Structure-Function of Interstitial Spaces: New Clues to Fluid-Balance Mechanisms

Department of Reconstructive and Plastic Surgery Research

Medical School of Wake-Forest University

The energy for fluid and solute transport is the work of the heart and

concentration gradients of water and solutes across extravascular spaces.

The net force determining fluid exchange is the resultant of hydrostatic and

osmotic pressures (Starling Principle) across capillary membranes.

Pc Pi ?

COPc COPi?

σ

(capillary osmotic reflection coefficient)

P(hydrostatic) /P(colloidosmotic) ---> filtration / adsorption

LYMPH FLOW

~5 liters ~15 liters (~6 – 10 liters in skin)

Plasma Interstitial space INTRACELLULAR30 liters

Porcine Skin

Layers corneum 2.5 mm = 2500 µm~11 mm epidermis

dermisadipose

cutaneous muscles

Pc-Pi =(COPc) –(COPi)

DIFV = kÛPc-Pi- [(COPc)-(COPi)].dt +ÛFl.dt

mj = m 0 +RTlnaj + PV + FE zj + ghnj

∂G/∂nj

concentration + pressure vol. + charge +gravityChem.potential

FORCES

GEOMETRYPHYSICOCHEMICAL PROPERTIES

Hudack and McMaster, 1933

L 4

~200 µµµµm3/cell

Swelling Kinetics of Dermal Explants

Time (min) Volume Change (Mean ± SE; n = 6)

4º C 37º C_____________ _____________

22 0.043 ± 0.002 0.047 ± 0.00448 0.062 ± 0.005 0.066 ± 0.00595 0.093 ± 0.008 0.087 ± 0.007

172 0.112 ± 0.006 0.101 ± 0.0071128 0.214 ± 0.005 0.173 ± 0.010

1440 0.246 ± 0.004 0.186 ± 0.012

3mm Hg

0

.05

.1

.15

.2

.25

.3

.35

0 500 1000 1500 2000 2500 3000

Time (min)

Y = a + b/(1+(x/c)d)

VO

LU

ME

CH

AN

GE

Swelling of Dermal Interstitium : Progress Curve at 4 and 37 ºC

a ~ 0

b = Volume(max)

c = Time(1/2)

d = αRate(1/2)

Swelling of Dermal ExplantsKinetic Parameters

(Mean ± SE n=3)

4 ºC 37 ºC

____________ ___________

Volumemax 0.458 ± 0.068 0.225 ± 0.074

Time1/2 (min) 1638 ± 688 426 ± 44

αRate1/2 0.476 ± 0.078 0.555 ± 0.101

y = a + Volume/[1+(x/time)αRate]

“EQUILIBRIUM” PRESSURE OF DERMAL INTERSTITIUM.

DESCRIPTIVE STATISTICS

Temperature Mean ± SE Max. Min. Difference P-value n

4 ºC 107.4 ± 22.3 211 50 60 0.012 7

37 ºC 47.3 ± 12.3 107 3 “ “ 7

==========================================================

37 ºC

4ºC4ºC

37ºC37ºC

Replicate samples equilibrated

in physiologic solutions of

known colloidosmotic pressure

within a 3 - 211 mmHg range.

Depending on pressure,

explants swell, de-swell or do

no change.

Swelling and De-Swelling of Dermal Interstitium

-.2

-.15

-.1

-.05

0

.05

.1

.15

.2

.25

0 500 1000 1500 2000 2500 3000TIME (min)

Vo

lum

e C

hang

eSwelling = 3 mmHg

De-Swelling = 107 mmHg

y = a + Volume/[1+(x/time)αrate]

De-swelling of Dermal Explants. Kinetic Parameters

Parameter 4 ºC 37 ºC____________ _____________ ___________

Volume (max) 0.408 ± 0.013 0.542 ± 0.021

Time (1/2) 182 ± 17 192 ± 25

αRate (1/2) 0.970 ± 0.075 0.698 ± 0.04 ===================================================

r2 0.9994 0.9997

0

10

20

30

40

50

60

0 50 100 150 200 250 300

TIME

1.88 ± 0.12 X10-6

3.05 ± 0.28 X10-6

RA

TE

X

10

-5

(min

-1)

DPressure (mmHg)

VOLUME-CHANGE VELOCITY AS A FUNCTION OF PRESSURE

0.00

.05

.09

.14

.20

.25

.30

.34

.40

0 200 400 600 800 10001200 14001600

Time

Iodoacetamide

Control

VO

LU

ME

CH

AN

GE

Swelling Parameters of Human Dermis after Inhibition of Anaerobic Glucose-Metabolism

Parameter Control Iodoacetamide

V(max) 0.265 ± 0.012 0.462 ± 0.093

T(1/2) 34.1 ± 7.4 149.2 ± 108.2

αRate(1/2) -0.885 ± 0.12 -0.606 ± 0.164

(172 X 10-5) (47 X 10-5)

r2 0.997 0.990

D 23 mmHg

The Magnitude of Interstitial Pressure-Gradients is larger than previously considered.

The fluxes in/out of Interstitium are related linearly to the Pressure Gradients.

The Resultant Interstitial Pressure includes significant contribution from cell processes that require generation of energy from glucose metabolism.

The Geometry of Interstitial Fluid Pathways is …complex.

Interstitial-water transfer as a function of

pressure and water activity

gradients

-.02

.02

.06

.1

.14

vo

l ch

an

ge

-20 0 20 40 60 80 100 120 140pressure

-.02

.02

.06

.1

.14

vo

l ch

an

ge

.979 .981 .983 .985 .987 .989aw

evaporationcolloidosmotic

(mmHg)

AB

A. Water transfer from interstitium to polymer solution. B. Water transfer from interstitium to air

∆G-∆G°= RT lna;

1atm . Vw = ~ 0.435 cal/mol

RT ~ 600 cal/mol

123 7 0-1 5 74 ms 47ms

2 mm

Magnetic Resonance Imaging: Transverse relaxation time

T2 reflects water’s freedom of motion

Correlates with aw

0

5

10

15

20

25

30

35

40T

2b

0 1000 2000 3000 4000

Distance b (um)

0

5

10

15

20

25

30

T2a

0 1000 2000 3000 4000

D is tan ce a (u m )

a

b

Water activity gradients in skin interstitium.

SPIN-SPIN RELAXATION TIME (T2)

a

b

Y = A+c exp(-t/T2)The envelop of the spin-echo peaks

decays exponentially with T2

40

45

50

55

60

65

70

75

80

85

90

95P

ressu

re m

mH

g

0 200 400 600 800 1000 1200

Depth (um)

Osmotic equilibrium-pressure of pig skin layers

Subpapillary plexus

How does the water reabsorbs?

• phase transition?• Cell-fibers mechanics?• elastic recoil?

L1 L2 L3 L4 L5

Blood vessel wall injury, inflammation

Vasodilatation���� extravasation of plasma proteins

Acceleration of coagulation pathways-���� Fibrin and

platelet clot ����hemostasis

The transfer of blood to the extravascular space is

stopped (or much slowed)

The clot is initial scaffold for tissue regeneration and repair and a source of signals for cell migration and

differentiation

Local factors influence transport and distribution of reactants and

their microscopic rate coefficients in extravascular spaces

cells� Tissue factor = reactive sinks

extracellular matrix� Glycosaminoglycanswater activity� hydration/dehydration reactions

.2

.3

.4

.5

.6

.7

.8

.91

1.1

1.2

0 20 40 60 80 100 120Pressure

0

5

10

15

20

25

30

35

0 20 40 60 80 100 120

Pressure

Surface-Mediated Diffusion-Limited Reactions.

Pressure Spectra and Source Intensity as a Function of Geometry

~150 µm~15 µm

FLU

X fX

a(f

mol/s)

Norm

aliz

ed F

lux

CELLS = ~ 2 X 106 /ml104 microcarriers~200 cells/microcarrier

BLOOD COAGULATION PROTEOLYTIC PATHWAYS

ACCELERATE DECELERATE (procoagulants) (anticoagulants)

Tissue factor (TF)* Tissue factor pathway inhibitor*Intrinsic loop** Antithrombin**Prothrombinase Protein C pathway**Thrombin activatable fibrinolysis inhibitor Fibrinolytic pathway

* Regulated by water activity

* Regulated by glycosaminoglycans

12

14

16

18

20

22

24

26

28

30

32

fXaT

F0.0

75 lo

ng

0 .1 .2 .3 .4 .5 .6 .7 .8 .9atm

RATE = a + b/ [1+((pressure-c)/d)2]

The rate of coagulation factor X activation is a function of the pressure (colloid osmotic)

Pressure units

TF + fVIIa ↔↔↔↔ TF/fVIIa + fX→→→→ fXa

RA

TE

pM

/sFACTOR Xa GENERATION IN DILUTED PLASMA UNDER OSMOTIC STRESS

GLYCOSAMINOGLYCANS

GALACTOSAMINOGLYCANS

Chondroitin sulfatesDermatan sulfates

GLUCOSAMINOGLYCANS

Heparan sulfatesKeratan sulfatesHyaluronan

Linear polysaccharides ; disaccharide units; variable sequences;

variable distribution; variable density at nano-micro scales

The Skin interstitium is a transfer-media composed of gelled heterogeneous layers with fluctuating interfaces

Material properties of gels and of this gel at the appropriate scales for cellular

and macromolecular rate process.

EVIDENCE FOR PRESURE AND CONCENTRATION GRADIENTS

• Water activity gradients �magnetic resonance microscopy

• Responses to water activity changes �Osmotic Stress techniques

• Water desorption isotherms

• “Swelling pressure” ; ∆V/∆P

• “Spontaneous” fluctuation in capillary blood flow with a frequency of 6-10 cycles/min ; 0.2 - 0.6 mm/s.

• Irregular distribution of reactive sinks• “Variable” lymphatic pressures (10 mmHg to -7mmHg)

“Physiology is Physics”

“We model to organize and to understand biological information”

• Large Integrative Model (emergence of biological properties from complexity)

• Focused, Simplest Possible Model (abstracts key properties for analysis and hypothesis testing)

COLLABORATIVE WORKING GROUPS MUST BE ESTABLISHED:

To incorporate broadening ranges of knowledge and technical expertiseinsuring that models are consistent with: Experimental Biological Observations, Mathematical Principles, Thermodynamic and Mechanical Laws, Computational Capabilities.