light-tissue interaction model: a tool for consumer … · a light-tissue interaction model can be...

LIGHT-TISSUE INTERACTION MODEL: A TOOL FOR CONSUMER HEALTH DEVICE DEVELOPMENTINDUSTRIAL, CONSUMER, ENERGY

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WHITE PAPERLIGHT-TISSUE INTERACTION MODEL: A TOOL FOR CONSUMER HEALTH DEVICE DEVELOPMENT

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EXECUTIVE SUMMARYA light-tissue interaction model can be a highly valuable tool for consumer

health, personal care and cosmetics companies, in order to understand

skin health, the effects of treatment on various skin chemistries, to enable

tracking of changes over time, and to more accurately render facial features

for computer imaging, e.g., foundation matching applications.

Skin is complex, but by understanding the visual appearance of skin and the effects of various skin chemistry on reflected spectrum, one can design treatments to achieve a desired outcome. Having a light tissue interaction model is an important tool in designing portable sensing systems to monitor skin remotely (i.e. outside the lab), and in a

consumer’s home environment. This paper describes a light tissue interaction model created using an industry standard Monte Carlo simulation. The model was validated using experimentally obtained spectra and was identified as being accurate to within 0.14% to 2.6%. A potential design of a remote sensing system using this model is described.

LIGHT-TISSUE INTERACTION MODEL: A TOOL FOR CONSUMER HEALTH DEVICE DEVELOPMENTWHITE PAPER

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INTRODUCTIONAn analytical model that links the reflected spectrum of skin with the interaction of light with various skin constituents, such as melanin concentration, blood concentration, blood oxygenation, water concentration and state of collagen matrix, can tell the story of skin health [1-5]. The model can take a snapshot in time or monitor changes over an extended period and link the visual appearance of skin with the underlying skin chemistry. This linkage from skin chemistry to analytical model could provide the foundation for creating more accurate treatments that target very specific skin outcomes, or diagnostic tools to monitor skin health, including melanin concentration, skin hydration, erythema, etc. Another different potential use of this analytical model could be a more realistic rendering of human skin in computer rendering [2], which would enable better foundation matching application.

One of the challenges for consumer health, personal care and cosmetics companies is a fundamental lack of ability to capture use data in a real-world target setting. Companies want to move testing from a controlled laboratory setting into consumer’s homes (remote testing). By collecting consumer/product usage test data remotely, more data can be collected efficiently in a real-world setting, resulting in better clinical data and improved insight studies. The ability to collect real-world data can improve the product development process, provide insight for new innovations, and gather evidence for claims. For companies interested in skin health, understanding light propagation through skin can provide a powerful tool to develop sensors to monitor a particular skin condition, such as anti-aging treatment, hydration treatment, etc. A validated skin model affords a more accurate prediction of the reflected spectrum with changing skin chemistry, enabling sensor designs that use the lowest number of wavelengths to capture the effect of a particular skin constituent, reducing the cost/complexity of the sensor hardware and making it feasible to take these measurements in a consumer’s home. The model also allows the examination of any cross-talk effect between different constituents in order to determine optimal sensor wavelengths and algorithms for measuring specific skin constituents.

To model light transport through skin, a topographic model of skin, which is very complex and contains different layers, is required. Monte Carlo simulations have been extensively used in bio-medical optics to describe light propagation through tissue [1,5,6]. These models are broadly accepted and easy to implement as they can be used for many complex tissue structures.

This report describes how we developed a model of light transport through skin using Monte Carlo Multi-Layer [5,7] simulation that models skin as a two-layer medium through which light propagates. Published spectra of haemoglobin, water, and melanin are used to incorporate their effects on skin spectra. This report describes the creation of a two-layer analytical model of skin, using Monte-Carlo simulation. Experimental data from various skin types were used to validate the model output. Effects of various skin constituents, such as melanin concentration, blood oxygenation, blood concentration and scattering from collagen fibers on the skin spectrum is studied. An example of a melanin concentration sensor has been used to illustrate how the model could be used to deliver results and to describe some of the challenges with designing sensors for non-lab skin health measurements.

SKIN MODEL

Due to its complex structure, a rigorous physical model of skin is not available. Skin is generally irregularly shaped and is made of homogeneous distribution of its constituents, such as hair follicles, glands, etc. arranged in a multi-layered structure. To understand skin/light interaction, skin is usually simplified into a more tractable distribution of layers. To develop a skin model to understand the interaction of light and skin, and what information the measured spectrum has about the skin, a simplified two-layer model of skin used. The two-layers are dermis and epidermis. The epidermis layer contains melanin and the dermis layer contains blood, water and collagen fibers. Figure 1 shows the diagram of the skin used to model light transport through skin.

FIGURE 1: Simplified two-layer model of skin. The black arrow indicates

incident light and the red arrow indicates reflected light

Epidermis

REFLECTED LIGHTINCIDENT LIGHT

MELANIN

BLOOD + WATER + SCATTERING Dermis


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LIGHT TRANSPORT THROUGH TWO-LAYERED MEDIUM

An analytical model of light transport through skin was developed using Monte Carlo simulation (Monte Carlo Multi Layer, MCML [7]) for various optical properties (absorption and scattering) for the two layers. Reflected light R for given absorption coefficients (µa1, µa2) and reduced scattering coefficients (µsp1, µsp2) of layers 1 and 2 respectively can be written as:

R = R1 (μa1, μsp1) R2 (μa2, μsp2) (1)

where R1 is the contribution to the reflected light from layer 1 and R2 is the contribution from layer 2. To obtain an analytical model of R2 the absorption and reduced scattering coefficients (µa1, µsp1) of layer 1 was fixed and the absorption and reduced scattering coefficients (µa2, µsp2) of layer 2 were varied for multiple Monte Carlo simulations. Figure 2 shows plot of R2 as a function of µa2 and µsp2. From the plot, a fit function f(µa2, µsp2) was determined which predicted the value of R2 for a given value of µa2, µsp2. The function, f, provided the analytical model of R2.

FIGURE 2: The reflected light, R as a function of µa2 and µsp2. A fitting

function f(µa2, µsp2) is determined from this scatter plot to obtain an

analytical model of R2.

To obtain the analytical model of R1, the values of µa1 and µsp1 were varied for given values of µa2 and µsp2 and MCML simulations were run for each setting. Figure 4 shows the simulated reflection R1 as a function of µa1 and µsp1. The fit function T(µa1, µsp2) that predicts R1 is the analytical model of R1. The thickness of the layer was assumed to be 60 µm.

FIGURE 3: Reflected light as a function of μa1 for various values of μsp1.

The function T(μa1, μsp1) that fits this data is the analytical model of R1. The thickness of the layer was assumed to be 60 µm.

Using the fit functions obtained from figures 2 and 3, the analytical model for light reflected by a two-layer medium is given by:

R = T(μa1, μsp1) f (μa2, μsp2) (2)

LIGHT TRANSPORT THROUGH SKIN

The reflected spectrum R(λ) of skin is obtained by using the skin model described by figure 1. The layer 1 in equation (2) is the epidermal layer and layer 2 is the dermal layer. In epidermal layer, the absorbing chromophore is melanosomes and in the dermal layer the absorption of light is due to blood and water. As the absorption and scattering coefficients are wavelength dependent, the reflectance spectrum is given by:

R(λ) = T(μam (λ),μspe(λ)) f (μad (λ), μspd (λ)) (3)

where μam is the absorption coefficient of melanin, μspe is the reduced scattering in the epi-dermal layer, μad is the absorption coefficient of the dermal layer, and μspd is the reduced scattering coefficient of dermal layer to which the collagen fibers contribute. The wavelength dependence of the melanosome absorption, μamel [8] is shown in figure 4. The absorption coefficient of epidermal layer is given by, μam=M μamel where M is the volume fraction of melanosomes in the epidermal layer.

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FIGURE 4: Absorption coefficient of melanosome as a function of

wavelength

The dermal absorption coefficient and reduced dermal scattering coefficient are given by:

μad = B(O μaoxy + (1-O) μadeoxy) + W μaw (4)

and

μspd = D * μsp500 + (1-O) μadeoxy) + W μaw (5)

where B is the average volume fraction of whole blood in the skin (whole blood = 150 g Hb/liter), O is the fraction of blood that is oxygenated (between 0 to 1), μaoxy is the absorption coefficient of oxygenated haemoglobin, μadeoxy is the absorption coefficient of deoxygenated haemoglobin, W is the average volume fraction of water, μaw is the absorption coefficient of water, μsp500 is the reduced scattering coefficient of skin at 500 nm (assumed to be 43 cm-1), f is the fraction of scattering due to scatterers that are smaller than the wavelength of light (Rayleigh’s scattering) and D is the fitting parameters that captures the deviation from the average value at 500 nm.

The wavelength dependence of absorption coefficient of oxygenated and deoxygenated haemoglobin [9] is shown in figure 5. Absorption coefficient of water is shown in figure 6.

Using the absorption coefficients described in figures 4-6 and equations 3-5 one can obtain an analytical skin reflectance spectrum for given skin parameters: M, melanin concentration, B, blood concentration, O, fraction of oxygenation, W, water concentration and D, amount of dermal scattering. Figure 7 shows a predicted spectrum of skin for a given set of skin parameters (M=0.021, B=0.0027, O=0.7, D=1.0 and W=0.65).

FIGURE 5: Absorption coefficient of oxygenated and de-oxygenated

haemoglobin

FIGURE 6: Absorption coefficient of water

FIGURE 7: Predicted spectrum of skin for a given set of skin properties

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R


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VALIDATION OF SKIN LIGHT TRANSPORT MODEL

To validate the skin model, reflected spectrum was obtained using the experimental setup shown in figure 8. A broadband light source (AmScope) was coupled to a fiber optic light guide to illuminate the skin. A multimode fiber was used to couple the reflected light into a spectrometer (Thorlabs CCS200). Reflected spectrum of the incident light is captured using a reflectance standard, Mstd. Then the reflectance spectrum of the skin was obtained from the forearm of subjects, Mskin. The true reflectance spectrum of the skin is then obtained by:

R = Mskin–bck

(6)Mstd–bck

where “bck” is the background reading. Figure 9 shows a typical spectrum of the standard and the skin obtained using the setup described above. The reflected spectrum shown in figure 10 is obtained using equation 6 and the measured spectra. Figure 10 also shows the best fit predicted spectra obtained using least-square fitting of the measured data to the analytical model of skin given by equation 3. The fitting parameters are the skin properties, M, B, O, W, and D.

FIGURE 8: The schematic diagram of the experimental setup used to

obtain skin reflectance spectrum. Light from a white light source is

used to illuminate the sample (forearm of a subject) using a light

guide and a ring illuminator. A multi-mode fiber is used to collect the

reflected light and coupled into a spectrum analyser.

FIGURE 9: Measured spectrum from the reference standard and skin

sample

FIGURE 10: Reflectance spectrum data obtained from the spectra in

figure 9. The solid line is the predicted spectrum for a skin sample

with the skin composition shown at the top.

From figure 10, good reproduction of the skin spectra can be seen using the analytical model. The values of skin parameters are within other published values [4,6]. Having an analytical model of skin that can be used to determine skin constituents enables one to investigate the effects of different skin constituents on the measured spectra.

To further validate the model and its ability to predict skin constituents, spectra from different subjects, expected to have different melanin concentrations, were obtained. Reflectance spectra from the forearm region of four different subjects were taken, using two Caucasian subjects (CA1, and CA2), one Middle-Eastern subject (ME), and one African American subject (AA). Fitting the analytical model to these spectra, the predicted melanin concentrations were: M=1.1% for CA1, M=1.9% for CA2, M=4.87% for ME, and M=6.67% for AA. The measured reflectance spectra (diamonds) and the predicted spectra using the analytical model of light transport of skin (solid black line) are shown in figure 11.

FIGURE 11: Measured reflectance spectra of four different subjects.

Fitting the analytical skin reflectance model to these spectra, melanin

concentration, M of these four subjects were obtained. Solid black

lines are the spectra obtained using the analytical model.

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Ring illumator

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Refected light

Sample (Arm)


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M=0.019, B=0.0015, O=0.57

FIGURE 12: Measuring increased blood flow by fitting analytical skin

model to the measured spectrum.

To validate the ability of the analytical model to identify changes on the same subject, erythema (superficial reddening of the skin) was induced on a subject by placing a warm towel on the forearm. Figure 12 shows the arm of the subject before and after application of the warm towel. Top pictures show the images of the subject’s arm before and after application of the warm towel. The plots on the bottom are the measured spectra and the predicted spectrum using the analytical skin model. As the erythema is induced, and fitting the measured reflectance spectra with our model, it predicts the oxygenation of the region has increased from ~0.57 to ~0.97 and the blood concentration by volume fraction has increased from 0.15% to 0.28% as blood flow increases to the region.

Having validated the model and its ability to predict skin reflectance based on skin properties such as melanin

concentration and blood oxygenation, the following section discusses how the model can be used to design a low-cost sensor for measuring skin constituents such as melanin.

AN EXAMPLE: DESIGNING A LOW-COST MELANIN SENSOR

Having an analytical model of light propagation through skin enables one to study the effects of different skin constituents on the reflected spectrum and consequently to design sensors that do not require us to acquire the whole spectrum. Using an analytical model like this, measurements could be taken in a lab environment with a multi-spectral imaging system [6,10-14], requiring expensive, large and complex equipment. This paper discusses how the model can be used to design a system suitable for use in a remote setting (e.g. a consumer’s home). The left plot in figure 13 shows the predicted spectrum of a representative skin, where melanin concentration is varied from 1% to 7%. By analysing the resulting spectra it can be seen that by measuring the reflected light intensity at two wavelengths and taking their ratio, R2/R1, one can arrive at a measure of melanin concentration. The plot on the right plots the value of R2/R1 as a function of melanin concentration. From this analysis it can be seen that if one were to construct a melanin concentration sensor it may be possible to construct a sensor that measures just the reflectance of skin at two wavelengths.

FIGURE 13: Effect of melanin on the reflected spectrum. The plot on

the left shows the predicted reflected spectrum of skin for different

values of melanin concentration. The plot on the right shows the ratio

of R2/R1 as a function of melanin concentration.

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To validate the hypothesis that it is possible to measure melanin concentration by measuring the reflectance at just λ1 and λ2, we measured R1 and R2 from the spectrum obtained from our four subjects that is shown in figure 11. Figure 14 plots the measured ratio of R2/R1 as a function of the melanin concentration obtained by fitting the whole spectra to our analytical model. From the plot one can see that the ratio alone was a good predictor of the melanin concentration. Using both the theoretical prediction and the experimental result, one can build a simple, low-cost sensor configuration with two LEDs to measure melanin concentration of skin.

FIGURE 14: Measured R2/R1 ratio as a function of melanin concentration

obtained fitting the complete spectrum from 400nm-800nm. R1 and

R2 are measured at two optimal wavelengths of the plot on the left.

POTENTIAL CHALLENGES TO DESIGNING REMOTE SENSORS

One of the key challenges when designing low-cost sensors that do not capture the whole spectrum is differentiating the overlapping effects of different skin constituents. Figure 15 plots the predicted spectrum of skin for different values of blood oxygenation levels, using the analytical model above. From the spectra it can be seen that taking the ratio of reflectance at an isosbestic point (the wavelength at which the absorption of

light is the same for oxygenated and de-oxygenated blood), R1, and at another wavelength, R2 can be a good measure of blood oxygenation. The plot on the right in figure 15 shows the ratio of R2/R1 as a function of blood oxygenation. There is a good correlation between blood oxygenation and the ratio of R2/R1.

FIGURE 15: The effect of blood oxygenation on reflected skin spectrum.

The plot on the left shows reflected spectra for different blood

oxygenation levels. The plot on the right shows the correlation

between the ratio R2/R1 and blood oxygenation level.

Figure 16 shows the effect of blood concentration on confounding the oxygen saturation estimation using the ratio of R2/R1 described above. The plot on the left shows the predicated reflected spectra of skin for various blood concentration levels. For these spectra, only the blood concentration was varied while keeping other skin properties (such as melanin concentration, and oxygenation) constant. The plot shows in the deviation of the ratio (R2/R1) from the nominal value (measured using spectra corresponding to B=0.9%). For a perfect oxygen saturation detector, the ratio R2/R1 should not vary as the blood oxygenation was unchanged in these spectra. From the plot, it can be seen that the ratio R2/R1 was varying by ~±20%, although the oxygen saturation was unchanged. We can therefore conclude that using the ratio of R2/R1 will lead to erroneous estimation of blood oxygenation.

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In order to properly account for the effect of blood concentration on the skin reflection spectrum, the oxygen saturation detector will require another measurement to take into account blood concentration. A third wavelength was chosen such that the reflection R3 at that wavelength is correlated to the blood concentration. The plot in figure 17 shows the value of -log(R3) as a function of blood concentration. It can be seen that -log(R3) is highly correlated to blood concentration. To account for the confounding effect of blood concentration, the new measure for oxygen saturation is O=R2/(R1 log(R3)). The plot on the left of igure 18 shows the deviation of the new oxygen saturation measured from the mean value. The plot on the right shows the deviation using just R2/R1. With the new measure of oxygen saturation, the estimated deviation is reduced from ±20% to ±2%.

FIGURE 16: Effect of blood concentration in confounding oxygen

saturation measurement. The plot on the left shows the effect of

blood concentration on the reflected skin spectra. The plot on the

left shows the deviation in the oxygen saturation estimation using

the ratio R2/R1.

FIGURE 17: The effect of blood concentration of the reflected spectrum.

The plot shows the correlation between -log(R3) with blood

concentration.

O =– R2

R1log (R3)

O =

R2

R1

FIGURE 18: Improved estimation of oxygen saturation using

measurements at three wavelengths. The plot on the left shows

the deviation from nominal using three wavelengths. The plot on

the right shows the deviation form nominal using two wavelengths

measurements.

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From the analysis above, a potential oxygen saturation detector would require three wavelength measurements to correlate to full spectral analysis. To support this assertion, a warm towel was placed on a subject’s forearm to induce increased blood flow. Spectra were collected before applying the warm towel, after applying the warm towel for five minutes, after removing it, fifteen minutes after removing the warm towel and an hour after removing the warm towel. At the hour mark there was no visible redness of the subject’s forearm. Using the analysis described in the section titled ‘Validation of skin light transport model’, blood oxygenation and oxygen concentration were determined for these time points. Figure 19 shows the measured blood concentration for the four time points. The plot on the above left shows oxygen concentration over time, obtained by fitting the skin model over the whole spectra. The plot on the right shows the three wavelength measurement over time. The plot on the right seems to follow the same general trend as the plot on the left, signifying the potential of using a three LED system to replace full spectral analysis for obtaining blood oxygenation.

FIGURE 19: Change in blood oxygenation over time measured using full

spectral analysis and three wavelength measurements.

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CONCLUSIONAn analytical model of light transport through skin was developed using multi-layer Monte Carlo simulation and a simplified two-layer model of skin. The model was validated using experimentally obtained skin reflection spectrum and successfully modelling the skin spectra of subject from different races and predicting their melanin concentration. The model successfully predicted increased blood flow and oxygenation on a subject’s forearm after inducing erythema. Using the analytical model, the effects of melanin concentration, blood concentration, and oxygen saturation were used to design hypothetical LED based sensors for single constituent concentration, blood oxygenation and concentration. The analytical model can be a powerful tool to understand the underlying skin properties, whose interaction

with light results in the reflectance spectra of light. Since the model inputs are physical parameters such as melanin concentration, blood concentration, blood oxygenation and tissue hydration, the model can be used to study the effect of individual skin constituents on the spectrum and also their combined effects. Using this model one can design sensors targeting specific skin constituents that can enable remote sensing within the consumer’s home environment, without having to collect whole spectra under lab conditions using complex equipment. For example, to study the efficacy of anti-aging treatment, one can design a sensor that only looks at the changes in melanin and dermal scattering to monitor the efficacy of treatment.


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REFERENCES[1] Lister, T., Wright, P. A., & Chappell, P. H., (2014). A

new Monte Carlo program for simulating light transport through Port Wine Stain skin. Laser Med. Sci., Vol. 29, No. 3., 1017-1028.

[2] Poirier, G. (2004). Human skin modelling and rendering. Master of Mathematics in Computer Science thesis. University of Waterloo.

[3] Stamnes, K., Chee Tsay, S., Wiscombe, W., & K. Jayaweera, (1988). Numerically stable algorithm for discreteordinate-method radiative transfer in multiple scattering and emitting layer media. Appl. Opt. 27, 2502–2510.

[4] Magnain, C., Elias, A., & Frigerio, J-M., (2007). Skin color modeling using the radiative transfer equation solved by auxiliary function method. J. Opt. Soc. Am, Vol.24, No. 8, 2196-2205.

[5] Jacques, S. L., (2009). Spectral imaging and analysis to yield tissue optical properties. J. Innov. Opt. Health Sci., Vol. 2, No. 2, 123-129.

[6] Choudhury, N., Samatham, R., & Jacques, S. L. (2010). Linking visual appearance of skin to underlying optical properties, using multi-spectral imaging. Proc. SPIE 7548, Photonic Therapeutics and Diagnostics VI, 75480G.

[7] Wang, L. H., Jacques, S. L., & Zheng, L. Q. (1995). Monte Carlo modelling of photon transport in multi-layered tissue Compute. Methods Programs Biomed. 47, 131-146.

[8] Jacques, S. L., & McAuliffe, D. J. (1991). The melanosomes: Threshold temperature for explosive vapourization and internal absorption coefficient during pulsed laser irradiation Photochem. Photobiol. 53, 769-776.

[9] Prahl, S. L., & Jacques, S. L., http://omlc.ogi.edu/spectra.

[10] Zuzak, K. J., Schaeberle, M. D., Lewis, E. N., & Levin, I. W. (2002). Visible Reflectance Hyperspectral Imaging: Characterization of a Noninvasive, in Vivo System for Determining Tissue Perfusion. Anal. Chem., 74(9),2021-28.

[11] Stamatas, G. N., & Kollias, N. (2007). In vivo documentation of cutaneous inflammation using spectral imaging. Journal of Biomed. Optics 12 (5), 1 - 7.

[12] Shi, T., & DiMarzio, C. A. (2007). Multispectral method for skin imaging: development and validation. Applied Optics 46 (36), 8619-8626.

[13] Binzoni, T., Vogel, A., Gandjbakche, A. H., & Marchesini, R. (2008). Detection limits of multi-spectral optical imaging under skin surface. Phys. Med. Bio. 53, 617-636.

[14] Klaessens, G. M., Noordmans, H. J., Roode, R., & Verdaasdonk, R. M., (2009). Non-invasive skin oxygenation imaging using a multispectral camera system: Effectiveness of various concentration algorithms applied on human skin. Proc. SPIE. 7174, 1-13.

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WHITE PAPER LIGHT-TISSUE INTERACTION MODEL: A TOOL FOR CONSUMER HEALTH DEVICE DEVELOPMENT

ABOUT THE AUTHORDr Niloy Choudhury is a Principal Physicist at Cambridge Consultants. He has almost two decades of scientific, industrial and academic experience of optoelectronics instrumentation and product development, with expertise in telecom optical components, biomedical imaging and industrial sensors. He is an expert in the design of biomedical instrumentation, optical coherence tomography and spectroscopy.

Dr Choudhury has worked as a senior scientist at GE Global research, where he conducted R&D on advanced photonics sensor technology and led multi-year, multi-million dollar projects. He was also an Assistant Professor in biomedical engineering at Michigan Tech, where he conducted research on label-free optical readout of cellular activation. His research also included study of skin/light interaction and its relation to visual appearance, nano-motion using low-coherence interferometry for understanding of hearing mechanics and micro-circulation of blood. His work has been funded by industry as well as NIH, and DoE. Dr Choudhury has authored and co-authored over 50 journal publications, patents and conference presentations.

For more information, or to discuss how this approach could fit your business, please contact:

Niloy Choudhury, Principal Physicist [email protected]

About Cambridge ConsultantsCambridge Consultants is a world-class supplier of innovative product development engineering and technology consulting. We work with companies globally to help them manage the business impact of the changing technology landscape.

With a team of more than 800 staff in the UK, the USA, Singapore and Japan, we have all the in-house skills needed to help you – from creating innovative concepts right the way through to taking your product into manufacturing. Most of our projects deliver prototype hardware or software and trials production batches. Equally, our technology consultants can help you to maximise your product portfolio and technology roadmap.

We’re not content just to create ‘me-too’ products that make incremental change; we specialise in helping companies achieve the seemingly impossible. We work with some of the world’s largest blue-chip companies as well as with some of the smallest, innovative start-ups that want to change the status quo fast.

Cambridge Consultants is part of the Altran Group, a global leader in innovation. www.Altran.com

http://www.Altran.com

Cambridge Consultants is part of the Altran group, a global leader in innovation. www.Altran.com

www.CambridgeConsultants.comUK § § §USA SINGAPORE JAPAN

light-tissue interaction model: a tool for consumer … · a light-tissue interaction model can be...

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