Mathematical Modelling of the

Optimum Pulse Structure for Safe

and Effective Photo Epilation Using

Broadband Pulsed Light

Caerwyn Ash PhD1, Kelvin Donne PhD2, Gwenaelle Daniel PhD2, Godfrey

Town2, Marc Clement PhD1

1. School of Medicine, Swansea University, Swansea SA2 8PP

2. University of Wales, Cardiff, CF10 3NS

2010

Statement of Disclosure

The following potential conflict of interest relationships

are germane to our presentation:

Salary and test equipment loan: CyDen Ltd., Wales

Travel grant: Swansea University, Wales

2010

IPL Pulse Structure Categories (time vs. wavelength)

Free Discharge

Square Pulse

Close Pulse Stacking

Spaced Pulse Stacking

Ash C, Town G, Bjerring P, (2008), Relevance of the Structure of Time Resolved Spectral Output to Light Tissue Interaction Using Intense Pulsed Light (IPL),

Lasers in Surgery and Medicine 40:83–92

Reference sources for Monte Carlo model parameters

P Bjerring, K Donne, M Clement, M Kiernan, The Importance of Temporal Profile in Selective Non-Ablative Wrinkle

Reduction using 585nm Light, 2002, White Paper

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boundary voxelization. Comput Meth Prog Bio 2008;89:14– 23.

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June, 2007.

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Investigated by Mathematical Modeling, Lasers in Surgery and Medicine, Volume 39 Issue 2, Pages 132 – 139.

F Sun, A Chaney, R Anderson, G Aguilar, Thermal Modelling and Experimental Validation of Human Hair and Skin Heated

by Broadband Light, Lasers in Surgery and Medicine 41:161–169 (2009)

Materials and Methods

• 5µm cell size

• Cartesian coordinate grid

• Values of tissue

properties taken from

abundance of peer

reviewed literature

• 1×107 photons

• Spectrum equals 10J/cm2

Physical Constants used for the various tissue layers

Materials and Methods

) 10 (1.7 )(µ -3.4812(melanin)a

We modelled the IPL spectrum as 600 differently coloured lasers (500 to 1,100nm) of different

intensities of 1nm bandwidth and fluence simultaneously.

Absorption by tissue chromophores taken from literature

SL Jacques. Origins of tissue optical properties in the UVA, visible and NR regions. In: Alfano RR, Fujimoto JG,

editors. Advances in optical imaging and photon migration, Vol. 2.Washington, DC:OSA; 1996:364–370.

Materials and Methods

Where T (x,y,z,t) is the local temperature in the tissue (K),

α is the thermal diffusivity of the tissue = [k/ρc]

c is the specific heat (J kg-1 K-1),

ρ is the mass density, (kg m-3),

k is the thermal conductivity of the tissue, (W m-1 K-1),

Q (x,y,z,t) is the volumetric thermal source term, (W m-3)

t is the time (seconds),

Following establishment of the photon distribution using the Monte Carlo technique, the

temperature distribution at any instant may be calculated by numerically solving the time-

dependent thermal diffusion equations. The temperature of the skin is governed by the

following bio-heat equation

Modelled Representation IPL Pulse types

Results

• Free discharge, Square Pulse and Close Pulse Stacking system attain temperatures above 70ºC

• Spaced pulse stacking system suggests that the device would need to deliver a greater fluence to attain

similar results than the other systems as much energy is lost during the prolonged off time between pulses.

• Spaced pulse stacking systems may require more internal water-cooling and active or parallel skin surface

cooling to generate and deliver energy safely.

Rate of modeled follicular temperature increase against time for different pulse structures

Results

• Longer pulse structures allow the epidermal layer to cool during the pulse

• Skin temperatures for all four systems indicating the peak temperature for the free discharge system

produced the highest absorbed temperatures thus probably causing greater patient discomfort. Such

systems probably use active or parallel cooling of the skin to prevent adverse reactions such as erythema,

hyperpigmentation.

Rate of epidermal temperature increase against time for different pulse structures

Discussion

• Systems were compared in this study with equal fluence of 10J/cm2

• Controlled repeatable and consistent delivery of optical energy was shown by square pulse

and close pulse stacking temporal profiles This controlled delivery will also provide repeatable

clinical results shot-to-shot. Whereas the free discharge systems, although simple in their

technology, inherently vary shot-to-shot and may cause disparity during treatment and during

the lifetime of the device*.

• The Monte Carlo model used for this study is two dimensional (2D) in its representation of the

light-tissue interaction. However, in reality the interaction of light with hair follicles is in three

dimensions (3D) This may explain the retained temperatures within the temperature modelling

and during exposure. The model is representative for a broad field as approximately the same

amount of photons jump into as out of the azimuthal plane.

• It has long been assumed that the optical properties of the various tissue layers do not

change during exposure to light. This may not be the case as during exposure absorption of

optical energy by chromophores cause heating and mechanically modify some biological

targets.

• Spectral Jitter during the pulse duration has not been considered

• Assumed constant treatment area for all devices

Project future Improvements

• Further development of Computer simulation will make possible open access to software to

predict system performance based on measured output IPL parameters

• Joint Collaboration with School of Computer Science, department of bioengineering and access

to IBM Blue Ice supercomputer to model tissue in 3D with a 1um cell size using parallel

processing to increase speed of results.

IBM Blue Ice

Conclusion

• The value of comparing the physics of light-tissue interaction against different

parameters is of significance to clinicians and system designers.

• The mathematical model assists in identifying positive theoretical options and avoids

experimental repetition. Mathematical modeling also facilitates viewing photon

deposition through skin and final depth in tissue.

• Computer modeling of different pulse profiles indicates square pulse and close pulse

stacking of sub-pulses are the most efficient in delivering optimal light doses to achieve

sufficient thermal transient in the follicle for effective hair reduction.

Thank You

• Many thanks to the Faculty of Applied Design

and Engineering at Swansea Metropolitan

University for their time and effort in producing

the Monte Carlo Software

• Travel grant from Swansea University to attend

ASLMS