f?om A to B in response to the osmolarity gradient. The result is

higher pressure in B, which drives water fiom B to A Eventually, the trammembrane

osmolarity and pressure dserences reach a point of equilibnurn where the net flux of

water across the membrane is zero. The pressure difference which exists between the two

chambers at this point is referred to as the osmotic pressure dserence.

Figure 1.5: A two-celled system. The celis are separateci with a semi-permeable

membrane and the ceiis contain solutions of drfferent osmolarity. The m w s represent

water crosshg the membrane in response to osmolarity and pressure gradients. Initidly,

(a) the net flux of water is ffom A to B in response to the osmolarity differenœ. resulting

in a higher pressure in B. Eventuaily (b) the pressure difference, hn between the cells

becornes great enough to d u c e the net flux of water between the œlls to zero. The

value of AIi at this point is the osmotic pressure diflerence.

16

The relationship between the osmotic pressure and the solute concentration of a solution

can be described by the equation:

Where the osmotic pressure, 4 is expressed in Pascals; A, are solute-solvent-condition

specific vinal coefficients pa(mUgfi; and c is the solute concentration WrnL]. For ideal

solutions, in which solute-solute interactions can be negleded, this equation can be

simplified to an expression known as the van't Hoff equation:

II = cRT

Where II is again expressed in Pascals; c is the concentration of dissociated species

(osmolarity) between the two chamben [m~=moVm']; R is the gas constant

[8.3 145 1 kgm2/(s2*rnolX)]; and T is the temperature KI. The osmotic pressure gradient,

AII, is determined by calculating II values for both solutions and taking the diference.

Sit's valve design is based on the concept of Stariing resistors, which are used to study

fluid dynarnics in blood vessels. A Starling resistor consists of a collapsible tube that is

attached to ngid tubes at both ends and surrounded by a rîgid chamber. The collapsible

tube is collapsed by pressurizllig the interior of the chamber. An extemal reservoir

supplies the fluid that flows through the collapsible tube.

Using such a device, Lyon et al. (1980) determined relationships between fiow (Q),

chamber pressure (PJ and fluid supply pressure (P,). For low Reynolds number flows, it

was shown that when fluid supply pressures were below the chamber pressure, the

coiiapsible tube remained closed and there was essentially no flow:

When fluid supply pressures were above the chamber pressure, the coiiapsible tube

opened, and fluid passed through the device. The outflow in this case depended on supply

pressure through the relationship:

Where R is the fiow resistance in the tube, dependent on fluid viscosity, tube length and

tube radius.

These relationships between supply pressure and outfiow were deemed ideal for a

glaucoma drainage valve: closed to flow when P,<P,, open to flow when P,>P,. However,

a Starling resistor only exhibits this behaviour if the Reynolds number of the flow is

sufficiently low, that is, less than 1 (Conrad. 1969). Treating aqueous humor as water at

18

37°C and assuming: a viscosity ( v ) as 7.46E-7 m2/s (Roberson & Crowe, 1993), a Bow

rate (Q) as 2p.L/min, and a typical tube diameter @) of 1 mm, the Reynolds number for

aqueous hurnor fiow is computed as:

This Reynolds number was l e s than 1, indicating that a glaucoma drainage implant

incorporating a Starling resistor-type valve could indeed provide a precise opening and

closing pressure. The challenge in adapting the Starling resistor for use in an implant was

to determine an appropnate rnethod of pressurizing the space around the coUapsible tube.

The pressure source had to be sescontaineci and constant.

Sit decided to use osmotic pressure to generate the opening and closing pressure of the

coilapsible tube. Like the Starling resistor, this "osmotic valve" consisted of a collapsible

latex tube housed in a rigid chamber. The collapsible tube was surrounded by a

semipermeable membrane "cuff'. The rigid chamber was filled with water, and the cuff

was filied with a solution of higher osmolarity (figure 1.6a).

Figure 1.6: Schematic drawings of the proposed osmotic valve in the open and closed

positions. h w s indicate fluid flow through the open valve. ' A indiates a space

filied with water, "B" indicates a space filleci with a solution of higher osmolarity; (a)

cross-section, (b) longitudinai cross-section.

This design is comparable to the simple two-celled system discussed in section 1.4.1; the

outer chamber containhg water is ce1 A, and the cuffis ce11 B. The major differences are

that celi B is inside of celi A, rather than the cells being beside each other; and there is a

collapsible tube running through ceIl B. (Note that any fluid passing through the lumen of

the coiiapsible tube does not corne into contact with the solution in cell B.) Following the

osmotic gradient, water moves from A to B. and the resulting pressure increase in B

collapses the latex tube (figure 1.6b). When the supply fluid pressure is just greater than

the osmotic pressure difFerence between A and B, water is forced out of the cuff, allowing

the coiiapsed tube to open and the supply fluid to pass through the lumen. Once the

supply pressure drops to a value below the osmotic pressure gradient, water moves from

A to B and the tube collapses.

1.4.3 DESIGN DETAILS

Sit's device (figure 1.7) incorporated a 12" length of collapsible latex tubing (%" diameter

Penrose Tube, Baxter Medical Supply, Mississauga ON) within a semi-permeable

membrane "cuff' (Spectra Por 2 Dialysis Tubing, 12000-14000 MWCO, 32mm-flat dry

width, Spectmm Medical Technologies, Houston TX). Note: the MWCO or Molecular

Weight Cutoffrating indicates the size of the srnailest molecules that are not permitted to

pass through the membrane, Le. molecules of a molecular weight less than 12000 atornic

rnass units are able to pass through and those greater than 14000 are retained.

Both ends of the collapsible tubing and semipermeable membrane were attached to %"

buMead fittings and secured with wire wraps. This assembly was housed in a @id

plexiglass chamber with holes for the buMead fittings on the ends. Fastened with

machine screws, the chamber iid compressed a rectangular gasket, providing a watertight

seal. Two !4" buMead fittings in the chamber lid served as tilling and bleed ports.

Figure 1.7: Sit's (1996) osmotically controiied vaive prototype.

This osmotic pressure cuntroiled valve was thought to be an improvement over currently

used devices because it would aüow more precise control over IOP. Slit valves in silicone

tubes, cornmonly used in current valved implants, will begin to elastically defom (Le.

open) at pressures lower than their nominal opening pressure. This means that fluid is

passing through the valve before it is supposed to open, making maintenance of a

consistent IOP difncult. In addition, the nominal opening pressure of a slit valve is greatly

dependent on the slit size and elastic properties of the tube. Thus it is not unusual for

"identicai" valves to have dserent opening pressures (Porter et al., 1997). On the other

hand, in the case of Sit's design, it was hypothesized that overcoming the osmotic

pressure difference would be a repeatable event. Thus, it was hoped that this design would

result in a consistent valve opening pressure.

1.4.4 VERIFICATION OF VALVE CHARACTER~STICS

Before testing the complete valve, Sit investigated the behaviour of the coliapsible tube

independently of the osmotic pressure cuE The purpose of this investigation was to

determine how pressure exerted on the coflapsible tube afFeas the flow through it. The

experimental apparatus (figure 1.8) consisted of the valve, without the dextran cufF. a

water reservoir to set the valve's closing pressure; and a fluid supply reservoir.

tId 4 fluid eupply. Pe source

Figure 1.8: Experimental apparatus used to determine how closing pressure affects flow

through the coffapsible tube.

4 &mal Pc eource

valve v

For the first set of experiments, the supply fluid was water. The water reservoir was set to

an arbitrarily chosen height of lOcm above the valve outlet, which translates into a closing

4 collection reeervoir

\

pressure (PJ of 7.4rnmHg. The height of the supply reservoir was incrementaily

>>

,

increased, and supply pressure (PJ and correspondhg flow through the valve were

recorded. The height of the water reservoir was then increased to 20- which translates

into a P, of 14.7mmHg and the experirnents were repeated.

In a second set of experiments, the supply fluid was changed to glycerol. Glycerol has a

viswsity three orders of magnitude higher than water and was expected to provide the

low Reynolds number flow expected in vivo.

When water was used as the supply fluid, results show that the valve aiways dowed a

s m d amount of oudlow (figure 1.9). However, there was a dramatic increase in flow

23

afker P, surpassed P,. Visual observations of the coiiapsible tube indicated that it remaineci

closed when P, was les than P,. However, dong the folded sides of the tube there

appeared to be small channels, through which water evidently passed prior to opening.

Figure 1.9: Enect of (a) 7.4 and (b) 14.7mmHg coiiapsiile tube closing pressures on

water flow at variable supply pressures.

When giycerol was used as the supply fluid, results show that the valve aiiowed no flow

until P, surpasseci P, (figure 1.10). n ie channels observed during the water tests were also

present during the glycerol tests. However, the flow resistance through the narrow

channels was hi& enough to prevent significant glycerol outtlow until P, > P,.

O 1 2 3 4

glycerol outfiow [mus]

O 1 2 3 4 5

glycerol outfiow [mus]

Figure 1.10: Enat of (a) 7.4 and @) 14.7mmHg coilapsible tube dosing prasurrs on

giycerol flow at variable supply pressures.

These preliminary tests, particularly those involving glycerol as the supply fluid, indicated

that flow through a wliapsible tube can indeed be regulated by exerting a closing pressure

on it f?om an extemal source. Further testing involved replacing the extemal pressure

source with the osmotic pressure source.

1.4.5 VERIFKATION OF O S M O ~ C VALVE CHARA~RISTICS

The purpose of Sit's next investigation was to deterrnine the feasibility of using an osmotic

pressure source to set the valve's closing pressure. The experimental apparatus (figure

1.1 1) consisted of: the valve, with the semi-permeable membrane cuff in place; a supply

reservoir; and a penstaltic pump.

\

4 collection rcsavoir valve b

Figure 1.1 1 : Experimentai apparatus used to determine fm'bility of usiag an osmotic

pressure source to set the valve's closing pressure.

26

The d w a s Wed with a 0.224rnM solution of 298 000 MW dextran (Sigma Chernicals,

St. Louis MO). Assurning the validity of using the van't Hoff equation in this situation by

neglecting solute-solute interactions, the vdue 0.224rnM corresponds to an osmotic

pressure of 4.3mmHg. (These values are assumed to have been selected arbitrarily by Sit,

as they do not have any obvious significance.)

Lnitial observations indicated that several hours were required for equilibrium to be

established across the semi-permeable membrane. For this reason, the glycerol supply

reservoir was set at a value of 4.6mrnHg, which is slightly greater than the osmoticdy

generated closing pressure. A peristaltic pump was used to maintain a constant fluid level

in the reservoir, and glycerol flow through the valve was monitored over a 24 hour period.

Figure 1.12: Glycerol £iow through valve using a 4.6mmHg supply pressure and

4.3mmHg osmoticaily generated closing pressure.

The results of this test show that the glycerol flow through the valve steadily increased as

a function of tirne (figure 1.12), supposedly because water moved from the dextran

solution in the cuff into the outer charnber, permitting the collapsed tube to open.

However, at the end of the 24 hour period, visual observations of the coiiapsible tube

indicated that it was completelj open. This was considered uncharacteristic for a tube

under pressure. It was believed that an improper seal caused dextran to leak into the outer

charnber. This elirninated the osmotic pressure difFerence and aliowed a very modest

supply pressure to fully open the coiiapsible tube.

Drainage implants for treatment of glaucoma provide a low-resistance outflow route for

aqueous humor, by-passing conventional drainage pathways. Drainage implants are

classified as "non-restrictive" or "restrictive" depending on their flow control mechanisms.

Non-restrictive flow devices rely on the formation of a filtration bleb to control outflow

and prevent over drainage. Short-term post-implantation hypotony is a chronic problem

with this class of devices, as the filtration bleb requires several weeks to form. Restrictive

flow devices incorporate flow-resistive elements, such as slit valves or conductive

matrices. Although they represent an improvement over non-restrictive devices, none of

the currently existing restrictive flow devices have exact an opening and closing pressure,

and hence they are unable to accurately control post-impiantation IOP.

28

Sit (1996) proposed a glaucorna drainage valve based on the concept of a Starling resistor.

The valve consisted of a flexible tube that is coilapses under pressure. Under low Reynolds

number conditions, the valve was hypothesized to remah closed until the fluid supply

pressure increased to values greater than the pressure used to cuiIapse the flexible tube.

This hypothesis was proven using glycerol as the supply fluid and an extemal pressure

source to coiiapse the flexible tube. In order to make the valve self-contained, the extemal

pressure source was replaced by surrounding the collapsible tube with a semi-permeable

membrane "cuff". The cuff was filied with a dextran solution, and the surrounding

chamber was filled with water. The closing pressure for the collapsible tube was generated

by the osmotic pressure difference between the dextran solution and water. DitFcuIties in

obtaining a watertight seal for the semi-permeable membrane prevented any usehl

experiments from taking place.

Due to the encouraging results obtained using an extemal source to set valve closing

pressure, Sit recommended fbrther investigation using an osmotically generated pressure.

However, modifications to the valve design would be necessary prior to any funher

testing. In particular, a better seal for the serni-permeable membrane was required.

It was hyphesied that :

1. A large sale model of an osmotically controlled valve, such as the one proposed in an

earlier study by Sit (1 996). would: (i) consistently open and close at suppiy pressures

above and below the osmotic pressure difference, respectively and (ü) respond to

pressure changes relatively quickly.

2. A correlation of operating characteristics could be made between a large-scale model

and an actual-sde valve, by applying the principles of similitude.

The long tenn goal was to develop a glaucorna drainage valve whose operating

characteristics are more prediaable than those of currently existing implants. In

particular, we wished to develop a valve that has consistent opening and closing pressures.

2.2 SPECIFIC OBJECTIVES

The initial project objectives were :

1. To construa and test a large-sale m ode1 of an osmoti c pressure controlled valve,

based on Sit's (1996) design and recomrnendations, in order to: (i) ver* that the

A Novtl G l u a m a Dnmige Vaive

30

valve has a consistent opening and closing pressure and (ü) that the valve was capable

of controllhg outflow and maintainhg a constant supply pressure.

2. To apply the prhciples of similitude in order to scde the valve to dimensions

appropriate for implantation. This would require the establishment of dimensionless

numbers using the Buckingham II Theorem. Analysis would focus on the factors

affecthg the buckling of the collapsible tube and resistivity of the serni-permeable

membrane to osmotic fiow.

3. To consmict and test an actual-scale prototype of the valve in order to (i) ver@ that it

had a consistent opening and closing pressure and (ii) enmre that it demonstrated an

adequate dynarnic response' to the characteristic pressure changes of the eye

Unforeseen difficulties due to the slow filtration properties of the dialysis membrane

impeded progress of the project considerably. The project become focused on completing

the first objective, which was segmented into the following tasks:

'For the purposes of this study, "adequate dynamic response" refers to valve opening and closing occurring within an hour as opposed to within a day. An instantaneous dynamic response is not desirable, as the device would respond to short term pressure disturbances, such as rubbing the closed eyelid. A response time of several hours to a day is considered too long, since prolonged exposure to an elevated IOP is thought to be harmfûl to the optic nerve. Therefore, a response time of 1 hour was arbitrarily selected as an adequate value.

31

1. To ident* problems encountered by Sit (1 996) and construct a bench-sale prototype

(Valve 1) of an osmotic pressure controiied valve based on the original design and

recomrnendations.

2. To v e e the operation of Valve I by recreating the tests performed by Sit (1 996)

using extemally and osmotically generated valve closing pressures.

3. To i d e n e aspects of Valve 1 which could be modifieci to facilitate a reduction in

response the , and design a second prototype (Valve II) irnplernenting those changes.

4. To test the operating characteristics of Valve II to ensure that the t h e response had

been adequately reduced.

5. To perform dynamic tests simulating in silu flow conditions and evaluate Valve II's

abiiity to control outnow and maintain a constant supply pressure.

Following a review of Sit's (1996) report, several problems with the original prototype

design were identifid It was suspected that the seal between the dialysis and collapsible

tubing, made with a combination of rubber bands and wire wraps, was not watertight. In

addition, the lack of suppon structure made the dialysis tube awkward to fil1 with the

dextran solution. The rectangular gasket between the chamber waüs and lid did not

provide a reliable seal.

These problems were rectified in the design of the new prototype, Valve 1 (figure 3.1).

Components that worked well initiaily were incorporated in the new design and included:

coliapsible tube (latex penrose tubing, '/;" diameter, 12" length, #20414-050, Baxter

Medical Supply, Mississauga ON)

regenerated cellulose semipermeable membrane (1 2000- 14000 MWCO didysis tubing,

45mm flat width, #2 1 - 1 52-8, Fisher ScientSc, Nepean ON; manufactured by

Membrane Filtration Products, San Antonio TX)

connectors and vents (Nalgene@ barbed bulkhead fittings, %" and '/." diameter,

# 16225-23 2 and # 1633 1 - 1 02 VWR Scientific, Mississauga ON )

Machining of plexiglass components was done in the University of Toronto, Mechanical

Engineering Machine Shop by Mr. Paul Kovar. Complete shop drawings are located in

Appendk A.

Figwe 3.1: (a)Valve 1, the new bench scale glaucoma drainage valve prototype, (b)

labeiied Valve 1 fiont view.

Aithough it was desirable for the dialysis membrane and cdapsible tubing to be

configured as concentric cylinders, there was no need for them to be joined. Therefore,

rather than aîtach the membrane directly ont0 the coiiapsible tube or bukhead fitting,

A Novel Glauanna haimgc Valve

34

cylindrical plexiglass rings were mounted on the inner s d c e s of the chamber endplates,

centred around the bulkhead fittings. The dialysis membrane was pulled over a tightly

fitting rubber O-ring placed around the plexiglass ring. A proper seal was achieved by

securing the membrane with a stainless steel, adjustable hose clamp (CHX-20, SmaU Parts

Inc., Miami Lakes FL). To prevent damage to the membrane, the outer edge of the

plexiglass ring was slightly contoured, and a piece of thin foam was placed around the

inner surface of the hose clamp. DEerent views of the new seal configuration are

illustrated in figure 3.2.

Figure 3.2: Vdve 1 diaiysis membrane seal (a) in situ photograph; @) cross sectional

schematic.

During the assembly of Valve I, it was noticed that the barbed ends of the bulkhead

fittings did not extend beyond the sealing rings. This made the process of pulling the

collapsible tube over the buIkhead f i h g extremely dficult, as there was very Little space

between the bukhead and the sealing ring. To r e m this oversight, the buikhead fittings

35

were extended with short pieces of rigid pipe. The cdapsible tube was originally meant

to be 12" long, as in Sit's (1996) valve. As a result of this last-minute modification, the

collapsible tube was shortened to a length of 9".

Uniike Sit's (1996) prototype, both ends of the dialysis membrane in Valve 1 could be

cunveniently sealed before the dialysis membrane was filied with dextran solution.

Through one of the chamber endplates, narrow tracts extended fiom the outside the

apparatus, and led into the space between the buikhead opening and the plexiglas ring

(figure 3.3). Flow through the tract was controiied by plug valves (HV3-3, #86727,

Hamilton Company, Reno NV) with luer connectors ($35030 and #3503 1. Hamilton

Company, Reno NV) . Dextran solution was injected into the dialysis membrane ushg a

luer-lock syringe attached to one of the valves, while the other served as an a i r bleeding

port. During experiments, pressure was monitored by attaching a pressure iine to one of

the ports.

Figure 3.3: Cross-sectionai M m of

Valve 1 chamber endplate,

iüustrating nIling ports and tracts.

Sit's (1996) experiments to determine the characteristics of flow through a coUapsible

tube using an extemally generated cioshg pressure were duplicated. This was to ensure

that nothing significant had been overlooked in the valve redesign or in recreating

experimentd conditions. Ornitting the dialysis membrane in the valve setup and using a

column of water to fbc the valve closing pressure (P,), the collapsible tube was co~ected

to a fluid supply reservoir of variable height (refer to figure 1.8).

P, was fixeci at 7.4 d g (arbitrarily chosen, Sit. 1996) and water flow through the

coiiapsible tube was recorded as the height of the supply reservoir was incrementaüy

changed. Pc was changed to 14.7 mmHg (arbitrarily chosen, Sit, 1996) and the

experiment was repeated. This set of experiments was then repeated using glycerol as the

supply fluid. Results are given in section 3 -3.1.

With operation of Valve I verified, the externaiiy generated P, was replaced with the

osmotically generated pressure source. The dialysis membrane was attached to the sealing

rings on the chamber endplates as previously described (section 3.1.1). and f led with a

0.224m.M dextran solution (industrial grade 298 000 MW, Sigma Chemicals, St. Louis

MO). The concentration of O.224mM was arbitrarily chosen by Sit and has no apparent

A Nowl Giuicwi Dmkgc Valve

38

significance. The chamber was fïiied with distdied water and a p d a i i y filled fume1 was

left co~ec ted to the chamber vent. The fume1 was Ieft open to the aîmosphere and the

water in it prevented air from being drawn into the chamber. The supply fluid was

glycerol, as used in Sit's experiments, to provide the low Reynolds number flows typically

passing through a glaucoma drainage implant.

Sit's experiments to test the flow characteristics of the osmotically controiied valve were

repeated. According to the van't Hoff equation, a dextran concentration of O.224m.M

produces an osmotic pressure gradient of 4. ImrnHg. The valve's P, was therefore

considered to be 4. lrnrnHg and the glycerol reservoir was positioned to provide a P, of

4.6mmHg (arbitrarily chosen by Sit). Since PB was greater than P , the valve was expected

to open. Results are given in Section 3.3.1.

3.3 RESULTS FOR VALVE 1 TESTING

3.3.1 COUAPSIBLE TUBE BEHAVIOUR

The results from these teas, where closing pressure (P3 was generated by an extemal

source. were compared with those obtained by Sit (1996). The fita set of tests, where the

supply fluid was water, are compared in figure 3 .S. When plotted on supply pressure (P,)

vs flow graphs, the data sets obtained by Sit and fiom Valve 1 do not overlap.

39

A difEerence between the fiow resistance of two valves was observed by cornparhg the

dopes (APJAQ) of the plots in figures 3 3 a ) and (b):

Assuming laminar flow conditions, flow resistance in tubes for viscous fluids is dependent

on fluid dynamic viscosity, tube length and tube cross-sectional area, as given by:

The tube length and cross sectionai a m were not necessarily exactly the same for both

vaives, and during both tests. It was known for certain that the lengths of the collapsible

tubes were difFerent, as discussed in section 3.1.1. The collapsible tube in Valve 1 was

only 9", compared to Sit's 12" tube. However, the difFerence in tube lengths did not

contnbute sigruficantly to the flow resistance difference, because resistance was greuter in

Valve I than in Sit's valve.

Another factor that might explain the dierence in flow resistances is the degree of

longitudinal tension in the coliapsible tube, since this would have an effect on

its cross-sectional area when open. A collapsible tube that was stretched lengthwise

would not open as much as a more relaxed tube. It was suspected that Valve 1's

collapsible tube had a higher degree of longitudinal tension than the tube in Sit's valve,

accounting for the higher flow resistance of Valve 1.

Figure 3.5: Cornparison of the flow characteristics of Sit's (1996) prototype and Valve 1

when water supply pressures were incrementally increased and closing pressures were

set with an extemal pressure source; (a) P, = 7.4 mmHg (b) P, = 14.7 mmHg.

41

Regardless of the flow resistance dieremes, both valves displayed a dramatic increase in

water flow through the tube when P, rose above P,.

O 1 2 3 4 5

glycerol oufflow [mUsJ

O Sit 199ô Valve I

O 1 2 3 4 S

glycerol oufflow (mus]

Figure 3.6: Cornparison of ihe flow characteristics of Sit's (1996) prototype and Vaive 1

when glycerol supply pressures were incrementaiiy increased and ciosing pressures were

set with an estemal pressure source; (a) P, = 7.4 m g ; (b) P, = 14.7 mmHg.

42

The second set of tests, where the supply fluid was giycerol, are compared in figure 3.6.

Both valves exhibited the sarne general behaviour in that neither of hem aiiowed glycerol

flow through the collapsible tube until P, rose above P,. This is the classic behaviour of

low Reynolds number flow through a Starling resistor, and is particularly noticeable Ui

figure 3.6@), where the value of P, was 14.7rnmHg.

A dserence between the flow resistance of two valves was observed by comparing the

slopes (AP jAQ) of the plots in figures 3.6 (a) and @):

Since & is less than %, the coliapsible tube length difEerences may have made a more

significant contribution to the difference in flow resistance than in the previous w e .

However, the tube lengths alone did not account for the different flow resistances, as

illustrateci by the ratio:

In this case, it was suspected that Sit's collapsible tube had a higher degree of longitudinal

tension than the tube P Valve 1. The resulting diierence in the tubes' cross sectionai

areas would account for the remaining 25% diifference in flow resistances.

Glycerol flow through Valve 1 dernonstrateci the characteristic behaviour of a cdapsible

tube under pressure, as described by the previously discussed relationships:

The outflow behaviour of Valve I when the extemally generated P, was replaced with an

osmotic pressure source is discussed in the next section.

3.3.2 Os~onc VALVE BEHAVIOUR

As indicated in figure 3.7, the behaviour of Valve 1 and Sit's prototype differed greatly

when P, was generated osmotically. Sit's valve appeared to open continuously over

several hours, while Valve 1 did not open at dl. In fact, no flow passed through Valve 1

until the glycerol supply level was raised to over 2OmmHg and even then ouMow

remained relatively constant at less than O. 1 mL/min.

Figure 3.7: Cornparison of the fiow characteristics of Sit's (1996) prototype and Valve 1

when glycerol supply pressure was frxed at 4 . 6 d g . A nominal valve closing pressure

of 4.1mmHg was generated osmoticaily with a dextran concentration of O.2NmM.

The faiure for Valve 1 to open at a P, of 4.6mmHg reuiforces Sit's theory that a dextran

solution leak slowly eliminated the osmotic pressure gradient in his valve, reducing P, to

almoa nothing. This explained the dinerence in the behaviour of the two prototypes, but it

did not account for why Valve 1 barely opened even when P, was four times pater than

In the next chapter, possible explanations for the fdure of Valve 1 to open are discussed.

There were three plausible explanations for Valve 1's failure to open:

învaiidity of the van? Hoff osmotic pressure equation, for dextran at the concentration

used in the study,

occurrence of concentration polarkation at the membrane surface, or

extremely low penneability of the dialysis membrane, resulting in long equilibration

Each of the possible explanations for Valve 1's failure to open were investigated.

Procedures and results for each investigation are discussed in the following three sections.

Sit (1996) assumed that the van't Hoff simplification of the osmotic pressure equation was

valid. Since Valve 1 did not open when P, was more than four times greater thm the

calculated osmotically generated P, the question arose as to whether or not the

calcuIation could be trusted.

In order to masure the actual osmotic pressure within the dextran cue a crude

manometer was conaructd. A pressure he, with luer connectors on both ends, was

connected to one of the Hamilton plug valves and run vertically dong the waii beside

Valve 1 (figure 4.1). Osmotic pressure, AII, was taken as the dierence in fluid height

between the dextran in the pressure line and the water in the fùmel.

A Novcl Glutcomp Iiniatgc Vaive

Figure 4.1 : Manometer configuration

The plug vaive was opened and the system was lefi overnight to ensure that equilibrium

wouid be achieved. The following day, the osmotic pressure was measured to be

42mmH& a full order of magnitude larger than the 4.16 mmHg predicted by the van't

Hoff equation. It was concluded that the van? Hoff equation underestimated the osmotic

pressure, and the non-shplified osmotic pressure equation,

would have to be used. Patently, the 0.224rnM dextran solution is not considered ideai

and solute-solute interactions can not be neglected.

A literanire review revealed several studies in which the vinal coefficients (A, values) of

de- (500 000 MW) dissolved in water were determined. Coefficients for dextran of

47

-300 000 MW were unavailable. Using three sets of coefficients, the osmotic pressure

values in table 4.1 were obtahed for a 0.224 mM solution.

Table 4.1: Cornparison of publistied values for virial coeficients (A,) of 500 000 MW

dextran and the calculated osmotic pressure values (n) for a 0.224mM solution.

Wijmans (1 985)

Although these values of II differ significantly, they illustrate that the measured osmotic

pressure of 42 mmHg is within a reasonable range, and that indeed the van? Hoff equation

is insufficient for the purposes of this project. Due to the lack of established Wial

coefficients for 300 000 MW dextran, the manometer was deemed the most reliable

method to determine the osmotic pressure for the experiments during this study.

Another possible cause of the delay in response tirne is the occurrence of concentration

polarkation. When water is forced, by an applied pressure, through a semi-permeable

membrane from a solution of high to low solute concentrations, there is a possibility of

solute accumulation at the membrane as show in figure 4.2. This creates a localized area

of very high solute concentration. Due to this high concentration gradient at the membrane

0.0867 2.98

A,---

89.9 34.5

surface, water will more readily move back across the membrane in response to the

osmotic gradient, in opposition to the applied pressure. The result is a decreased net flux

of water across the membrane. If concentration polahtion occurred in Valve 1, it would

take longer for water to lave the dextnui cuff and thetefore longer for the cdapsed tube

to open.

dextran O

a m a

Figure 4.2: Water flux (mm) amss a semipermeable membrane. (a) Without appIied

extemai pressures, net water flux is into the demm solution. (b) Applied fiuid supply

pressure on the dextran side of the membrane reverses water flux and creates localized

area of hi@ dextran concentration at membrane. so that net flux is reduced by water

rnoving back across the membrane in response to the osmolarity difference.

With the same experimental set up used for the osmotic valve behaviour tests, a test to

determine the extent of concentration polarkation effécts on Valve 1 was perfonned. The

height of the glycerol supply reservoû was incrementaliy increased, then decreased, and

the correspondhg outflow measurements were recordeci at each step. Minimum supply

49

pressure was 18mmHg, at which glycerol outflow just began, and maximum supply

pressure was 6OmmHg, at which point the catalogues used to raise the reservoir became

unstable.

The hypothesis for this experiment was that due to concentration polarization effects, the

coiiapsible tube in Valve 1 would close more easily than it opened. The hysteresis in the

data (figure 4.3) indicated that at any given supply pressure, glycerol outflow was Iower as

P, increased than when it decreased.

O S 10 15 20 25

average glycerol o M o w (mumin]

Figure 4.3: Resuits of test to determine conœntmtion polafization effects on glycerol

flow thmugh Valve I. Glycerol outflow measurements were recorded as supply pressure

was incrementally increased from 18 to 6OmmHg. then incrementally d e c d

50

This higher resistance to glycerol flow as the valve opened confirxned the hypothesis that

concentration polarization was occurring. However, this test was only designed to be a

crude indicator of concentration polarization. The degree to which concentration

polarization actuaily affecteci the operation of the valve was observed more ciearly in a

later experiment, discussed in section 4.3.3.

4.3 MEMBRANE PERMEABILITY & EQW~LIBRIUM TIME CONSTANT

In earlier discussion on Valve 1's P , it was established that when fluid P, was increased to

a level above P, the coilapsible tube opened. This occurred instantaneously when P, was

generated by an extemal source. When P, was generated by the osmotic pressure cuff. it

took time for the water leave the cuff before the collapsed tube opened. If the pressure

inside the cuff were to be measured as a fùnction of time during this process. it would

resemble the curve in figure 4.4.

Figwe 4.4: Hypothesized relationship between pressure inside the dextran &and time

at a constant value of P,, greater than P,.

51

Note the unsp&ed (ie. unknown) t h e scale. The unanswered question was: At what

point in t h e will enough water have crossed the membrane in order to estabîish

equiiibrium between the fluid supply pressure and osmotic pressure? (For the purposes of

this project, the term "equilibrium" refers to the point at which the pressure within the

dextran cuff no longer changes with respect to time.)

It was dficult to plan experiments with the valve since the uctual equilibrium t h e scale

was unknown. Therefore, the valve was mat hematically modelled in order to d e t e d e a

theoreticd equilibrium time scaie. However, before the valve was modelied as a whole

unit, the focus was piaced on the flow across the dialysis membrane.

4.3.1 MODELUNG FLOW ACROSS THE DIALYSE MEMBRANE

Intuitively, the length of tirne required for the valve to reach equilibrium should be

dependent on the rate at which water crosses the dialysis membrane. The water flux

should be dependent on surface area of the membrane, the net potential diifference driving

the water across the membrane, and membrane permeability. The "net potential

difFerenceW can be defined as:

where Apt is actual pressure difEerence between the dextran cuff and outer chamber at any

given point in tirne, and AII is the osmotic pressure difference betwem the dextran cuff

and outer chamber. At equilibrium, Ap, is equal to AIL

The equation goveming volume flow across the membrane is therefore:

where dV1dt is the volume flow rate across the membrane [ d m i n ] , k is membrane

permeability [mUrnin/m2/rnmHg], A is the membrane surface area [m2], and P, is the time

dependent net potentiai dserence [rnmHg].

The volume of the opened collapsible tube, and thus the volume of water required to be

displaced from the cuff, could be calaiiated using the valve's dimensions. Similarly, the

surface area of the membrane could also be caiculated. The net potentiai dEerence over

tirne could be measured using the manometer. A membrane permeability value of 1.5-

1 .7mvmin/m21rnm~g was provided by the manufacturer (Membrane Filtration Products,

San Axitonio TX), however this value was likely determined using distilled water only.

Therefore, the quoted permeability value would neglect the realities of solute interactions

with the membrane, such as pore clogging and concentration polarkation.

In order to ensure the accuracy of any calculation for the equilibrium time scde, the actual

membrane permeability, under Valve 1' s experimental conditions, was verified ushg the

procedure described below.

The actual or effective membrane perrneability was determined by connecting the

manometer and aiiowing the system to reach equilibrium overnight. In the rnoming, a

6mm diameter pipette was attached to the top of the manometer and filled with dextran

solution. Throughout the day, water moved across the dialysis membrane f?om the

dextran side to the water side.

The fluid level in the pipette, which led into the dextran tue was monitored as a fùnction

of t h e . Knowing the cross-seaional area of the pipette, the water flux across the dialysis

membrane was calculated. Taking the dope of a flux vs pressure plot (figure 4.5) and

dividing by the surface area of the membrane resulted in a permeability value of

0.03 137mUmin/rn2/mrnH& which is fifty times less than the value quoted by the

manufacturer.

Figure 4.5: Determination of the water fiw across 14K MWCO diatysis membrane as a

function of driving pressure. Caiculating the slope of this curve and factoring in

membrane mfhce area yields a permestbility value of 0.03 137mWmia/m1/mmHg, whch

is specific to Valve 1 parameters.

The next sep was to mode1 the valve as an entire unit.

The response time of the valve is determined by how quickly the collapsible tube opens

and closes. In order for the volume of the coilapsible tube to change, fiuid must lave the

dextran cuff. As illustrated in figure 4.6, there are two fluid pathways in and out of the

dextran cuff. (i) across the dialysis membrane, and (fi) through the manometer tube.

Figure 4.6: Volume changes in the dextran cuE V, is the volume of giycemI in the

coiiapsibie tube, V, is the volume of water crossing the dialysis membrane. and Vh k the

volume of dextran solution in the manometer tube.

Treating the dextran cuEas a control volume that does not change in shape, and the

dextran solution as an incompressible fluid, the law of conservation of mass applies and

the net volume change mua be zero:

The volume of dextran in the manometer tube is a hnction of its cross-sectional area, &;

and the height of the fluid, h. Height can be expre~sed in terms of the net potential

As discussed in the previous section, the volume of water crossing the dialysis membrane

is a funaion of membrane permeability, k; membrane surface area. 4; and Pt.

Combining Q. 0, and O produced an expression for the change in collapsible tube volume

in terms of net potential difference.

It was assumed t hat Pt changed exponentially with respect to tirne by a function of the

Where r is the equilibrium t h e constant and indicates how quickly the exponential

fiindon decays. The assumption regarding the nature of P, was verified by plotting

experimental data (section 4.3.3) on a log-hear graph, on which the data points formed a

straight h e . Substituthg Pt into 0, and intergrating from time O to =, we obtain:

Where AV, is the change in volume of the collapsible tube as it opened or closed, and P,

is the initial net potential difference. Rearranghg the equation for AV, produced an

expression for the valve's t h e constant, 5:

Parameter values for Valve 1 (opening) were:

The value for AV, was an estimate, based on the observations of the "tapered" shape of

the wllapsible tube when opened. The value for P, was initial net potentiai difference

58

measured when the glycerol P, was raised to 8OmmHg. This P, was generated by placing

the supply reservoir on the shelfabove the workbench. According to these parmeters, a

tirne constant of 1200 minutes was expected.

For scaling purposes, it would be important to know how r would change if the

manometer was removed. Setting 4 to zero resulted in a r of 1160 minutes, a 4%

reduction.

4.3.3 ACTUAL EQUILIBRATION TIME CONSTANT

Although the above calculation may have accurately described the system, the actual

response time was still unknown. Therefore, with the set-up depicted in figure 4.7,

experiments were performed to determine exactly how long the valve does take to reach

Figure 4.7: E.uperimental apparatus for &termining system response t h e .

59

The est step of the experiment was to measure the initial cuff pressure (Am, which was

equal to the valve's osmotically generated closing pressure. At tirne zero, the glycerol

reservoir was raised from its initial OrnmHg position to give a P, of 80 rnrnHg. A

centrifugai pump (Albany Pump Company, Toronto ON) ran continuously to rem the

reservoir and a standpipe maintained a constant fluid level for the duration of the

experiment. Changes in the cuff pressure (ApJ according to the manometer were recorded

as a funaion of time until steady state was reached. The reservoir was then lowered to its

initial position and cuff pressure changes were again recorded until steady state.

Results from three tests to determine Valve 1's response time are show in figure 4.8. Al1

three tests were perfonned without replacing the dialysis membrane or dextran solution.

O 500 t 000 1500 2000 2500 tmie [min]

Figure 4.8: Cornparison of Valve 1 tirne response data h m successive experiments

using the same dialysis membrane, 0.224mM dextran fiIling solution. and glycerol P, of

80mmHg. The descendhg curves represents net ptential merence, Ab-II). while the

vaive is opening, while the ascending curves represents A@$) whik the valve is

closing. The value of AIi was the osmotic pressure gradient measured More each

experiment; and Ap, was the timedependent pressure dinerenœ between the dextran

d a n d the outer chamber. Order of experiments: 0,O.X.

As discussed in section 4.3.2, A(p,-II) was expected to change exponentiall y with respect

to time. This hypothesis was confirmed when the data for each experiment was

transformed to a log-linear sale by ploning ln[A@JI)] vs tirne (figure 4.9). The data was

fit with a regression curve and expressions for A(pt-TZ) as a funaion of time, were

obtained in the fom:

The tirne constant, t = -l/k provided an indication of the equilibration the s d e . Time

constants were the buis for cornparison between the experirnents discussed in this section

and in the following sections.

O 100 200 504 400 500 600 ame [min]

O 200 400 600 800 lm Wnc (min)

Figure 4.9: hg-iinear regression curve fit for Valve 1 time respome data. Daia was h m

experiment "O" from figure 4.8; (a) valve opening; (b) valve closing. Note that

absolute values of A(R-T]n were used for convenience.

62

A complete set of regression cuwe calculations is given in Appendix C, while table 4.2

contains a surnmary of the tirne constants calculated for ail three experiments.

Run #

1 (0)

2 (0)

Table 4.2: Cornparison of system time çonstants for Valve 1. Values are mean * SEM.

3 (x)

Tirne constants ranged fiom 864-1245 minutes when the reservoir was raised (opening the

valve) and tiom 300-1000 minutes when the reservoir was retumed to its initial level

(closing the valve). Observe that the range of r was higher during valve opening, as

water left the dextran cug than during valve closing, as water returned to the cuE This

indicated that there was higher flow resistance at the membrane when water ieft the cuff

than when water retumed to the cuff This phenornenon indicated that concentration

polarization was occuming.

TIME CONSTANT [min]

1245k30 1 3OOi7

On average, the expenmentally determined time constants were lower than the s of 1200

minutes predicted by the mathematical model. R e d that an assumption was made

regarding the volume of the collapsible tube when opened. If the value for AV, was

reduced by 6mL. the estimateci s would be 890 minutes. Since the AV, value used in the

A N m l Glurcoma Dramagc Vdvc

Valve Opening

87W2 1

864k5

Valve Closing

784i10

1 OOm45

63

original calculation was crudely determined, the probability for overestirnation was hi&.

It was concluded that the equation for r would accurately mode1 the system, if a good

estimate of AV, was avaiiable.

It was interesting to note that in successive experiments the time constants increased

significantly. The increasing time constants suggea that the membrane's pores becarne

blocked over time, decreasing pemeability and increasing flow resistance across the

membrane. The exception to this general trend was the 300 minute valve closing tirne

constant for the last run, for which there was no obvious explanation. The entire group of

experirnents was performed using the sarne piece of dialysis tubing, and took a week to

complete. It was possible that by the end of that period the membrane had lost some of its

flow resistance, due to some form of 6bre degradation. Dialysis membrane is intended for

short-term, one-time use, and the week of stress may have taken its toll.

It was very encouraging to observe that, in response to a change in P,, the pressure in the

dextran cuff maintained a constant P,, ifgiven enough time to equilibrate. However, an

equilibrium time constant of 20 hours was considered to be too large a response time sale

for a giaucuma drainage valve. Certainly, the long equilibration time scale made dynarnic

testing of the valve too impractical to attempt.

Membrane fouling over the , resulting in increased time constants, remained an important

A Novci Gluicoau hinage Vaive

64

issue that must be addressed before an osmotically controlled glaucoma valve can be

developed much tiirther. However, for the purposes of this project, the primary issue was

the unacceptably long tirne to reach steady state with a fresh membrane and how to

decrease it. The steps taken to ammplish this objective are discussed in the next chapter.

In order for the osrnotically controlled valve to be considered feasible, the response t h e

had to be reduced. Factors affecthg the response time of Valve 1 were identified, and

where possible, modifications were made in order to reduce response time. In this

chapter, factors affecting response tirne, modifications to Valve 1, and testing of the

modified valve are discussed.

Three factors were identified that would have the most significant effect on the response

tirne: (i) the permeability of the membrane, (ii) the filtration surface area, and (üi) the

volume of fluid required to cross the membrane.

Membrane pemeability is afFected by pore size and pore density. M e r contacthg several

companies it was determineci that 32 mm flat width (dry) dialysis tubing is not available

with a higher MWCO than 14 000 or with a higher pore density than

2 . M OP poresrinch'. Since this was the tubing currently being used, it b e r n e obvious

that in order to change the membrane, an entirely new apparatus would have to be built.

Increasing the fütration surface area could be accomplished by lengt henuig the didysis

tube andor widening the diameter. Either of these changes would require the

construction of a new apparatus.

Since it was desirable to avoid designing a new valve if possible, the focus shifted to

reducing the volume of fiuid to be displaced across the membrane. By shortening the

coilapsible tube, a smaiier volume of fluid would need to be displaced in order to open and

close the valve. This was easily accomplished by extending the buikhead fittings with

pieces of plastic tube and trimming the coUapsible tube (figure 5.1). The volume of the

collapsible tube when open was reduced fiom 22.5mL to 6.5rn.L. During the experiments

performed in the previous chapter, the dialysis tubhg was observed to stretch slightly

when the glycerol reservoir was raised. Therefore, a wire mesh cage was placed around

the dextran cuEin an attempt to reduce deformation and variations in volume.

Figure 5.1 : Modifications to Valve i, a shortened coliapsible tube with wire mesh cage

around the dialysis membrane.

67

The estirnated time constant for the modified valve was calculated to be 336 minutes.

The experhents to determine tirne constant that were discussed in section 4.1.3 were

repeated with the modified valve.

After shonening the collapsible tube in Valve 1, the response time data show in figure 5.2

was obtained. Time constants were calculated for experiments run on the modified valve

(regression analysis given in Appendix C), and compareci with the previously obtained

time constants (table 5.1).

Figure 5.2: Cornparison of Valve 1 (3" collapsible tube) response tirne data h m

successive experiments using the sarne diaiysis membrane, 0.224mM dextran filling

solution. and glycerol P, of 8OmmHg. The descendhg curves repmnt net potential

difference. A@-m. while the valve is opening, the ascending cuve repmnts A@I-n)

while the valve is closing. The value of A I i was the osmotic pressure Merence

rneasured More each experiment; and Ap, was the tirnedependent pressure Merence

between the dextran &and the outer chamber. Order of experiments: O.O.X. Note

ihe unavailabte data for the "valve closing" sîages of the first two nrns. Due to the long

duration of the e.riments, the apparatus occasionaily had to be lefi unattended.

During îhe first two nuis, N~culties with the glycerol supply pump resulted in the

depletion of the glyceml supply. With P, reduaxi to zero. the valve closed before anyone

renrnied.

A Novrl Glaucoma üninage Valve

I TIME CONSTANT [min] II

Table 5.1: Cornparison of system time constants for Valve 1 with the original 9" and

Run #

1 (0)

2 (0)

3 (x)

shortened 3" mllapsible tubes. Values are mean i SEM

For the first two mns with the modified version of Valve 1, the experimentally detennined

time constants were consistent with the mathematical model's prediction of 336 minutes.

As with the original version of Valve 1, the time constant for the last run was significantly

higher than the values obtained for ht two. This was again suspected to be a result of

clogged pores in the dialysis membrane.

Data not available

Although shonening the tube reduced the t h e to reach steady state, the timescale was still

considered too large. Therefore the valve was redesigned to incorporate a different style

of membrane with a higher permeability. The new design is discussed in the next chapter.

C

Valve Opening

9" Tube

87&2 1

864*5

1 245+1 O

Valve Closhg

3" Tube

334k5.6

36W7.0

63 7 î5 .5

9" Tube

784*1 O

1 OOW45

30W7

3" Tube

* *

I

625*5. 1

A new prototype, Valve II (figure 6.1) was designed in an effort to hrther reduce the

system response t h e . Sipnificant changes included:

shorter collapsible tube and larger membrane surface area

100 000 MWCO ultrafiltration membrane

membrane support plates

Plexiglass wmponents for Valve II were constnicted in the MechMcal Engineering

Machine Shop by Mr. Jeff Sansorne. Complete technical drawings and specifications are

located in Appendk B.

pl4 WdV-

cuiiapiible tube

1

o-nng

uMMm&rae

Figure 6.1: Valve II (a) photograph; (b) Iabeiled cross-sectional view

6.1.1 COLLAPSIBLETUBE L E N G ~ 6 MEMBRANE SUWACEAREA

The length of the coilapsible tube was shortened fiom 9" to 1%". By trial and error, it was

determined that a length of 1" is the shortest tube that would fulIy coiiapse. The additional

%" was added for safety.

Since the size of dialysis tubing had to be changed. it was also decided to switch to a flat

(sheet) style of membrane. As a result, the increase in membrane surface area was

constrained only by the size of membranes available. The type of membrane selected (see

next section) was sold in 18"xl8" sheets. An 8%" filtering surface diameter was selected

so that four filters per sheet could be obtained. The actual useable diarneter of the fiiter

was 7%". as the outer %" was compressed between the two halves of the apparatus.

The changes in collapsible tube length and filtration surface area between Valve 1 and

Valve II were expeaed to significantly reduce response time. The anticipateci difference

was estimated using the equilibrium time constant equation, derived in section 4.1.3:

If membrane permeability, manometer tube area, and initial net potential difTerence were

the same for both Valves I and II, the diEerence in time constants could be compared by

the ratio:

Where :

& = 0.02054 m2

%O= 0.0285 m2

AV,,=-22.5 rnL

c AV,=-2.4mL

Comparison of the two equilibrium tirne constants suggested that more than a ten-fol(

reduction in response tirne could be expected due to Valve II dirnensional modifications

alone, i.e.

hcreasing the membrane penneability reduced the estimated time constant for Valve II

even fiirther.

Rat sheet filtration membranes are available with wide variety of pore sises. To decrease

water flw resiaance, and fiirther d u c e Valve II's response tirne, a 100 000 MWCO

ultrafiltration membrane made fiom polyethersulfone was selected (HFK 13 1, Koch

74

Membrane Systems, Wiimington., MA). This pore size would allow a greater water flux

than the previously used diaiysis membrane and would continue to reject 300 000 MW

Dextran.

The clean water flux for this membrane was listed as 200-300 gdonslsq.ft./day, at a

constant pressure of 30psi. For a 0.224mM solution of 300 000 MW dextran, the

manufacturer estimated a flux of 30-50 gallonslsq.tt./day at 30psi (Rice, 1999). This flux

range was converteci to a permeability range of O.OS4543-0.0909O5 mL/min/m2/rnmHg.

For safety, the h u m u m value of 0.054543 mllmin/m2/mmHg was assumed for

dculations.

According to tirne constant equation, s is inversely proportional to permeability.

Therefore, the ratio of time constants between Valves I and II berne:

By changing valve dimensions and membrane pemeability, the time constant predicted by

the mathematical mode1 was reduced by a factor of 23.9 Le. the expected value of s was

lowered nom 1200 minutes to 50 minutes. Note that the prediaed r-reduction factor of

75

23.9 was calculateci using membrane permeability values determineci as water le$ the

dextran solution (valve opening). These k-values took concentration polarization eEects

into account, therefore a predicted r-reduction factor for valve closing could not be

accurately det errnined .

In Valve I, it was observed that increases in glycerol supply pressure caused the dialysis

membrane to stretch. As the membrane stretched, its volume increased, lowering the

pressure inside the cuf This would d o w fluid to pass through the coliapsible tube before

the valve was supposed to open, at supply pressures below P,.

If the colapsible tube opened due to membrane deformatioq it would behave Iike an

elastic valve. This would cause the valve to behave as a flow restrictor, rather than a true

valve with a specific opening and closing pressure. Thus, it was desirable for the

coliapsible tube to open not due to membrane deformation, but excluszvefy due to the

volume changes resulting fiom water crossing the membrane. This would only occur if

the volume within the membrane remained constant at all times.

In Valve Ii, the change in volume required to open the coilapsible tube was approhately

2.4rnL. With the 8%" diameter membrane, a O. lmm centre deformation translated into a

1 -2rnL change in volume (calculations in Appendix D). This was a significant cause for

76

concern, since a relatively indistinguishable deformation had the ability to provide 50% of

the volume change required to open the wilapsible tube. Hence, it was critical to ensure

that membrane deformation was negligible, which made some fonn of membrane support

structure necessary.

In order to prevent membrane deformation, the support stmcture had to be in contact with

the membrane. However, it was critical that this contact area be rninimized so as not to

interfere with fiow across the membrane, thus negating the benefits of possessing a large

filtration area. Patently, the support structure had to be made of a rust-resistant material,

strong enough to resist deformation under normal operating pressures up to 80 mmHg

(baseci on glycerol supply pressures used with Valve 1).

An ideal solution to the problem was to sandwich the membrane between disks of

perforated stainiess steel. Various types of sintered plates and perforated grates were

rejected because they were not avaiiable in the thicknesses necessary to resist deformation.

Eventudly, a pair of ?Af'-thick cast iron drain covers ( M g ' s Plumbing Supply, Toronto

ON) were deemed deformation-proof and treated with TremcladO rut-resistant enarnel.

Intended for floor drains, the covers have a fairly solid surface. To prevent undesirable

resistance to flow across the membrane, disks of expanded metal and fine mesh were used

to provide a 3mm clearance between the drain wvers and membrane (figure 6.2).

Figure 6.2: Membrane support structure. consining of cast iron drain mers and mesh-

covered expandeci metal grate (cross-sectional view).

6.2.1 DDC~~ZAN RETENTION

The solution used to fil1 the model's upper chamber was made 6om industrial grade

300 000 MW dextran. The industrial grade designation means that, although the avenge

weight of the molecules is 300 000, there could be a signifiant number of molecules

falling within in a wide range of values above and below the mean. There was concern

that the smaller dextran molecules would pass through the 100 000 MWCO ultrafiltration

membrane, whose pores were sigrufïcantly larger than those of the previously used 14 000

MWCO dialysis tubing. If a large number of molecules was able to pass through the

membrane, osmotic pressure values in Valve II would not be as high as those obtained

with Valve 1.

To determine ifenough dextran was behg retained by the membrane to provide a

sufficient osmotic gradient, an osmotic pressure test was performed. Valve II was

assembled, and the lower and upper chambers tiUed with distilled water and 0.224rnM

dextran solution, respectively. The lower chamber was co~ec ted to a reservoû of

distilled water (note: the water reservoir replaced the fùnnel used in Valve 1). A pressure

line was co~ec ted to one of the plug valves in the upper chamber, and extended vertically

to serve as a manometer, as with Valve 1. Both charnbers were lefi open to the

atmosphere and sat undisturbed ovemight. The following day, the osmotic pressure

readiig was taken and compared with the typical values obtained with Valve 1. Resuits

are presented in section 6.3.1.

Tests to detemine Valve II response time were performed as previously described

(section 4.1.3).

6.2.3 VALVE II DYNAMIC RESPONSE

Up to this point, valve performance was tested using a constant fluid supply pressure,

which is not representative of in situ conditions. In situ, a valve would be responsible for

the maintenance of a constant pressure (Le. IOP). The following test replaces the constant

presnue supply reservoir with a standpipe and a constantflow supply pump. The

purpose of this investigation was to detertnine whether or not Valve II could maintain a

constant "IOP" at severai d i f ren t supply flow rates.

The experimental apparatus (figure 6.3) for these dynamic response tests was based on

one used by Porter et d (1997), for in vitro testing of actual glaucoma drainage implants.

Comparing the apparatus to the eye, the glycerol flow provided by the pump represents

aqueous humor flow, and the pressure in the standpipe represents IOP. Obviously, Valve

II represents a glaucoma drainage implant, which controls "aqueous humor" outflow in

order to maintain a constant "IOP".

standpipe b 4 manorneter

UI 7'"

Figure 6.3: Experimental apparatus for testing dynamic response of Valve II.

The fira s e p was to record the initial AU. Since the connective tubing and standpipe

were initially empty, P, was OmrnHg and the coUapsible tube was closed. The pump was

tmed on, producing a fiow of 1.8mUs (Re = 0.3 66). Glycerol fiiled the connective

tubing and the standpipe. The fluid level in the standpipe rose until P, was sufficient to

A Novel Giuuxinu DNnigc Vdve

80

open the valve. Glycerol flow, measured at the valve's outlet with a graduated cylinder,

and the change in fluid levels in the manometer and standpipe were recorded as a function

of the . When ail three variables reached steady state, the flow setting on the pump was

increased to 4.0mVs (Re = 0.8 1). Changes in the three variables were again record4 as a

function of tirne, and when steady state was reached, the flow setting on the pump was

decreased to O S d s (Re = 0.102). These three flow settings were selected in order to

represent a range of Reynolds numben below 1.

The osrnotic pressure dEerence obtained in Valve II was 40 mmHg. This was

comparable to the 40-43 mmHg pressures typically obsewed using Valve 1, and indicated

that the majority of dextran molecules were retained by the ultrafiltration membrane. Had

the osmotic pressure gradient in Valve II been significantly lower than that of Valve 1,

dextran concentrations would have had to be increased in order to obtain a sirnilar osmotic

pressure. Othenvise, with two dEerent valve closing pressures. it would have been

difficult to compare the performances of the two valves.

6.3.2 VALVE II RESPONSE

The response t h e results for Valve II are shown in figure 6.4. Tirne constants were

calculated, and compared with those obtained fiom Valve 1 data (table 6.1).

O 50 100 t50 .O 250 350 400 time [min]

Figure 6.4: Cornpanson of Valve II response time data from successive experiments

using the same ultrafiltration membrane. 0.224mM dextran f i lhg solution. and glycerol

P, of 8OmmHg. The descending m e repi'esents net potential merence. while

the valve is openhg the ascending c w e represnts A@-m while the valve is closing.

nie value of was the osmotic pressure gradient measured before each e.uperiment;

and AR was the rimedependent pressure dinerenœ between the de.nran cuff and the

outer chamber. Order of experiments: 0.0 .x+.

A Novcl Glwobau Drunage Vdve

I TIME CONSTANT [min]

Valve Openin

Valve 1

9" Tube 1 3" Tube 1 I I

3 (x) r 1245130 ( 637k5.5 1 60.3I1.1

Valve Closhg

9" Tube 1 3" Tube 1

* Data not available

Table 6.1 : Cornparison of system time constants between Valve 1 (original 9" and

shortened 3" collapsible tubes) and Valve II. Values are mean * SEM.

When the A(pJ) data was ploaed on log-linear axes, some of the data sets produced a

slight curve rather than a araight line. This phenomenon was not observed with data

coiiected using Valve 1. By adding a correction factor, +, to the net potential difference

term, A@JI++), the curves were araightened. Values for 4 were determined based on

the valve which produced the straightest curve, and ranged from 0.1 to 7.OmmHg.

The necessity for correction factors was probably due to the use of a manometer to

measure p,. Although the manometer was a readily avaiiable, inexpensive, and low

maintenance means of pressure measurement, it had a limited dynamic response. When

the glycerol reservoir was raised &om O to 80mrnHg the change in net potential dserence

was Unmediate, but the change in manometer fluid level was not. It took approximately

83

30 seconds for the manometer fluid level to reach a peak valve, due to the flow resistance

in the manorneter tube. The time constants obtained for Valve 11 indicate a rapid

response. Therefore, it was suspected that the net potential difEerence began to change

before Ap, had reached its peak value according to the manometer. Thus, correction

factors were necessary to compensate for the inaccurate initial data. In cornparison, the

response of Valve 1 was slow enough that the manorneter's delay had no noticeable effea.

Valve II demowtrated a significantly faster response than both versions of Valve 1. This is

consistent with earlier predictions that: (i) a ten-fold reduction in response tirne would be

achieved by shortening the coiiapsible tube and increasing the membrane surface area, and

(ü) that increasing membrane permeability would contribute to further response t h e

reduction. These combined changes reduced s's between Valve 1 and Valve 11 by a

factors of 16-24 for valve opening (which wrresponded to the predicted weduction

factor of Z3.9), and 40-50 for valve closing.

Valve II time constants did not appear to increase with successive uses of the

ultrafiltration membrane, hdicating that no significant amount of pore clogging occurred.

Due to the larger pore diameter and Valve II's smaller required water flux, the pores of

the ultrafiltration membrane had less probability of becoming clogged (compared to Valve

1). therefore more experiments would be required for any trend to become apparent.

A NovcI G f w c a ~ Dmhgc Valve

84

The relatively rapid response time demonstrated by Valve II made it practical to consider

performing dynamic tests.

The results from the dynamic tests provided some interesting information regarding the

behaviour of Valve II (figure 6.5). The fluid level in the manometer was expressed as the

net potential difference, A(p,-II), as in previous experiments. The fluid level in the

standpipe, representing supply pressure or 'TOP" was expressed as A(p,-LI). Ideally, at

aeady state for each of the tests, A@,-II) should equal to A(p&).

During the tests, A(pJ1) quickly recovered fiom changes to Bow settings and a consistent

pressure was maintained around the coilapsible tube. This indicated an osmotic pressure

source works well as Valve II's self-contained closing pressure generator.

O 100 200 300 400 500 600 700 time [min]

- read left - read lefl - read right

set supply flow change su ply change supply at 1.8mUs 1 h to 4mbs fiow to O.5mUs

Figure 6.5: Results h m Uuee consecutively run dyaamic tests on Valve II. Changes in

ouifiow. net potentiai Merence. A@,-II); and supply net potential W e ~ n c e , A@,-II)

were monitored as a constantomte giycerol flow was pumped through the valve. m e n

the variables reached steady m e . the experiment was repeated for a new flow rate.

A SP

h & A L) &

P A A

9

1- I b o e a œ ~ a I I

C I S m -

œ m - * - - .

1 . œ m O 8.0 O

A 4 a 0 6 3 O

n t f

h -L

œ - & a O

O m

a 1 1 t . 1 a I a I a 1 1

8 u 1 I . v w 1 8 u m u

Throughout the first test (0-220 minutes), A@,-II) was approxirnately qua1 to A@JI),

and both variables were zero at aeady state. This indicated that at a constant flow of

1.8rnL/s, Valve II does an excellent job of maintainhg a constant supply pressure of AII.

5

-4

# œ

-3

-2

m

- - 1

I D

O

During the second test (220-450 minutes), A@,-a is consistently 5mmHg above A(prII).

At this higher flow rate, 4.OmUs, the cdapsible tube was nearly fully open. Although not

A Novcl G h c m u Dnmrgc Vaivc

evident on the pressure vs. t h e plot, the fluid level in the standpipe was actualiy

oscillating by *2mmHg. This observation was explained using the "tube law".

Figure 6.6: The tube law. Graphical represeniation of the relationship between

transwall pressure and cuUapsibIe tube compression. ~ececioglu et al.. 198 11

The tube law describes the non-linear relationship between transwall pressure and

coilapsible tube compression. The general expression for tube volume as a iùnction of

pressure is given as:

87

Where V is the volume of the collapsible tube as it changes shape, Vo is the maximum

volume of the collapsible tube, p is the pressure within the tube, and p, is the pressure

outside of the tube. The constant K is determined by tube materials and dimensions,

includiig: Poisson's ratio (v), Young's modulus (E), tube radius (R), and wall thickness

(hl.

As iliustrated by the varying slopes on the plot in figure 6.6, the collapsible tube is fairly

stiffat VNo < 0.27. relatively compliant at 0.27 < VN, < 0.92, and becornes very stifYat

VN, > 0.92. During the second stage of the experiment. it was suspected that VN, had

reached its upper limit for cornpliance. The collapsible tube resisted inflation, allowing

only some of the glycerol supply to pass through. The "extra" glycerol accumulated in the

standpipe, and the supply pressure increased untü the latex yielded. The "extra" glycerol

drained and the process repeated itself, approxirnately every 3 seconds. This phenornenon

indicated that the collapsible tube itself plays a significant role in determining the upper

limit of an osmotic valve's operating range.

During the third test (450-610 minutes). A(p,-11) was consistently lower than A(p,-II). At

steady aate. A@,Q was oscillating by *2.5mmHg, at an average value 8mmHg below

A@JI). In this situation, the wliapsible tube would be expected to fuUy close, reducing

outflow to zero until A@,-m was equal or greater than A@,-II). Although the collapsible

tube appeared fuily closed, there were srnail channels dong its sides that remained open.

A Novd Glaucomn hinage Vdvc

These channels were large enough to d o w the glycerol to dnp slowiy at a rate of

0.5mUs. The size of these channels depends on factors sUch as tube thickness and

material properties. In order for the vaive to close, a tube would have to be selected that

would have srnalier side channels when fùlly collapsed. This phenornenon indicated again

that the coliapsible tube itself plays a signifiant role in determining the valve's operating

chmct eristics .

These results suggested that Valve II would only maintain "IOP at AI1 if the glycerol

supply flow was set within a certain range. Flow rates of OSmUs and 4.0mUs were

clearly outside of this range, while 1.8mUs was within the range. Since the arnount of

aqueous humor production in the eye varies throughout the day, it is crucial that a

drainage device be able to maintain a consistent 10P regardless of flow vdume. The

challenge would be to select a coliapsible tube such that: (i) the valve's upper flow limit is

larger than the highest expected aqueous humor flow; and (ü) flow through the side

channels is negligible.

Valve 1 was designed and constructed, taking Sit's (1996) recommendations into account.

Significant aiterations to Sit's original design included: improvement of the diaiysis

membrane seal, addition of dextran f i h g pons, and cylindrical construction of the outer

shell.

Operation of Valve 1 was verified by setting the valve closing pressure with an extemai

water reservoir, and o b s e ~ n g the outflow as a function of supply pressure. DifEerences

between the flow resistances of the two prototypes was likely due to differences in

collapsible tube characteristics, specifically, length and longitudinal tension.

Valve 1 did not open as expected when the collapsible tube had an osmotically generated

closing pressure. An investigation reveaied that the van't Hoff equation underestirnated

the actual osrnotic pressure of the dextran solution. The actual osmotic pressure was

determined using a manometer and supply pressures were raised accordingly. In addition,

it was determined that the amai diaiysis membrane permeability was 50 tirnes lower than

the manufacturer's quoted value. Further testing revealed that Valve 1 had an extremely

slow response tirne, with time constants (5) ranging between 870 and 1250 minutes d u ~ g

valve opening, and from 740 to 1 O00 minutes during valve closing. These experimental

90

values were consistent with the expected values detemiined using a mathematical model.

The volume of the fully open coUapsible tube has a great impact on the value of T. In an

attempt to reduce response the, the collapsible tube in Valve 1 was shortened.

Experimental values for s ranged from 330 to 640 minutes dunng valve opening. This

was a signincant reduction, but it was not enough.

Valve II was constructed in an effort to fùnher reduce response time. It featured a

coilapsible tube even shorter than in the modified version of Valve I, a membrane with a

higher permeability, and a larger membrane surface area. Response tirne was drarnatically

reduced, with values of r ranging between 47 and 60 minutes during valve opening, and

from 18 to 20 minutes during valve closing.

Dynamic testing of Valve II indicated that osmotic pressure works well as a self-contained

source of pressure. However, it was observed that the collapsible tube irnposed significant

limitations on the operation of the valve. At higher supply flows, the collapsible tube

opened to a certain volume and then appeared to resist further inflation. The result was an

oscillating TOP" with an average value 5rnmHg above II. At lower supply fiows, the

coUapsible tube was not compietely collapsed. Glycerol passed through the side channels,

and the oscillating T O P had an average value 8mrnHg below II. These observations

suggested that selecting an appropnate collapsible tube would be the greatest challenge in

constmcting a useable osmotically controiled glaucoma valve.

As discussed in chapter two, the objective of this project wax

To construa and test a large-scale mode1 of an osmotic pressure controiied valve,

based on Sit's (1996) design and recommendations, in order to: (i) ver@ that the

valve has a consistent opening and closing pressure and (ü) veriS, that the valve

capable of controliing outflow and maintainhg a constant supply pressure.

Valves 1 and II both opened at supply pressures greater than the osmotically generated

closing pressure, and closed at supply pressures less than the closing pressure. However,

as observed in the dynamic experiments using Valve II, being "open" or "closed" did not

necessarily mean that a constant supply pressure of AI1 could be maintainecl.

Valve II's ability to control outtlow and maintain a constant supply pressure was

dependent on the supply flow rate. When the valve was open, the collapsible tube

appeared to resist fûrther expansion beyond a certaii? point. Thus, at high supply flow

rates, fluid accumulated in the standpipe, and the supply pressure oscillated, having an

average value above the set closing pressure, An. When the valve was closed,

incompressible channels remained dong the sides of the coUapsible tube. Thus at low

flow rates, fluid did not accumulate in the standpipe, and the supply pressure oscillated,

having an average value below AII. At mid-range flow rates, supply pressure was

maintained at AIX.

1.3.1 VALVE DESIGN AND EXPERTMENTAL APPARATUS

The ha that a supply pressure of AI1 could not be maintained at low flow rates

constitutes a major flaw in the valve design. Side channel formation in a coilapsible tube is

unavoidable. However, the use of a thimer-wded tube may reduce the radius of the

channels and hence increase resistance to flow. Altematively, rather than a round tube, it

rnay be worihwhile to consider using two separate pieces of latex that have been sealed

dong the sides. In this configuration, there would be no folds in the latex and side

channels would not form.

Pnor to any fkther testing, it is suggested to replace the manometer with a strain gauge-

based pressure transducer. Eiirninating the manometer would simplify the mathematicai

mode1 of the device. More importantly, the response of a strain gauge would be faster and

readings could be recorded by a datalogger during the lengthy experiments. It would also

be useful to place a strain gauge-based pressure transducer at the base of the standpipe in

the dynamic test apparatus in order to accurately record pressure oscillation.

1.3.2 FUTURE WORK

As it is, the valve can not maintain a supply pressure of AII at low fiow rates. Outflow,

via the side channels in the collapsible tube, must be reduced to a neghgible amount if the

valve is to operate properly. Mer this is accomplished in the large-scale prototype,

design of a scaled-dom valve may begin.

Cheryan, Munir. WZtrajîZtration H d b o o k . Technomic Publishing Company, Inc. Lancaster, Pemsylvania, 1986.

Conrad , William A Pressure-Flow Relationships in Collapsible Tubes. IEEE Transactions on Biomedical Engineering BME16(4): 284-295, 1969.

Davson, H. [ed]. The Eye. Academic Press, New York, New York, 1969.

Edsman, K. and Sundeloef, L.D. Interaction Virial Coefficients in Some Mixed Polymer Solutions. Polymer 29(3), 53 5-540, 1988.

Ethier, C.R. Personal Communication. 1997- 1999.

Fatt, lrving and Weissman, Barry A. PhysoZogy ofthe Eye: An ln@&ction to the Vegetutive Functions. Butterwort h-Heinemann, Boston, Massachusetts 1 992.

Feher, Joseph J. and Ford, George D. A Simple Student Laboratory on Osmotic Flow, Osmotic Pressure and the Reflection Coefficient. American J w m d of PhysioIogy 13 ( 1 ) : S 10420, 1995.

Francis, Brian A, et al. Characteristic of Giaucoma Drainage Implants during Dynarnic and Steady-state Flow Conditions. Ophthalmology. 105(9): 1708- 17 14.

Freedman, JefEey. Clinical Experience With the Molteno Dual-Chamber Single Plate Implant. Ophthulmic Surgery. 23(4): 238-241, 1992.

Gaube, Johann. Pfennig, Andreas. Stumpf. Matthais. Vapor-Liquid Equilibrium in Bhary and Ternary Aqueous Solutions of Poly(ethy1ene glycol) and Dextran. Journal of Chernical and Engtneering Data 38(1): 163- 166, 1993.

Guyton, Arthur, C. And Hall, John E. Textbook of Medicai Physiology. W .B. Saunders Company, Philadelphia, Pennsylvania, 1996.

Hitchings, R.A. et al. Use of One-piece Valved Tube and Variable Surface Area Explant for Glaucoma Drainage Surgery. Ophthalmoogy 94(9): 1079- 1083, 1987.

Heuer, Dale K. et al. Which is Better? One or Two? A Randomized Clinid Trial of Single-plate versus Double-plate Molteno Implantations for Glaucomas in Aphakia and Psuedo phakia. Ophthalmology W(l0): 1 5 1 2- 1 5 1 9, 1 992.

Jonsson, G. Boundary Layer Phenomena During Ultrafiltration of Dextran and Whey Protein Solutions. Desdination 5 1 : 6 1-77, 1984.

Joseph, N.H. et al. A One-Piece Drainage System for Glaucoma Surgery. Tr~72sactiuns of the Ophthulmologrcul Societies of the United Kingdom 1 O5 : 6 5 7-663, 1 9 86.

Kececioglu, 1. McClurken, M.E. Kamm, R.D. Shapko, AH. Steady, supercritical flow in cullapsible tubes. Part 1. Experimental Observations. Journal of Fluid Mechanics. 109: 367-389, 1981.

Knipin, Theodore, et al. Valve Implants in Filtering Surgery. Amerzcm J m m I of Ophtholmology 8 1(2): 232-235, 1976.

Krupin, Theodore, et al. A Long Krupin-Denver Valve Implant Attached to a 180 O

Scleral Explant for Glaucoma Surgery. Ophhzlmology 95(9): 1 174- 1 180, 1988.

Krupin, Theodore, et al. Knipin Eye Valve with Disk for Filtration Surgery. OphthaZmology 1 O 1 (4): 65 1-657, 1 994.

Lyon, Carol K. et al. Flow through Collapsible Tubes at low Reynolds Numbers: Applicability of the Waterfdl Model. Circulation Research 47(1): 68-73, 1980.

McClurken, M.E. Kececioglu, 1. Kamm, R.D. Shapiro, AH. Steady supercritical Bow in coilapsible tubes. Part 2. Theoretical Studies. Jmml of Fluid Mecbics . 1 O9: 39 1 - 415, 1981.

Normann, Richard A. Principles ojBioimtnrmentation. John Wiley and Sons, New York, New York, 1988.

Pilliar, R.M. MMS-420 Biomateriais. Course Notes and Lectures, 1997.

Porter, Jeffiey M., et al. In Vitro Flow Testing of Glaucoma Drainage Devices. Ophthalnmlogy 1 O4(l O): 1 70 1 - 1707, 1 997.

Prata, Joao A. et al. In Vitro and In Vivo flow Characteristics of Glaucoma Drainage Implants. Ophrhalmology 1 O2(6): 894-904, 1995.

Pusch, Wolfgang. Osmotic Pressure of De- Tl 0 Solutions. Desaiimtion 68: 69-73, 1988.

Rice, Wdliam. Koch Membrane Systems R&D. Personal Communication. 1998- 1999.

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Roark, Raymond J. Young, Warren C. Fornulas for Stress and S W n . McGraw-Hill Book Company, New York, NewYork, 1975.

Robenon, John A. and Crowe, Clayton T. Engineering FluÎdMechanics. Houghton Mifflin Company, Boston, Massachusetts, 1993.

S herwood, Lauralee. Humun Physiology: From Cells to Systems. West Pub iishing Company, Mimeanapolis, Minnesota, 1 993.

Shields, M. Bruce. Textbook of Glmcoma. Williams & Wilkins, Baltimore, Maryland, 1987.

Sit, Arthur J. A Novel Glaucoma Drainage Implant: Preliminary Report. Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario. 1996.

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Thomas, John V. Glaucoma Surgery. Mosby-Year Book Inc, St. Louis , Missouri, 1992.

Werner, Eüiot B. Normal-Tension Glaucoma The Glaucomas. Mosby-Year Book Inc, St. Louis, Missouri, 1996.

White, T.C. Clinicd Results of Glaucoma Surgery Using the White Glaucoma Pump Shunt. Anncrls of OphthImology 24(10): 365-373, 1992.

Wijmans, J.G. Nakao, S. Van den Berg, J. W.A. Troelstra, FR. Smolders, C.A. Hydrodynamic Resiaance of Concentration Polarization Boundary Layers in Ultrafiltration. Journal ofMembrane Science 22: 1 17- 13 5, 1985.

Varma, Rohit. Minckler, Don S. Anatomy and Pathophysiology of the Retina and Optic Nerve. The GIaucumm. Mosby-Year Book Inc, St. Louis, Missouri, 1996.

APPENDE A . Drawings for Valve I

Large Outlet Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A l

Small Outlet Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A2

Sealing Ring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A3

Endplate (Outer Shell) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A4

Outer Shell with Enclplate Attached . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A5

APPENDIX B . Drawings for Valve iI

Cross Section O AssembIed Valve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B1

BoxTop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

BoxSides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B3

Topplate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B4

TopWall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . BS

Bottom Wall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B6

Bottom Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B7

APPENDIX C . Regression Analysis Output

Valve 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cl

Valve 1 (modified) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C7

ValveII . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cl1

REGRESSION ANALYSE

VALVE: Valve l(9" tube) RUN: #î, valve opening

m: 48.5rnrnHg DATE: August 26 1998

O 50 100 150 200 250 300 350 400 time [min]

Regression Output: TlME CONSTANT: Constant 3.290436 Std Err of Y Est 0.020476 TAU: -870.2 R Squared 0.9751 92 LOW TAU: -850.0 No. of Observations 47 HlGH TAU: -891.4 Degrees of F reedom 45 +/- 20.7

X Coefficient(s) -0.001 1494 36 Std Err of Coef. 2.73221 E-05

REGRESSION ANALYSE

VALVE: Valve I (9" tube) RUN: #1, valve dosing

46.5mmHg DATE: August 26 1998

O 200 400 600 800 1000 time [min] l2Oo I

Regression Output: TlME CONSTANT: Constant 2.56421 9 Std E r of Y Est 0.01 91 31 TAU: -784.3 R Squared 0.997992 LOW TAU: -774.6 No. of Observations 15 HlGH TAU -794.1 Degrees of Freedom 13 +/- 9.8

X Coefficient(s) -0.001 27508 Std Err of Coef. 1 S864E-05

REGRESSlON ANALYSIS

VALVE: Valve 1 (9" tube) RUN: #2, valve opening

46.0mmHg DATE: August 29 1998

O 100 200 300 400 500 600 time [min]

Regression Output: TlME CONSTANT: Constant 3.409326 Std Err of Y Est 0.007339 TAU: -864.1 R Squared 0.998614 LOW TAU: -859.0 No. of Observations 42 HlGH TAU -869.2 Degrees of Freedom 40 +/- 5.1

X Coefficient(s) -1.1 573E-03 Std Err of Coef. 6.81723E-06

VALVE: Valve 1 (9" tube) RUN: #2, valve closing Cr 46.0mmHg

DATE: August 29 1998

O 200 400 600 800 1000 i time [min] I

i

Reg ression Output: TlME CONSTANT: Constant 2.73057 Std EIT of Y Est 0.064339 TAU: -789.0 R Squared 0.97663 LOW TAU: -762.0 No, of Observations 21 HlGH TAU: -818.1 Degrees of Freedom 19 +/- 28 .O

X Coefficient(s) -0.001 267367 Std Err of Coef. 4.497694E-05

REGRESSION ANALYSE

VALVE: Valve 1 (9" tub) RUN: #3, valve opening

f l 46.2mmHg DATE: Septernber 1 1998

O 1 O0 200 300 400 500 600 1 tirne [min] i

Regression Output: TlME CONSTANT: Constant 3.357364 Std ER of Y Est 0.01 9366 TAU: -1244.8 R Squared 0.9821 38 LOW TAU: -121 5.9 No. of Observations 34 HlGH TAU -1275.2 Degrees of Freedom 32 +/- 29.7

X Coefficient(s) -0.00080331 6 Std Err of Coef. 1.91 51 E-OS

REGRESSION ANALYSIS

VALVE: Valve I (3" tube) RUN: #1, valve opening

& 48.3mmHg DATE: Odober 27 1998

Regression Output: T1ME CONSTANT: Constant 3.397354 Std Err of Y Est 0.033966 TAU: -334.2 R Squared 0.991691 LOW TAU: -328.7 No. of Obsewations 32 HlGH TAU -339.9 Degrees of Freedom 30 +/- 5 -6

X Coefficient(s) -0.002991 8335 Std Err of Coef. 4.999989E-O5

VALVE: Valve 1 (3" tube) RUN: #Ki, valve opening a 52.3rnmHg

DATE: November 4 1998

250 500 tima [min]

Regression Output: TlME CONSTANT: Constant 3.524992 Std Err of Y Est 0.01 1536 TAU: -637.6 R Squared 0.997099 LOW TAU: -632.1 No. of Observations 40 HlGH TAU: -643.2 Degrees of f reedom 38 +/- 5.6

X Coefficient(s) -0.OOi 56833592 -637.61 9 Std Err of Coef. 1 -37231 03E-05

REGRESSION ANALYSIS

VALVE: Valve 1 (3" tube) RUN: #3, valve opening

AT 48.3mmHg DATE: November 16 1998

250 500 time [min]

Regression Output: TlME CONSTANT: Constant 3.493055 Std EIT of Y Est 0.045696 TAU: -360.7 R Squared 0.98899 LOW TAU: -353.8 No. of Observations 31 HlGH TAU -367.9 Degrees of Freedom 29 +/- 7.1

X Coeffcient(s) -0.0027721 4986 -360.731 Std Err of Coef. 5.431 502E-05

VALVE: Valve 1 (3" tube) RUN: #3, valve dosing

& 48.1mmHg DATE: November 16 1998

Regression Output: Constant Std Err of Y Est R Squared No. of Observations Degrees of Freedom

TlME CONSTANT:

TAU: 652.0 LOW TAU: 657.2 HlGH TAU: 646.9

+/- 5.1

X Coefficient(s) 0,001 5337208 Std Err of Coef. 1.205788E-05

VALVE: Valve II RUN: #2, valve opening

+ 40.76 + 5.0 = 45.76mmHg DATE: June 2 1999

-2 1 1 1 I

t I 9

1

O 50 100 150 200 250 time [min]

Regression Output: TlME CONSTANT: Constant 2.6561 59 Std Err of Y Est 0,185416 TAU: -53.6 R Squared 0.972393 LOW TAU -52.0 No. of Observations 33 HlGH TAU -55.2 Degrees of Freeâom 3 1 +/- 1 .S

X Coefficient(s) -0.01 8666831 -53.571 Std Err of Coef. 0.000564904

VALVE: Valve Il RUN: H, valve opening AT++: 42.3 + 2.7 = 45.02mmHg

DATE: June 1 1999

ta 150 2m 1 time [min] 1 l

! 1

Regtession Output: TlME CONSTANT: Constant 2.8261 68 Std Err of Y Est 0.082899 TAU: -59.6 R Squared 0.990731 LOW TAU: -58.4 No. of Observations 24 HlGH TAU: -60.9 Degrees of Freedom 22 +P 1 -2

X Coefficient(s) -0.01 676991 2 -59.6306 Std Err of Coef. 0.0003458183

REGRESSION ANALYSE

VALVE: Valve II RUN: W , valve ciosing A%++ 40.0 + (-2.4) = 37.6 mmHg

DATE: June 2 1999

O 10 M 30 40 50 time [min]

Regression Output: TlME CONSTANT: Constant 2.631 86 Std Err of Y Est 0.057422 TAU: -1 8.6 R Squared 0.994045 LOW TAU: -1 8.2 No. of Observations 14 HlGH TAU -19.0 Degrees of Freedom 12 +/- 0.4

X Coefficient(s) -0.0538841 65 -1 8.5583 Std Err of Coef. 0.0012039121

REGRESSION ANALYSIS

VALVE: Valve il RUN: #3, valve opening

39.1 + 7.4 = 46.5mmHg DATE: June 3 1999

r 1 l I i

O 50 400 150 tOO 250 #KI tirne [min]

Regression Output: TlME CONSTANT: Constant 2.638358 Std Err of Y Est 0.1 11 882 TAU: -60.3 R Squared 0.991312 LOW TAU: -59.2 No. of Observations 28 HlGH TAU: -61.4 Degrees of Freedom 26 +/- 1.1

X Coefficient(s) -0.01 6597389 -60.2504 Std Err of Coef. 0.000304729

REGRESSION ANALYSIS

VALVE: Valve II RUN: #3, valve closing M++: 39.1+ 0 = 39.1 mmHg DATE: June 3 1999

i f O 1 O 20 30 40 54 60

time (min] ! I l i I i

Regression Output: TlME CONSTANT: Constant 2.720793 Std Err of Y Est O. 1 323 TAU: -1 9.9 R Squared 0.983501 LOW TAU: -1 9.3 No. of Observations 19 HlGH TAU -20.6 Degrees of Freedom 17 +/- 0.6

X Coefficient(s) -0.05021 71 6 -1 9.91 35 Std Er of Coef. 0.001 57749

VALVE: Valve il RUN: M, valve opening M+@ 40.1 + 6.4 = 46.5mmHg

DATE: June 4 1999

I

-1 ! 1 1 T r

1 L ,

O 20 40 613 8Q 100 120 140 time [min]

Regtession Output: TlME CONSTANT: Constant 2.640947 Std Err of Y Est 0.07874 TAU: -46.8 R Squared 0.98481 4 LOW TAU: -45.6 No. of Observations 25 HIGH TAU: 48.1 Degrees of Freedom 23 +/- 1.2

X Coefficierlt(s) -0.021 358329 -46.8201 Std Err of Coef. 0.000553022

REGRESSION ANALYSIS

VALVE: Valve Il RUN: #4, valve dosing AT* 40.1 + (-2.5) = 37.6mmHg DATE: June 4 1999

Regression Output: TIME CONSTANT: Constant 2.66055 Std Err of Y Est 0.1 û6595 TAU: -1 8.0 R Squared 0.9861 58 LOW TAU: -1 7.6 No. of Observations 28 HlGH TAU: -1 8.4 Degrees of Freedom 26 +/- 0.4

X Coefficient(s) -0.05561 1 343 -1 7.981 9 Std En of Coef. 0.001 2921 385

APPENDIX D - DEFORMATION CALCULATIONS

CALCULATIONS FOR SUPPORT PLATE DEFORMATION

General deformation equation for a solid round plate, firmly supported around perirneter (Roark & Young, 1975):

where:

a = plate radius [O. 107% ml E = Young's modulus [8.53e10 Pa] q = applied pressure [9800 Pa] t = plate thickness [0.002 ml v = Poission's ratio [0.3] r = point of interest dong plate radius [ml

(e.g. at centre of plate, r = O; at outside edge, r = a) y = vertical deformation at r [ml

Rewrite y(r) in terms of known variables:

Substitute known values and simplify:

y(r) = -9.87e-5 + 0.016941r2 - 0.72688r4

Treat y(r) as a constant, and rearrange to standard quadratic fom:

Let x = ? and solve for x using quadratic formula: 1

Apply boundary condition: r = 0.10795, y = O

General equation for volume o f rotation around y-axis:

Substitute equation for r(y) detemineci above:

Integrating and setting y, = -O. lmm (arbitrary small value):

V = 1.204045~-6m3 = 1.2mL

Therefore it can be concluded that small membrane deformations result in large volume changes.