Callus Thickness Determination Adjuvant to Tissue Oximetry

Imaging

Gennadi Saiko

1,2 a

Swift Medical Inc., 1 Richmond St. W., Toronto, Canada

Ryerson University, Toronto, Canada

Keywords: Diabetic Foot Ulcer, Oximetry, Turbid Tissues.

Abstract: Introduction: Corns and calluses are thickened skin due to repeated friction, pressure, or other irritation.

While in many cases, calluses are harmless, if not removed timely, they may lead to skin ulceration or

infection. Thus, the removal of calluses is an essential part of surgical debridement. Often, healthcare

professionals experience problems with their identification. This study aims to develop an approach for

callus thickness determination using hyperspectral imaging. Methods: Based on the two-layer tissue model

developed by Yudovsky D et al., 2010, we have developed a computationally simple way of extracting the

epithelial thickness from spectral measurements of skin reflection. We have performed a numerical

evaluation of the proposed algorithm: generated the reflectance spectrum using the two-layer model, added

noise, and reconstructed the epidermal thickness L using the proposed method. To evaluate performance,

we have used the following parameters: thickness of the epithelium: 0.1-2mm, dermal blood concentration:

0.2%, 3%, and 7%, blood oxygen saturation: 60%, 80%, and 99%. Results: We have found that the model

reasonably well extracts epidermal thickness L in the 0.1-1.5mm range. Beyond that, the reflectance signal

does not bring information about underlying layers. The most significant factor, which impacts estimation,

is the scattering coefficient of the epidermis. Other factors can be mainly ignored. Conclusions: The

proposed model can be easily implemented in image processing algorithms for hyperspectral/multispectral

imaging systems.

https://orcid.org/0000-0002-5697-7609

1 INTRODUCTION

Corns and calluses are thickened skin areas due to

repeated friction, pressure, or other irritation. They

are created by the accumulation of undifferentiated

keratinocytes in the outermost layer of skin. Though

the cells of calluses are dead, they are resistant to

mechanical and chemical impacts due to extensive

networks of cross-linked proteins and hydrophobic

keratin intermediate filaments containing many

disulfide bonds. Calluses are the natural reaction to

irritation of the palmar or plantar skin. Too much

friction occurring too fast for the skin to develop a

protective callus will cause a blister or abrasion

instead.

Several risk factors like foot deformities (e.g.,

bunions, hammertoe) and not wearing socks or

protective gloves facilitate callus formation.

While in many cases, calluses are harmless, if

not removed timely, they may lead to skin ulceration

or infection, which is of particular importance for

patients with diabetes. They can also cause the

patient to try offload the affected painful area,

placing excessive stress on the asymptomatic side.

Thus, the removal of calluses is an essential part

of surgical debridement. However, in many cases,

healthcare professionals experience problems with

their identification. While corns are typically clearly

visible, calluses are often unsightly. Consequently,

some areas of dead skin can be missed during

debridement.

Therefore, a clinical tool that will help identify

suspected areas would be of great clinical utility.

In (Yudovsky, 2010) the authors proposed

estimating blood saturation, melanin content, and

epidermis thickness from spectral diffuse reflectance

measurements. Using Monte Carlo simulations, the

authors solved the radiative transfer equation and

applied an inverse method to retrieve physiological

parameters. However, the technique is suitable

Saiko, G.

Callus Thickness Determination Adjuvant to Tissue Oximetry Imaging.

DOI: 10.5220/0010852400003123

In Proceedings of the 15th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2022) - Volume 2: BIOIMAGING, pages 147-152

ISBN: 978-989-758-552-4; ISSN: 2184-4305

147

mainly for a single-point assessment and cannot be

extended to imaging geometry due to computational

complexity.

This problem is closely related to the maximal

detection depth problem discussed analytically

(Saiko, 2012) and using Monte Carlo (Saiko, 2014).

This study aims to develop an approach for

callus thickness determination using hyperspectral or

multispectral imaging

2 METHODS

2.1 Tissue Model

The skin is a multi-layer structure. Typically, it is

subdivided into three primary layers: epidermis,

dermis, and subcutaneous tissue. However, each of

these layers can be split into several respective sub-

layers.

However, considering the spectrum's visible

range, the light penetration depth does not exceed

2mm, and subcutaneous tissue does not contribute

much to the reflectance. Thus, in this case, we can

consider the skin as a two-layer structure: the

bloodless epidermis and underlying, blood-

containing tissue, which has optical properties of the

dermis.

We will approximate the epidermis as a slab of

thickness L

. In the normal case, the epidermis is not

more than 100-120μm thick; however, it can be

several millimeters thick in the callus. Such as light

does not penetrate more than 2mm into the dermis;

we can approximate it as a semi-infinite layer.

2.2 Optical Tissue Model

Thus, we can model the skin as a two-layer

structure, where a slab with optical parameters (

) and thickness L

covers a semi-space with

optical parameters (

). Here and after that,

indexes 0, 1, and 2 refer to the air, epidermal, and

underlying tissues, respectively. Thus, our ultimate

goal will be to find L

from optical measurements.

In (Yudovsky, 2009) the authors investigated

such model using a two-flux Kubelka-Munk

approach with mismatched external boundary and

matched interlayer interface and found that the

reflectance of such a two-layer model can be

expressed as

11 1 2 1 2

((,) (,)) (,)R RRn Rn Rn

ωω ω

−− −

′

=−+

(1)

Here R

(n,

) is the reflectance of the semi space

with the index of refraction n and reduced albedo

(

/( )

μμμ

), and R' is the "reduced

reflectance," which varies in the range from 0 to 1.

The reflectance of the semi space with

mismatches boundary can be written as (Saunderson,

1942)

01 10

(1 )(1 )

rrR

−

−−

−

(2)

Here r

is the specular reflectance for the light

coming from air to the tissue, r

is the specular

reflectance of the light coming from the tissue into

the air, R

is the diffuse reflectance of the tissue. The

diffuse reflectance of the semi space with optical

properties (

) can be found using the Kubelka-

Munk (K-M) model

Ra a=− −

(3)

Where

()/aSKS=+

. In (van Gemert, 1987),

the authors expressed K-M absorption and scattering

coefficients K and S through μ

and μ'

While the reduced reflectance R' can be found

analytically, a semi-empirical approach (Yudovsky,

2009) with fitting parameter a gives more accurate

predictions of tissue reflectance

tanh(Y )

1/ (1 1/ )tanh(Y )

αα

′

+−

(4)

Here

1111

Y( )

ζμ μ

(5)

where

is the root of the characteristic equation

ln((1 ) / (1 ))

ζζ

+−

(6)

2.3 Physiological Considerations

In the general case, the skin contains melanin

located in the bottom, basal layer of the epidermis.

However, there are two considerations why we can

ignore its impact in the case of callus. Firstly,

calluses are mainly located on plantar surfaces (sole

and palm), which are melanin-free. Secondly, for

other body locations, one can expect that the skin's

normal processes are disrupted, so most likely, the

skin will not form melanin protection in the case of

the callus/corn. Thus, we can ignore melanin, which

significantly simplifies our calculations.

BIOIMAGING 2022 - 9th International Conference on Bioimaging

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In this case, we have the epidermal slab with

quite universal optical characteristics, which are not

affected by a skin type, and thus, should have low

interpatient variability. So, we can tabulate its

optical properties (

The optical properties of the dermis are a little

bit more tricky case. In the spectrum's visible range,

they will be affected by blood, namely its

concentration and composition (oxygenation). For

the normal dermis, blood concentration is typically

considered to be close to 3%. However, a callus may

hide blood pools in some cases, where the blood

concentration will be obviously higher. Furthermore,

oxygenation of the blood varies from 97-99% for the

arterial blood up to 60% for the venous blood. In the

general case, the light samples both arterial and

venous compartments, so the measured SO2 is

somewhere between these values. However, to test

the method, it is better to check the whole range.

2.4 Algorithm

The method can be described as the following:

1. Measure R at several wavelengths

2. Tabulate parameters (

) and seed

realistic n,

and (

), e.g., healthy tissue

3. Calculate R

(

) and R

(ω

) using the K-M

model (Eq.3)

4. Calculate R_(n

, ω

) and R_( n

, ω

) using Eq.2

5. Calculate R':

(, )

(, ) (, )

RRn

Rn Rn

ωω

−

−−

−

6. Calculate Y

by solving Eq.4

7. Using tabulated values (

) and

from

Eq.6, find L

using Eq.5.

8. Update Y

, and recalculate R.'

9. Calculate R

RRR

−

10. Calculate R

by reversing Eq.2

11. Calculate K and S and then update (

)

12. Repeat steps 3-11 with updated (

) if

required

2.5 Parameters

2.5.1 Absorption

In the absence of melanin, the epidermis absorption

can be modeled as the background absorption of

human flesh (Jacques, 1996):

1,aafl

μμ

where

7 3.255

7.84 10

afl

μλ

−

=×

[mm

-1

]. Here, the wavelength

λ is measured in [nm].

The absorption of the dermis can be modeled as

a combination of background-, oxyhemoglobin-, and

deoxyhemoglobin related absorption

,2 ,

(1 )

(2* (1 2)* )

aafl

aHbO aRHb

cSO SO

μμ

=− +

++−

(7)

Here c is the blood concentration in the dermis,

SO2 is the oxygen blood saturation, HbO2 and RHb

refer to oxyhemoglobin and deoxyhemoglobin,

respectively. Absorption coefficients for

oxyhemoglobin- and deoxyhemoglobin are well

known (Prahl, 2002). Blood typically occupies

around 0.2-0.6% of the physical volume of the

dermis (Lister, 2012). However, other groups report

much higher values: up to 7% (Jacques, 1996).

2.5.2 Scattering

The reduced scattering coefficient for dermis and

epidermis also follows a power law (Mourant,

1998):

−

∝

, with k=1.3. Therefore, we can

set a reference value at a particular wavelength and

simulate its dependence on the wavelength with this

power law. In particular, we can assign values at

633nm (Meglinski, 2002) for the living epidermis

(

=9mm

-1

) and reticular dermis (

=5mm

-1

), which

represent the bulk of the tissue in healthy epidermis

and dermis, respectively. However, for callus

assessment, we can expect that the bulk of the callus

is similar to the stratum corneum (

=14mm

-1

Thus, we can write

41.3

'6.110

−

=×

and

41.3

'2.210

−

=×

, respectively.

2.5.3 Index of Refraction

The index of refraction measurements in the human

skin was summarized in (Bashkatov, 2011). The

measurements in the visible spectrum range give

their values from 1.433 to 1.449 for the epidermis

(Ding, 2006). In particular, we can set 1.448, 1.447,

and 1.433 for 442, 532, and 633nm, respectively.

The dermis contains more water. Thus, its index of

refraction is slightly (typically by 0.01-0.05 (Ding,

2006)) less, which will result in almost negligible

scattering on the dermis/epidermis interface (<<1%).

Thus, we will ignore this difference and set n

2.5.4 Noise

To make our synthetic spectrum more realistic, we

have added noise to the simulated spectra. If we

consider a consumer-grade camera with an 8-bit

Callus Thickness Determination Adjuvant to Tissue Oximetry Imaging

149

depth, we can estimate that the measurement's

experimental error for this camera is

1/ (2 1) 0.004−≈

. Based on these assumptions, the

realistic noise is

=0.001. However, we have added

Gaussian noise with

=0 and

=0.004.

2.6 Test Scenarios

Four optical parameters (

) can

characterize the two-layer K-M model. These

parameters can be further described by five tissue

parameters: power-law values for (

blood concentration c, and blood oxygenation, SO2.

The most uncertain parameters in the experiment

are the scattering coefficient of the epithelium

(

=9mm

-1

or 14mm

-1

for living epidermis and

stratum corneum, respectively), blood concentration

in the dermis, c (0.2-7%), and blood oxygen

saturation, SO2 (60-99%).

We will keep other parameters (

) fixed:

7 3.255

7.84 10

μλ

−

=×

and

41.3

'2.210

−

=×

respectively.

2.6.1 Seed Parameters

We have seeded the algorithm with the following

parameters: scattering coefficient of the epithelium'

=14mm

-1

(stratum corneum), blood concentration

in the dermis, c =3%, and blood oxygen saturation

SO2=80%.

2.6.2 Test Parameters

We have selected the following values to evaluate

the model: the scattering coefficient of the

epithelium

=9mm

-1

and 14mm

-1

. Blood

concentration: 0.2%, 3%, and 7%. Oxygen

saturation: 60%, 80%, and 99%.

The epithelium's thickness, L

was 100, 200,

400, 600, 800, 1000, 1500μm.

3 RESULTS

We have performed a numerical evaluation of the

proposed algorithm. For these purposes, we

generated the reflectance spectrum using the two-

layer model (Eq.1), added noise and reconstructed

the thickness L

using steps 2-7.

We sampled reflectance at 470, 540, and 630 nm

to measure epidermal thickness, processed them

using the algorithm, extracted L

for each

wavelength, and averaged them to get a single value

. To calculate statistical values (mean and standard

deviation), we repeated them five times for each

thickness for each parameter set.

3.1 Dependence on Oxygenation

The dependence of the extracted thickness as a

function of the actual thickness for various blood

oxygenations (60, 80, 99%) is depicted in Fig. 1.

Other test parameters were as following

scattering coefficient of the epithelium 14mm

-1

blood concentration: 3%.

It can be seen that the oxygenation barely

impacts the results.

Figure 1: The extracted thickness as a function of the actual

thickness for various SO2 (60 (green triangle), 80 (red

square), and 99 (blue rhomb) %).

=14mm

-1

, c= 3%.

3.2 Dependence on Blood Content

The dependence of the extracted thickness as a

function of the actual thickness for various blood

concentrations (0.2, 3.0, and 7.0 %) is depicted in

Figure 2: The extracted thickness as a function of the

actual thickness for various blood concentrations (0.2

(blue rhomb), 3.0 (red square), and 7.0 (green triangle) %).

=14mm

-1

, SO2= 80%.

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Fig. 2. Other test parameters were as following

scattering coefficient of the epithelium 14mm

-1

blood oxygenation: 80%.

3.3 Dependence on Scattering

Coefficient

The dependence of the extracted thickness as a

function of the actual thickness for various scattering

coefficients of the epithelium (14mm

-1

and 9mm

-1

) is

depicted in Fig. 3.

Other test parameters were as following

blood concentration: 3%., blood oxygenation: 80%.

Figure 3: The dependence of the extracted thickness as a

function of the actual thickness for various scattering

coefficients of the epithelium (14mm

-1

(blue rhomb) and

9mm

-1

(red square)). c=3%, SO2= 80%.).

3.4 Maximal Detected Thickness

To detect the maximal thickness, which can be

identified by our method, we have performed

emulation of reflectance spectra for tissues with

maximal blood content (7%). In this case, we can

expect that the impact of the underlying layer will be

maximal.

Figure 4: The dependence of the extracted thickness as a

function of the actual thickness for maximal blood

concentrations (c= 7.0 %).

=14mm

-1

, SO2= 80%.

The dependence of the extracted thickness as a

function of the actual thickness for maximal blood

concentrations (c= 7.0 %) is depicted in Fig. 4.

Other test parameters were as following: scattering

coefficient of the epithelium 14mm

-1

, blood

oxygenation: 80%.

4 DISCUSSION

We have found that the model reasonably well

extracts epidermal thickness L for the range of

thicknesses 0.1-1.5mm. Beyond that, the reflectance

signal does not bring information about underlying

layers. In this case, the epidermis can be viewed as a

semi-infinite layer.

We have found that SO2 barely impacts results.

So, in realistic scenarios, it can be ignored.

Blood content slightly impacts results.

Underestimation of the blood content pushes the

graph up (overestimates the thickness slightly).

Overestimation of the blood content pulls the curve

down (underestimate the thickness slightly).

However, its effect for L>0.4mm is relatively small

and can be discarded for estimation purposes. For

L<0.3mm, the error can be >40%. However, it

should be noted that our lower case scenario (0.2%)

is significantly smaller than our seed value (3%). In

realistic settings, it could be expected that the seed

value could be selected closer to actual values, so its

effect can be ignored.

The most significant factor, which impacts

estimation, is the scattering coefficient of the

epidermis. 30% error in evaluating the scattering

coefficient (9mm

-1

instead of 14mm

-1

) leads to a

significant underestimation of the thickness. It

should be noted that for 0.1-0.8mm thickness, it can

be corrected using the optical path:

1_ 1_

actual s actual perceived s seed

μμ

≈

However, in

realistic conditions, one can expect that the callus

consists of dead cells primarily, so it should not be

an issue. However, this strong dependence

underscores the importance of using realistic

numbers.

The obtained maximal detection depth

estimation agrees with the assessment of maximal

defect detection depth developed in (Saiko, 2021)

and elaborated in (Saiko, 2022a).

Speaking of the extension of the model to other

scenarios, it should be mentioned that we excluded

melanin from our model (see Section 2.3 for details).

In most other cases it cannot be ignored. If

Callus Thickness Determination Adjuvant to Tissue Oximetry Imaging

151

necessary, the melanin can be accounted for by a

quasi-two layer model (Saiko, 2022b).

In the future, we plan to validate this approach in

phantom experiments.

5 CONCLUSIONS

We have proposed an approach for optical callus

thickness determination. Numerical simulations

show that it can accurately detect epidermis

thickness up to 1.5mm. Due to its computational

simplicity, it can be easily implemented in image

processing algorithms for multispectral and

hyperspectral imaging systems

REFERENCES

Yudovsky D, Pilon L, 2010, Rapid and accurate

estimation of blood saturation, melanin content, and

epidermis thickness from spectral diffuse reflectance.,

Appl Opt. 49(10):1707-19.

Saiko G, Douplik A, 2012, Real-Time Optical Monitoring

of Capillary Grid Spatial Pattern in Epithelium by

Spatially Resolved Diffuse Reflectance Probe, J.

Innov. Opt. Health Scie. 05 (02): 1250005.

Saiko G, Pandya A, Schelkanova I, Sturmer M, Beckert

RJ, Douplik A, 2014, Optical Detection of a Capillary

Grid Spatial Pattern in Epithelium by Spatially

Resolved Diffuse Reflectance Probe: Monte Carlo

Verification, IEEE J Sel. Top. Quant Electronics,

20(2): 7000609

Yudovsky D, Pilon L, 2009, Simple and accurate

expressions for diffuse reflectance of semi-infinite and

two-layer absorbing and scattering media. Appl Opt.;

48(35):6670-83.

Saunderson JL, 1942, Calculation of the color of

pigmented plastics, J Opt Soc Amer, 32(12):727–736.

Van Gemert MJC, Star WM, 1987, Relations between the

Kubelka-Munk and the transport equation models for

anisotropic scattering, Lasers Life Scie, 1(98): 287–

298.

Jacques SL, Origins of tissue optical properties in the

UVA, visible, and NIR regions, in Advances in

Optical Imaging and Photon Migration, R. R. Alfano

and J. G. Fujimoto, eds. (Optical Society of America,

1996), Vol. 2, pp. 364–370

Prahl S, Optical absorption of hemoglobin, World Wide

Web: http://omlc.ogi.edu/spectra/hemoglobin/

hemestruct/ index.html, 2002.

Lister T, Wright PA, Chappell PH, 2012, Optical

properties of human skin, JBO 17(9): 090901

Mourant JR, Freyer JP, Hielscher AH, Eick AA, Shen D,

Johnson TM, 1998, Mechanisms of light scattering

from biological cells relevant to noninvasive optical-

tissue diagnostics, Appl Opt, 37(16): 3586–3593.

Meglinski IV, Matcher SJ, 2002, Quantitative assessment

of skin layers absorption and skin reflectance spectra

simulation in the visible and near-infrared spectral

regions, Physiol. Meas. 23, 741-753.

Bashkatov AN, Genina EA, Tuchin VN, 2011, Optical

properties of skin, subcutaneous, and muscle tissues:

A review, J. Innov Opt Health Scie 4(1): 9-38.

Ding H, Lu JQ, Wooden WA, Kragel PJ, Hu X-H, 2006,

Refractive indices of human skin tissues at eight

wavelengths and estimated dispersion relations

between 300 and 1600 nm, Phys. Med. Biol. 51, 1479-

1489.

Saiko G, Douplik A, Contrast Ratio during Visualization

of Subsurface Optical Inhomogeneities in Turbid

Tissues: Perturbation Analysis. In Proc of the 14th Int

Joint Conf on Biomed Eng Systems and Technologies

(BIOSTEC 2021) - v 2: BIOIMAGING, 94-102, DOI:

10.5220/0010374100940102

Saiko G, Douplik A, Visibility of capillaries in turbid

tissues: an analytical approach, SN Comp. Scie

(submitted)

Saiko G, Improved optical tissue model for tissue

oximetry imaging applications, Adv Exp Med Biol

(submitted)

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