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1 November 2008 Crosstalk and error analysis of fat layer on continuous wave near-infrared spectroscopy measurements
Author Affiliations +
Abstract
Accurate estimation of concentration changes in muscles by continuous wave near-IR spectroscopy for muscle measurements suffers from underestimation and crosstalk problems due to the presence of superficial skin and fat layers. Underestimation error is basically caused by a homogeneous medium assumption in the calculations leading to the partial volume effect. The homogeneous medium assumption and wavelength dependence of mean partial path length in the muscle layer cause the crosstalk. We investigate underestimation errors and crosstalk by Monte Carlo simulations with a three layered (skin-fat-muscle) tissue model for a two-wavelength system where the choice of first wavelength is in the 675- to 775-nm range and the second wavelength is in the 825- to 900-nm range. Means of absolute underestimation errors and crosstalk over the considered wavelength pairs are found to be higher for greater fat thicknesses. Estimation errors of concentration changes for Hb and HbO2 are calculated to be close for an ischemia type protocol where both Hb and HbO2 are assumed to have equal magnitude but opposite concentration changes. The minimum estimation errors are found for the 700/825- and 725/825-nm pairs for this protocol.

1.

Introduction

Near infrared spectroscopy (NIRS) is increasingly used as an optical noninvasive method to monitor the changes in tissue oxygenation in brain,1, 2, 3 breast,4 and particularly in muscle tissues.5, 6, 7 Continuous wave near-infrared spectroscopy (cw-NIRS) is based on a steady state technique where the changes in the detected light intensities at multiple wavelengths are converted to concentration changes of oxygenation sensitive chromophores. Typically, cw-NIRS is used in muscle physiology studies to calculate oxygen consumption and blood flow values. Spatially resolved spectroscopy8 along with frequency and time domain techniques are other NIRS methods9, 10 that have the capability of quantifying absolute concentrations.

NIRS techniques suffer inaccuracies for the heterogonous tissue structures when the homogeneous medium assumption is made for the sake of simplicity.11, 12 In fact, there are solutions based on complex layered models 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 for NIRS. The degree of inaccuracy because of the homogeneous medium assumption depends on the region of interest, geometry, optical coefficients of the structures in the tissue, source-detector distance, and the choice of NIRS technique. 11, 12, 14, 21, 22, 23, 24, 25, 26, 27 Hence, the estimated parameter (i.e., absorption coefficient change) could be related to a layer’s (or to combination of layers) property, or it may not be related to any property of any one of those layers at all.12, 14, 28

Muscle tissue has superficial skin and fat layers. A Fat layer has varying thicknesses between subjects and has a lower absorption coefficient than the underlying muscle layer, masking the muscle’s optical parameters, hence making it difficult to determine the optical coefficients and quantify concentration changes in the lower muscle layer. It has been shown experimentally that adipose tissue causes sensitivity and linearity problems, 25, 29, 30, 31, 32, 33, 34, 35 underestimation of oxygen consumption36 in muscle cw-NIRS measurements in which modified Beer-Lambert law (MBLL) with a homogeneous medium assumption is used. These problems are mainly related to the so-called partial volume effect, which refers to the fact that hemodynamic changes occur in a volume smaller than that assumed by homogeneous medium assumption.23, 24, 37

Crosstalk in NIRS measurements refers to the measurement of chromophore concentration change although no real change happens for that chromophore but for other chromophores’ concentrations.23, 24, 38, 39, 40, 41 This is caused again by the homogeneous medium assumption with the use of mean optical path length instead of wavelength-dependent partial optical path length in the tissue layer of interest where the concentration changes occur (i.e., muscle or gray matter in the brain). There are detailed studies on the analysis of the crosstalk effect for brain measurements, while as we know, there is only one study of Iwasaka and Okada42 on the crosstalk effect for muscle measurements, where the analysis was done for a fixed fat thickness of 4mm .

The effect of adipose tissue layer on cw-NIRS measurements with the homogeneous medium assumption using MBLL is investigated in our study by Monte Carlo simulations for a two-wavelength system. Simulations were performed for a homogeneous layered skin-fat-muscle heterogeneous tissue model with varying fat thickness up to 15mm . The wavelengths are in 675-to775-nm range for the first wavelength and in 825-to900-nm range for the second wavelength, and in total 24 wavelength pairs were used. For the considered wavelengths and fat thicknesses, mean partial path lengths in the three layers and detected light intensities were found. An error analysis for estimated concentration changes was analyzed by partitioning the error into an underestimation term for a real change in muscle layer and a crosstalk term, where the aims are the investigation of the fat layer thickness effect and a search for wavelength pairs that result in low errors. An error analysis for a particular measurement protocol of vascular occlusion is also discussed.

2.

Theory

2.1.

Homogeneous Medium Assumption

The cw-NIRS technique relies on the MBLL to convert detected light intensity changes into concentration changes of chromophores. For a single light absorber in a homogeneous medium, light attenuation is given by1

Eq. 1

ODλ=ln(IoI)=ϵλcDPFλr+Gλ,
where superscript λ indicates a particular wavelength, ODλ is optical density, Io is the intensity of the light sent into the tissue, I is the intensity of the detected light, ϵλ and c are the specific absorption coefficient (OD/cm mM1 ) and concentration (millimolar) of the chromophore in the medium, respectively; r (in centimeters) is the minimal geometric distance between light source and detector, and DPFλ is the differential path length factor. DPFλ equals mean optical path length of the photons (Lλ) divided by r . Also, the Gλ factor is due to medium geometry and light scattering. The absorption coefficient of the medium μaλ is equal to ϵλc . The change in the logarithm of detected light intensity (ΔODλ) is proportional to concentration change of the absorber ( Δc , assumed to be homogeneous and small), given by ΔODλ=ϵλΔcLλ , a differential form of the MBLL. Here it is assumed that Gλ and Lλ do not change during measurement. This formula and Eq. 1 of MBLL neglect the variation of Lλ with μaλ . In fact, Lλ should be replaced by its mean value computed over the range of absorption coefficient43 from 0 to μaλ . Nevertheless, MBLL formulation can still be used to determine concentration changes for small absorption changes for which Lλ remains nearly constant.22, 43, 44 Light scattering change is another issue.44

For tissues where the main light absorbers are Hb and HbO2 ,

Eq. 2

ΔODλ=(ϵHbλΔ[Hb]+ϵHbO2λΔ[HbO2])DPFλr,
assuming a homogeneous tissue medium. For a two-wavelength cw-NIRS system, concentration changes are estimated using MBLL as follows;

Eq. 3

Δ[Hb]MBLL=(ϵHbO2λ2ΔODλ1(DPF)λ1)(ϵHbO2λ1ΔODλ2(DPF)λ2)r(ϵHbO2λ2ϵHbλ1ϵHbO2λ1ϵHbλ2),

Eq. 4

Δ[HbO2]MBLL=(ϵHbλ1ΔODλ2(DPF)λ2)(ϵHbλ2ΔODλ1(DPF)λ1)r(ϵHbO2λ2ϵHbλ1ϵHbO2λ1ϵHbλ2).
The MBLL subscript indicates that estimated concentration changes are found using a homogeneous-medium-assumption-based MBLL formulation. In general, a wavelength-independent DPF is used in the MBLL calculations.

Note that for the considered muscle measurements, [Hb] ([HbO2]) refers to combined concentrations of deoxyhemoglobin and deoxymyoglobin (oxyhemoglobin and oxymyoglobin) since hemoglobin and myoglobin have very similar absorption spectra.45

2.2.

Underestimation Error and Crosstalk

For muscle cw-NIRS measurements, a more realistic tissue model should contain skin, fat, and muscle tissue layers. Measured optical density change can be written as22

Eq. 5

ΔODλ=Δμa,sLsλ+Δμa,fLfλ+Δμa,mLmλ,
where Lsλ , Lfλ , and Lmλ are the mean partial path lengths of the detected light and Δμa,s , Δμa,f , Δμa,m are the homogeneous absorption changes in the skin, fat, and muscle layers, respectively. Assuming that the concentration changes mainly occur in the muscle layer, Eq. 5 becomes

Eq. 6

ΔODλ(ϵHbλΔ[Hb]m+ϵHbO2λΔ[HbO2]m)Lmλ,
where Δ[Hb]m and Δ[HbO2]m are the real concentration changes in the muscle layer. Substituting Eq. 6 for measured optical density changes ΔODλ in Eqs. 3, 4, the estimated concentration changes using MBLL can be written as24

Eq. 7

Δ[X]MBLL=UXΔ[X]m+CXΔ[O]m
where X represents the chromophore being either Hb or HbO2 and O represents the other chromophore, HbO2 or Hb, Δ[X]m and Δ[O]m are the real concentration changes in the muscle layer, UX corresponds to the underestimation of Δ[X]m , and CX represents crosstalk from other chromophore Δ[O]m to estimated Δ[X]MBLL , given by

Eq. 8

UHb=ϵHbλ1ϵHbO2λ2lλ1ϵHbλ2ϵHbO2λ1lλ2ϵHbλ1ϵHbO2λ2ϵHbλ2ϵHbO2λ1,

Eq. 9

UHbO2=ϵHbλ1ϵHbO2λ2lλ2ϵHbλ2ϵHbO2λ1lλ1ϵHbλ1ϵHbO2λ2ϵHbλ2ϵHbO2λ1,

Eq. 10

CHb=ϵHbO2λ1ϵHbO2λ2ϵHbλ1ϵHbO2λ2ϵHbλ2ϵHbO2λ1(lλ1lλ2),

Eq. 11

CHbO2=ϵHbλ1ϵHbλ2ϵHbλ1ϵHbO2λ2ϵHbλ2ϵHbO2λ1(lλ2lλ1),
where lλ=Lmλ(DPFλ×r) . For a theoretical case of zero skin and fat thicknesses, mean optical path length Lλ will be equal to Lmλ , which can be accurately measured by time or frequency domain NIRS systems. Hence, this value can be used to find DPFλ factor, i.e., DPFλ1=Lmλ1r and DPFλ2=Lmλ2r . Underestimation terms UHb and UHbO2 then have ideal values of 1 because both lλ1 and lλ2 are equal to one. Crosstalk terms CHb and CHbO2 are null since lλ1 and lλ2 would be one, making their difference zero. However, in practice, there are these superficial layers and measurement of Lmλ alone is not possible. Magnitudes of crosstalk terms CHb and CHbO2 are proportional to the difference of lλ1lλ2 . For the use of wavelength independent DPF, CHb and CHbO2 are zero when Lmλ1=Lmλ2 . Hence, one of the ways to minimize crosstalk is to utilize a wavelength pair for which partial optical path length in the layer of interest (i.e., gray matter in the brain) are equal.46 In summary, the magnitude of underestimation and crosstalk terms depend on the wavelength dependence of specific absorption coefficients, choice of DPFλ factors, which are used instead of unavailable Lmλr .

A common definition for crosstalk is the ratio of the estimated concentration change of the chromophore X for which no change happens to the estimated concentration change of the chromophore O for which real change is induced,40, 46 denoted as COX . According to this definition and previous formulation, CHbO2Hb and CHbHbO2 are

12.

Eq. 12a

CHbO2Hb(%)=100×CHbUHbO2,

Eq. 12b

CHbHbO2(%)=100×CHbO2UHb.
In this study, underestimation error (in percent) refers to (1UX)×100 for the corresponding UX factor. For the crosstalk, formulas given in Eqs. 12a, 12b are used. The estimation error for the concentration change of chromophore X in the muscle layer using MBLL is given by

Eq. 13

EMBLL=100×(Δ[X]MBLLΔ[X]m)Δ[X]m%.
In this analysis, small concentration changes are assumed so that partial path length in the muscle layer remains constant such that calculated UX and CX terms along with underestimation and crosstalk errors are constant values for specific wavelength pair and fat thickness.

3.

Methods

3.1.

Tissue Model

For the simulations, three homogeneously layered skin-fat-muscle heterogeneous model is used. Skin thickness is taken to be 1.4mm and muscle thickness is infinite. Reduced scattering coefficients of the three tissues and absorption coefficients of skin and adipose tissues are taken from Simpson 47 For the muscle tissue, the absorption coefficient is calculated with the equation

Eq. 14

μa,mλ=μa,wλVw+[tHb][ϵHbO2λStO2+ϵHbλ(1StO2)]+μa,b,
where μa,wλ is the water absorption coefficient, Vw is water fraction of muscle tissue, [tHb] is total hemoglobin concentration, StO2 is oxygen saturation, and μa,b is background absorption. In the calculation, Vw , StO2 , and [tHb] are taken as 70%, 70%, and 100μM , respectively, as typical values.48, 49 The μa,wλ values are taken from the study of Hollis.50 The background absorption coefficient of muscle tissue μa,b is taken as 0.072cm1 so that the calculated μa,m798nm equals the experimentally found in vitro value of Simpson 47 since absorption at this isobestic point is unaffected by the oxygen saturation of the hemoglobin. Table 1 lists the absorption and reduced scattering coefficients of the three layers used in the simulations.

Table 1

Optical properties of the skin, fat and muscle tissue layers used in the simulations (for log base e ).

λ (nm) μa (cm−1) μs′ (cm−1)
SkinFatMuscleSkinFatMuscle
6750.2320.0970.32124.8112.248.53
7000.1910.0890.25423.1712.038.08
7250.1720.0890.24321.9911.877.89
7500.1650.0920.28820.9711.677.69
7600.1590.0930.30620.5311.617.50
7750.1460.0870.29119.9111.507.21
8000.1270.0830.28419.0711.366.99
8250.1210.0850.30918.2411.126.78
8500.1220.0860.34317.5711.096.60
8750.1220.0910.36816.9810.976.43
9000.1340.1250.39316.3010.886.32

3.2.

Monte Carlo Simulations

In a Monte Carlo simulation of photon propagation in biological tissues, a stochastic model was constructed in which rules of photon propagation were modeled in the form of probability distributions.51 In the simulation, photons were launched with initial direction along z axis (the axis perpendicular to tissue layers) from a point source. For a photon traveling in layer i , which has absorption coefficient μa,i , scattering coefficient μs,i , and reduced scattering coefficient μs,i [which is equal to (1g)μs,i , where g is the mean cosine of the single scattering phase function and is called anisotropy factor], successive scattering distances are selected using a random variable l=ln(R)μs,i , with R having a uniform distribution over (0,1]. The remaining scattering length Δli for photons crossing tissue boundary from medium i to medium j is recalculated by Δlj=Δliμs,iμs,j . Isotropic scattering is utilized using principle of similarity.52 Scatter azimuthal angle was uniformly distributed over the interval [0,2π) . Fresnel formulas are used for reflection or transmission at the boundaries.51

Total distance traveled in layer i by a photon (Li) was found by summing scattering lengths taken in this layer. Photon propagation was continued until it escapes the medium or travels 220cm in length (10ns) . For those reaching the surface, exit (survival) weight (w) is calculated using Lambert-Beer law as w=w0exp[i(Liμa,i)] , with w0 accounting for reflections and refractions at the boundaries encountered by the particular photon when there are refractive index mismatches.22 Because of the symmetry of the medium considered, photons reaching a ring (thickness is dr , distance from center of ring to the light source is r ) were taken as the photons reaching the detector. The mean partial path length in medium i (Li) for the detected photons was found using the formula Li=j=1NLi,jwj(j=1Nwj) , where Li,j is the total path length taken in medium i by detected photon j with weight wj , and N is total number of detected photons. Refractive indices of air and tissue layers were taken to be 1 and 1.4, respectively.53 Each simulation was performed using 5×107 photons and the dr thickness is taken to be 0.5cm .

4.

Results

4.1.

Path Lengths and Detected Light Intensity

We performed Monte Carlo simulations to calculate the mean partial path lengths for the 11 distinct wavelengths given in Table 1. Note that Li,r,hfλ represents the mean partial path length in layer i ( s , f , or m for skin, fat, and muscle, respectively, as used in Sec. 2.2), for a source-detector distance r (in centimeters), at fat thickness hf (in millimeters) and wavelength λ . Also Li,r,hf denotes the mean±standard deviation of the mean partial path length in layer i computed over all wavelengths.

The term Lmλ is the most important variable affecting the underestimation error and crosstalk, as shown in Fig. 1 . The value of Lm,3.0,hfλ decreased linearly with a higher slope for 0hf7mm , while the slope decreased for hf> 7mm . The value of Lm,3.0,0 is 11.5±1.20cm and that of Lm,3.0,7 is 2.35±0.43cm . Above 10mm of fat thickness, Lm,3.0,hfλ decreased much more slowly but eventually approached null, where Lm,3.0,15=0.20±0.04cm . It was possible to infer a considerable wavelength-dependent variability in Lm,3.0,hfλ . The value of Lm,3.0,hfλ was found to increase from 675to725nm , while it had a decreasing trend from the 725-to900-nm range. This finding can be explained by the wavelength dependence of the optical properties of muscle and fat tissues given in Table 1. The coefficient of variation ( CV=standard deviation/mean) of Lm,3.0,hfλ values over 11 wavelengths increased from 11% at hf=0mm to 23% at hf=15mm .

Fig. 1

Mean partial path length in the muscle layer for various wavelengths in the range 675to900nm and fat thicknesses up to 15mm estimated by Monte Carlo simulations (r=3.0cm) .

064019_1_016806jbo1.jpg

The value of Ls,3.0,hfλ was found to be the least varying mean partial path length with respect to hf variation with values ranging from 1.78to2.39cm having a maximum at around hf=6to7mm for all considered wavelengths. In contrast to Lmλ,r,hf , Lf,r,hfλ and mean path length increased with increasing hf as expected. The value of Lf,3.0,hf ranged from 1.84±0.13cm at a 1-mm fat thickness to 21.77±1.24cm at hf=15mm , while the mean path length ranged from 13.03±1.26cm at hf=0mm to 24.17±1.30cm at hf=15mm . The mean path length had a decreasing trend with local peaks at either 700 or 725nm and either 775 or 800nm .

An increase in the fat layer thickness caused an increase in the detected light intensity. These increases in the detected light intensities for the 11 wavelengths expressed as mean±standard deviation were 74±28 , 272±97 , and 537±184% at hf=4 , 8, and 15mm , respectively, with respect to detected intensities at hf=0mm (r=3.0cm) .

With increase in source-detector distance, Lmλ and mean path length increased, while detected light intensity decreased. In particular, Lm,4.0,0=15.31±1.65cm , and Lm,4.0,7=4.31±0.75cm .

4.2.

Underestimation Error

Underestimation errors were calculated for a two-wavelength cw-NIRS system under varying fat thicknesses. The two wavelengths were chosen to fall before and after the isobestic point at around 800nm . Hence, there were 24 wavelength pairs λ1λ2 , where λ1 is between 675 and 775nm and λ2 is between 825 and 900nm . DPF was taken to be wavelength independent with a value of 4.37 found for hf=0 and λ=800nm . Underestimation error for the pair λ1λ2 is denoted by EX,r,hfλ1,λ2 , where the first subscript refers to the chromophore, the second and (if present) third subscripts refer to source-detector distance (in centimeters), and the hf value (in millimeters), respectively. For the all considered λ1λ2 pairs, EX,r,hf showed mean±standard deviation of the absolute values of the underestimation errors EX,r,hfλ1,λ2 .

Figures 2a and 2b show EHb,3.0,hf and EHbO2,3.0,hf along with minimum errors for EHb,3.0,hfλ1,λ2 and EHbO2,r,hfλ1,λ2 . The 725900-nm pair gives the minimum values for EHb,3.0,hfλ1,λ2 except at hf=0mm , for which the 700825-nm pair gives the minimum error. The 675825-nm pair gives the minimum error for EHbO2,r,hfλ1,λ2 from hf=0mm up to and including 10mm , and at higher hf values, the 760825-nm pair is the minimum error producing pair. Both the errors EHb,3.0,hf and EHbO2,3.0,hf exhibited a steep increase in the fat thickness range <5mm and a decreasing slope beyond this value. Interestingly, EHb,3.0,hf began at a lower value compared to EHbO2,3.0,hf but had a larger slope in this range. As expected, EHb,3.0,hf and EHbO2,3.0,hf approached a complete underestimation error (100%) at hf=15mm . For the no-fat-thickness case, EHb,3.0,0 was 6.1±3.5% and EHbO2,3.0,0 was 28.9±5.8% . The slopes of the least-squares fits to the absolute values of underestimation errors in hf=0to5mm range were 11.5%mm (R2=0.94) for EHb,3.0λ1,λ2 and 9.1%mm (R2=0.91) for EHbO2,3.0λ1,λ2 .

Fig. 2

Plots of (a) EHb,3.0 (%) and (b) EHbO2,3.0 (%), which are the mean±standard deviation of absolute respective underestimation errors computed over all considered λ1λ2 pairs for fat thicknesses up to 15mm . Minimum individual errors for EHb,3.0,hfλ1,λ2 and EHbO2,3.0,hfλ1,λ2 are shown as stars.

064019_1_016806jbo2.jpg

There is wavelength pair dependency in the underestimation errors. The value of EHb,3.0λ1,λ2 decreased in magnitude for an increase in λ2 , while that of EHbO2,3.0λ1,λ2 increased, for fixed λ1 at a given hf . This change of variation over λ2 was higher for EHbO2,3.0λ1,λ2 . The variation of λ1 —for fixed λ2 at a given hf —led to a high range of change for EHb,3.0λ1,λ2 , where 700 and 725nm lead to lower errors. Underestimation errors for hf=2mm are given in Table 2 to show wavelength pair effect. The wavelength pair dependency of underestimation errors decreasd with hf increase. CV values of absolute underestimation errors were 56.5% (20.0%) at hf=0mm and 0.3% (0.4%) at hf=15mm for EHb,3.0λ1,λ2 (EHbO2,3.0λ1,λ2) over the considered λ1λ2 pairs.

Table 2

Underestimation errors EHb,3.0,2λ1,λ2 (in percentages) and EHbO2,3.0,2λ1,λ2 (in percentages) for the considered λ1∕λ2 pairs.

λ1 (nm)675700725750760775
λ2 (nm)
82532.421.618.028.732.429.2
EHb,3.0,2λ1,λ2 (%)85032.021.217.427.631.126.9
87531.820.916.826.830.225.4
90031.620.516.126.029.423.9
82536.538.140.438.237.239.2
EHbO2,3.0,2λ1,λ2 (%)85041.443.045.643.943.146.0
87544.746.449.247.747.050.5
90047.149.052.150.850.154.3

For longer source-detector distance of 4.0cm , errors are lower. Here, EHb,4.0,0 and EHbO2,4.0,0 were 5.7±2.3 and 26.7±5.7% , respectively. The slopes of the least-squares fits in the 0to5-mm fat thickness range are 9.9%mm (R2=0.89) for EHb,4.0λ1,λ2 and 8.0%mm (R2=0.88) for EHbO2,4.0λ1,λ2 . Again above hf=10mm , EHb,4.0 (EHbO2,4.0) became very high, with values above 87.3±2.3% (92.1±1.5%) .

4.3.

Crosstalk Analysis

Crosstalk was calculated using Eqs. 12a, 12b for the two-wavelength system represented by COX,r,(hf)λ1,λ2 , where the superscripts refer to particular wavelength pair and first, second, and third (if present) subscripts represent crosstalk type, source-detector distance (in centimeters), and hf value (millimeters), respectively. Crosstalk was computed for the same λ1λ2 pairs in underestimation error computations. DPF was assumed to be taken as wavelength independent, for which case crosstalk defined by Eq. 12 resulted in DPF independence. Not that COX,r,(hf) represents mean±standard deviation of absolute values of crosstalk COX,r,(hf)λ1,λ2 for the all λ1λ2 pairs.

In general, CHbO2Hb,3.0λ1,λ2 had positive values, while CHbHbO2,3.0λ1,λ2 had negative values. The minimum-error-producing pairs for CHbO2Hb3.0λ1,λ2 were the 675825-nm pair at hf=0mm up to including 5mm, the 760825-nm pair at hf=6 ,7, and 9mm ; and the 675850-nm pair at other hf values. Also CHbHbO2,3.0λ1,λ2 had the minimum errors for the 760825-nm pair at hf=0 ,1,2,4,5,6,7,8,9, and 10mm , for the 675825-nm pair at hf=3mm ; for the 675850-nm pair at hf=11 ,12,13, and 14mm ; and for the 750825-nm pair at hf=15mm . The values CHbO2Hb,3.0 (about 9.5%) and CHbHbO2,3.0 (about 14.2%) were nearly constant in the hf=0to3-mm range, as shown in Fig. 3 While in the hf=3-to14-mm CHbO2Hb,3.0 increased up to 25.0±34.9% , CHbHbO2,3.0 showed an increasing trend in the hf=3to10-mm range, with CHbHbO2,3.0,10=20.3±10.2% . The slopes of the least-squares fits in these respective hf ranges to the absolute crosstalk values were 1.4%mm (R2=0.1) for CHbO2Hb,3.0λ1,λ2 and 0.9%/mm (R2=0.1) for CHbHbO2,3.0λ1,λ2 .

Fig. 3

Plots of (a) CHbHbO2,3.0,hf (%) and (b) CHbO2Hb,3.0,hf (%), which are the mean±standard deviation of absolute respective crosstalk computed over all considered λ1λ2 pairs for fat thicknesses up to 15mm . Minimum individual errors for CHbHbO2,3.0,hfλ1,λ2 and CHbO2Hb,3.0,hfλ1,λ2 are shown as stars.

064019_1_016806jbo3.jpg

In Table 3 , crosstalk values are given for hf=-0 -, 5-, 10-, and 15-mm values for all wavelength pairs. Similar to the increase seen in the mean values the standard deviations of absolute crosstalk over considered wavelength pairs showed dramatic increases as the fat thickened. The CHbO2Hb,3.0λ1,λ2 had CV values of 64.9, 82.3, and 159.2% at hf values of 0, 5, and 15mm , respectively. The CHbHbO2,3.0λ1,λ2 had lower CV values of 31.0, 47.0, and 57.6% at hf=0 , 5, and 15mm . However, CHbHbO2,3.0λ1,λ2 had higher magnitudes in general. Examining the results from Table 3, we can observe that both absolute values of crosstalk are less than 11% for pairs 675825 , 675850 , 675875 , 750825 , 760825 , 760850 , and 775825nm for hf<10mm . In addition to these pairs, CHbO2Hb,3.0,hfλ1,λ2 had low crosstalk values also for pairs 675900 , and 700825nm . Higher crosstalk magnitudes where computed for the choice of a higher λ2 for a fixed λ1 at a given hf .

Table 3

Crosstalk values CHb→HbO2,3.0,hfλ1,λ2 (in percentages) and CHbO2→Hb,3.0,hfλ1,λ2 (in percentages) for different λ1∕λ2 pairs and hf=0 , 5, 10, and 15mm .

Fat thickness λ1 (nm) CHb→HbO2,3.0,hfλ1,λ2 (%) CHbO2→Hb,3.0,hfλ1,λ2 (%)
675700725750760775675700725750760775
λ2 (nm)
825 7.8 14.3 16.2 9.1 5.1 7.9 1.34.28.85.02.66.8
0mm 850 10.8 16.2 17.9 12.3 9.2 12.1 2.25.711.98.46.013.3
875 13.1 18.0 19.7 14.8 12.1 15.0 2.97.014.511.28.718.9
900 15.7 20.6 22.4 17.8 15.1 18.5 3.68.317.414.211.625.3
8254.1 16.3 20.9 7.6 2.4 9.1 0.6 4.912.74.11.28.1
5mm 850 4.0 20.0 23.8 14.1 10.3 16.3 0.77.718.89.96.820.3
875 8.7 22.9 26.4 18.1 14.9 20.5 1.810.124.114.911.531.1
900 12.0 25.7 29.3 21.4 18.4 24.3 2.611.928.819.115.441.3
82510.3 18.2 24.5 5.9 2.4 9.6 1.3 5.716.23.0 1.1 8.7
10mm 850 3.0 24.1 29.0 16.3 10.9 20.4 0.510.427.112.27.329.0
875 9.6 27.8 32.1 21.6 17.2 25.6 2.014.136.619.914.247.8
900 18.3 34.0 38.0 29.4 25.9 33.6 4.520.956.334.827.493.6
82517.7 15.1 21.8 2.0 8.6 6.5 2.1 4.513.51.0 3.6 5.5
15mm 8502.8 21.6 26.8 13.4 6.4 18.1 0.5 8.623.29.33.923.9
875 6.9 27.0 31.6 21.1 15.7 25.7 1.413.435.419.012.548.2
900 24.8 39.2 42.8 36.1 32.7 40.4 7.130.288.358.846.1209.4

Crosstalk values for a source-detector distance of r=4.0cm results in slightly smaller values. At hf=0 , 5, 10, and 15mm , CHbO2Hb,4.0,hf was 9.0±5.6 , 11.5±9.2 , 19.3±17.6 , and 22.6±27.4% , and CHbHbO2,4.0,hf was 14.1±4.4 , 15.3±7.5 , 20.1±10.0 , and 20.6±11.0% , respectively.

5.

Discussion

We showed that the presence of a fat tissue layer causes underestimation error and crosstalk problems in cw-NIRS muscle measurements and that these problems are fat-thickness dependent. The main cause of these problems is the homogeneous medium assumption in the MBLL calculations with the use of a constant path length instead of fat thickness and wavelength-dependent mean partial path length in the muscle layer. The fat layer has a lower absorption coefficient than the underlying muscle layer and it has been shown30, 32, 33, 54 that as the fat layer thickens, probed volume by NIRS system also increases (the “banana” gets fatter). However, as the banana gets fatter, probed muscle volume decreases ( Lmλ decreases). Thicker fat layer leads to an increase in Lλ and Lfλ and detected light intensity for the considered wavelengths in the 675to900-nm range, as shown in Sec. 4.1. Similar findings were reported in the literature such as the inverse relation between Lm and hf found by simulation studies 25, 30, 31, 34, 35, 54, 55, 56 and by theoretical investigations.55 Higher detected light intensities have been also reported for thicker fat layer.32, 33, 54, 57

There is also a strong wavelength dependency of Lmλ . The concentration of HbO2 (taken as 70%) is higher than [Hb], and for longer wavelengths, ϵHbO2λ is higher, which result in μa,mλ increasing, leading to a decrease in Lmλ and Lλ for longer wavelengths. In experimental studies, wavelength dependency has been reported58, 59, 60 only for the DPF factor, since it is impossible to measure and isolate Lmλ from a layered structure. Duncan 61 reports DPF values of 4.43±0.86 (5.78±1.05) at 690nm , and 3.94±0.78 (5.33±0.95) at 832nm in the forearm (calf) for r=4.5cm . In the same study, a significant female/male difference in the DPF values was shown, with values of 4.34±0.78 for females and 3.53±0.55 for males in the forearm at 832nm . For r> 2.5cm , DPF has been shown to be almost constant by van der Zee, 60 where it was also stated that a female/male difference was present with mean DPF values of 5.14±0.43 for females versus 3.98±0.46 for males at 761nm in the adult calf, but no difference was observed in the adult forearm (both DPF are 3.59±0.32 ). A general trend of DPF decrease in 740-to840-nm range was also found by Essenpreis, 58 although no significant female/male difference was observed. In these studies, a female/male difference was attributed to fat/muscle ratio differences, although statistics concerning fat thicknesses were not present about the subjects in the studies.

In this study, we investigated the error in the estimation of the concentration changes using MBLL with homogeneous medium assumption under two headings: an underestimation error and crosstalk. We showed that fat thickness has a strong effect on both. The means of both absolute underestimation errors and absolute crosstalk over the considered wavelength pairs were calculated to be high for thick fat layer, as stated in Sec. 4.2, 4.3. As stated, a decrease of Lmλ with increased hf and the use of a fixed DPF value in MBLL calculations because of the homogeneous medium assumption leads to rise in underestimation error. Crosstalk depends on Lmλ but not the used DPF value when a wavelength-independent DPF is used. The wavelength dependency of ϵHbO2λ and ϵHbλ as well as the difference between them also affect crosstalk.

The choice of wavelength pair had a significant impact on the errors. The variability in the absolute underestimation errors for different wavelength pairs is higher for low fat thickness values while the variability in the absolute crosstalk for different wavelength pairs increases with increasing fat thickness. The means of absolute underestimation errors and absolute crosstalk were found to be higher for EHbO2,3.0,hf and CHbHbO2,3.0,hf . These findings are related to wavelength dependency of Lmλ and specific absorption coefficients. Note Lmλ has a decreasing trend at longer wavelengths and ϵHbλ (ϵHbO2λ) is higher (lower) for wavelengths less than 798nm , the isobestic point. In more detail, the reason for a higher underestimation error of EHbO2,3.0,hf with respect to EHb,3.0,hf can be explained by ΔODλ2 (Lmλ2) being more heavily weighted by the real concentration change of Δ[HbO2]m in the muscle layer than Δ[Hb]m . In the MBLL equations, measured ΔODλ ’s are assumed to be proportional to DPF ×r instead of unavailable Lmλ . Wrongly used DPF ×r overestimates the Lmλ (leading to underestimation error for concentration change), however, the degree of path length overestimation is higher for longer wavelength since Lmλ decreases with wavelength. Hence, the path length overestimation because of homogeneous medium assumption is higher for measured optical density change ΔODλ2 leading to more underestimation error for Δ[HbO2]MBLL .

There is one previous study on crosstalk for muscle cw-NIRS measurements by Iwasaki and Okada.42 This analysis was done for a fixed fat thickness of 4mm , a two-wavelength system was assumed, λ2 was fixed at 830nm , and r was taken as 2.0 or 4.0cm . The 720830-nm and 780830-nm pairs were found to be the favorable pair selections resulting in minimal crosstalk. In our study, the 775825-nm pair also gave low crosstalk values along with the 750825 - and 760825-nm pairs, for both CHbO2Hbλ1,λ2 and CHbHbO2λ1,λ2 . Iwasaki and Okada42 found negative CHbO2Hbλ1,λ2 values and positive CHbHbO2λ1,λ2 values; however, we calculated not only opposite signs but also different magnitudes. These could be due to choice of muscle absorption coefficients, the values in this study range between 2.1 to 3.7 times higher than the values used in our study. We also looked at the effect of fat thickness variation on crosstalk and found a rise in the mean of absolute crosstalk values over the considered wavelength pairs for an increase in fat thickness. Moreover, other λ2 values were studied, up to 900nm . There was an increase in crosstalk amplitudes for an increase in λ2 for values higher than 825nm for a fixed λ1 at a given hf value. The absolute values of CHbO2Hb,3.0λ1,λ2 and CHbHbO2,3.0λ1,λ2 were calculated to be less than 11% for the 675825 , 675850 , 675875 -, 750825 -, 760825 -, 760850 -, and 775825-nm pairs for hf<10mm .

Arterial occlusion is employed in cw-NIRS measurements to estimate muscle oxygen consumption. In this case, ideally blood volume remains constant, while Δ[HbO2]m decreases and Δ[Hb]m increases in equal magnitudes in the probed volume. Using Eq. 13, the estimation errors were found to be 10.6±5.2 , 30.7±4.6 , and 54.6±4.1 % for Δ[Hb]MBLL and 15.1±4.3 , 34.3±3.7 , and 57.1±3.2% for Δ[HbO2]MBLL at hf=0 , 2, 4mm respectively, computed over 24 wavelength pairs ( r=3.0cm , DPF=4.37 ) These estimation errors for the two chromophores are closer compared to the differences between underestimation errors (Sec. 4.2) due to the crosstalk. The estimation error for Δ[Hb]MBLL is higher than the underestimation error EHb,3.0,hf , while estimation error of Δ[HbO2]MBLL is lower than the underestimation error EHbO2,3.0,hf . For this protocol, the minimum estimation errors were found for the 700825 - and 725825-nm pairs. For a fixed λ2 , the estimation errors for the occlusion protocol were found to be low for choice of 700 or 725nm as λ1 , while for fixed λ1 , errors rise for an increase in λ2 , for both Δ[HbO2]MBLL and Δ[Hb]MBLL .

The error analysis in this study showed the clear failure of the homogenous medium assumption and the requirement to correct cw-NIRS measurements even for low fat thickness values, although it was stated that correction may not be required for less than 5mm fat thickness by Yang 57 There are already several proposed approaches for cw-NIRS measurement corrections, in particular for mV̇O2 . Several investigators25, 32, 55 have proposed correction algorithms using theoretically determined Lm . Niwayama 56, 62, 63 combined the results of simulations and experiments (for Lm , detected light intensities, and experimental sensitivities) to obtain correction curves for mV̇O2 . Utilizing these corrections, the variance of the experimental mV̇O2 results were reduced,56, 63 moreover, a higher correlation was found between mV̇O2 values measured by P31 -NMR and corrected mV̇O2 values measured62 by cw- NIRS. Yet another correction algorithm was proposed by the same group in which a relationship between detected light intensity and measurement sensitivity was utilized as an empirical technique to reduce the variance in mV̇O2 findings due to fat thickness.32, 33, 64 Yang 57 proposed a correction for intensity of cw-NIRS measurements using a polynomial fit to detected intensity change with fat thickness. Lin 65 used a neural-network-based algorithm for spatially resolved reflectance, first to find the optical coefficients of the top layer and then that of the layer below, assuming the top layer thickness is known. There are also broadband cw-NIRS techniques. One method orthogonalizes the spectra collected at a long source-detector distance (r) to the spectra collected at a short r and maps to the long r space.66, 67 Another one uses multiple detectors and the derivative of attenuation with respect to distance, utilizing a particular wavelength sensitive to fat thickness.68, 69

Figure 4 shows four cw-NIRS measurement sensitivity curves. The first curve from our study is the calculated Δ[HbO2]MBLL computed for the ischemia protocol (for unit magnitude and opposite Δ[Hb]m and Δ[HbO2]m ) using DPF=4.37 , at a 750850-nm pair (r=3.0cm) . The computed Δ[Hb]MBLL for the same conditions (not shown) has a slightly higher sensitivity. The sensitivity curve of Niwayama 63 is proposed for muscle measurement correction by dividing the calculated concentration changes by itself—given by exp[((hf+hs)8.0)2] , using the 760840-nm pair for r=3.0 cm, we take hs to be 1.4mm . The curve of Niwayama 63 indicates higher sensitivity than the one our curve predicts. For the computed Δ[HbO2]MBLL , taking a lower DPF value of 4.0 (the value used in the Niwayama 63) leads to a higher sensitivity. Yet another curve is derived from the experimental resting state oxygen consumption curve of van Beekvelt 36 [ mV̇O2=0.18to0.14×log10(hf+hs) ml of O2min1100g1 , used DPF=4.0cm , r=3.5cm , three wavelengths a 770850905-nm system, we take hs as 1.4mm ) by normalizing it to its value at a 0-mm fat thickness. The study had 78 volunteers with highest fat (plus skin) thickness of 8.9mm (approximating a 7.5-mm fat thickness), hence shown up to hf=8mm . It is closer to our curve for low-fat-thickness values (<4mm) but presents higher sensitivity for higher fat thickness values and becomes closer to the curve of Niwayama 63 van Beekvelt 36 reports a 50% decrease in experimentally found oxygen consumption (mV̇O2) for fat thickness (including skin) in a range from 5to10mm . Niwayama 56, 63 reports of a roughly 50% decrease in cw-NIRS measurement sensitivity for a twofold increase in fat (including skin) thickness, but the range for fat thickness is not given. In our study, we calculated a nearly 55% decrease in the Δ[HbO2]MBLL and Δ[Hb]MBLL for the ischemia protocol at 750850 and 775850nm (the closest pairs to the wavelengths used in the mentioned studies) for hf increase from 3to6mm , while the decrease becomes nearly 34% for hf=2to4mm , and 70% for hf=4to8mm .

Fig. 4

Normalized oxygen consumption curve of van Beekvelt 36 (denoted by VB), measurement correction curve of Niwayama 63 (denoted by NW), computed Δ[HbO2]MBLL for ischemia protocol (for unit magnitude and opposite Δ[Hb]m and Δ[HbO2]m changes, obtained for the 750850-nm pair) using of DPF values of 4.37 (denoted by DPF=4.37 ) and 4.0 (denoted by DPF=4.0 ).

064019_1_016806jbo4.jpg

MBLL calculations are based on a linear approximation for the relationship of optical density change to absorption coefficient change, which leads to deviations for large concentration changes, as shown by Shao 70 The presence of the fat layer deteriorates the linearity of measurement characteristics investigated by Lin 25 In our study, we assumed small concentration changes. In quantitative studies aimed at oxygen consumption calculations, concentration change rates within small time scales during ischemia are typically used. In the experimental study of Ferrari, 71 a difference of Δ[HbO2]Δ[Hb] was computed for ischemia alone and for ischemia with maximal voluntary contraction. For these measurements, desaturation rates were computed with constant DPF and with changing DPF values found using time-resolved spectroscopy with the same experiment protocols. Similar rate values were calculated within short time scales.

The effect of fat layer thickness on cw-NIRS measurements is very explicit and dominant; note, however, that partial path length values, detected intensities, underestimation errors, and crosstalk are all subject to both intrasubject and intersubject variability because of optical coefficients’ variability of tissue layers, variability in physiological status, muscle anatomy differences, and anisotropy in the skin72 and in the muscle.73

An increase in the source-detector distance leads to lower errors because of increased Lm , however, signal-to-noise ratio (SNR) also decreases since detected intensity decreases leading to a trade-off. It may be possible to discover an optimal source-detector distance based on optimization of SNR maximization and error minimization,35, 54 by also taking into account the fat thickness of the subject.

6.

Conclusion

The fat layer influence on muscle cw-NIRS measurements based on MBLL calculations with homogeneous medium assumption was investigated for both underestimation error and crosstalk using Monte Carlo simulations for a two-wavelength system. Although the computed values of underestimation errors and crosstalk are dependent on the “true” optical coefficients of the tissue layers, and hence could change for each subject, an explicit finding is that the mean values of the absolute underestimation errors and absolute crosstalk computed over the considered wavelength pairs increase for the thicker of the fat layer. The means of absolute underestimation errors EHbO2,3.0,hf and absolute crosstalk CHbHbO2,3.0,hf over the considered wavelength pairs were found to be higher, while due to the crosstalk, the estimation errors for the concentration changes of the two chromophores were calculated to be closer for the ischemia protocol. These errors also depended on the wavelength pair selection for the two-wavelength system with greater impact on the crosstalk. This dependency of wavelength leads to the fact that correction algorithms should be dependent on the choice of wavelengths, although different wavelength combinations can have very similar sensitivities. The measurement of the fat thickness values and providing information about it should become a standard routine, as suggested by van Beekvelt 74 for the cw-NIRS measurements.

Acknowledgments

This study was supported by the Boğaziçi University Research Fund through projects 04X102D and 04S101 and by Turkish State Planning Organization through projects 03K120250 and 03K120240. The doctoral fellowship for Ömer Şayli by TÜBİTAK (The Turkish Scientific & Technological Research Council) is gratefully acknowledged.

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©(2008) Society of Photo-Optical Instrumentation Engineers (SPIE)
Ömer Sayli, Ertugrul Burtecin Aksel, and Ata Akin "Crosstalk and error analysis of fat layer on continuous wave near-infrared spectroscopy measurements," Journal of Biomedical Optics 13(6), 064019 (1 November 2008). https://doi.org/10.1117/1.3028008
Published: 1 November 2008
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