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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 39, NO. 2, FEBRUARY 1992
The Relationship of Surface Reflectance Measurements to Optical Properties of Layered Biological Media Weijia Cui and Lee E. Ostrander, Senior Member, IEEE
Abstract-Reflectance from a turbid biological tissue is discussed for a diffusive light source illuminating the surface of the medium, and is related to the optical property distribution within the medium and to photon propagation through the medium. A three-dimensional photon diffusion model with closed form is developed to describe the photon diffuse intensity in a homogeneous medium. The solution is extended by numerical methods to the medium with layered structure. The concepts of photon flux paths and of reflectance indexes are utilized, together with reflectance data, to extract information about the internal optical properties of a medium. The flux path concept was corroborated by successfully detecting in vivo and ex vivo layered differences in optical properties within the biological medium. These studies suggest that the optical properties of subdermal tissue can be measured from light reflectance and that the effect of the upper skin layers can be eliminated.
INTRODUCTION EASUREMENT of the influences exerted upon light by biological media as the light travels through the media is key to several noninvasive measurements of physiological variables, such as arterial blood flow and of microcirculation [ 11-[3], blood volume concentration [4], and blood oxygen concentration [5]-[7]. Noninvasive imaging of blood flow beneath the surface of in vivo skin [8] has also been suggested as an application. In recent years, techniques have been extended in efforts to extract information about light absorption of in vivo muscle and brain from light which has travelled through the upper layers of skin and bone [9], [lo]. The optical properties in each layer-epidermis, dermis, subcutaneous tissue, muscle, and bone-contribute to the reflectance at the surface [lo], [ 1 11. The effect of each layer depends upon its optical properties and upon measurement conditions such as the source-detector separation [ 121. However, determining the contributions of
M
Manuscript received April 2, 1990; revised August 1, 1991. This paper was based upon a thesis by W. Cui submitted in partial fulfillment for the degree of Doctor of Philosophy in the Department of Biomedical Engineering at Rensselaer, with support from NSF Grant BCS-9008533. W. Cui was with the Department of Biomedical Engineering, Rensselaer Polytechnique Institute, Troy, NY 12180. He is now with the BOC Technical Center, Murray Hill, NJ 07974. L. E. Ostrander is with the Department of Biomedical Engineering, Rensselaer Polytechnique Institute, Troy, NY 12280. IEEE Log Number 9104917.
the different layers to surface reflectance measurements has remained a frustration. This paper relates surface photon flux to the photon propagation within a layered turbid medium using photon diffusion theory. Methods are discussed for extracting layering information from surface measurements and these methods are corroborated through ex vivo and in vivo experiments with biological tissue. THEORETICAL STUDY Difision Equation Modeling While numerical solution is generally necessary for models of photon diffusion in layered media, a closedform solution illustrates the simple case in which the medium is a uniform homogeneous diffusing material in a half space. The photon diffuse intensity, or space irradiance, \k (W/cm2) and the photon flux @at location ( r , 4 , 0) in the medium can be described as [ 131
v 2 w - , 4, 0)
-
k2wI-, 4,
e)
= ~ ( r4, ,
e)
(1)
4
F = -DV\k
(2)
where (I-,4, 0) are coordinates in a spherical system, S(r, 4 , 0) is the source term for diffused photons, and d is the diffusion coefficient (mm). The inverse of k is diffusion length (in mm); and furthermore, k2 is computed as k2 = E,/D = 3C,[Cs(1
- p)
+ E,]
(3)
where C, is the absorption coefficient (mm-I), E, is the scattering coefficient (mm-I) and p is the anisotropy parameter of the medium with values between - l and l . Isotropic scattering yields a value of p = 0, while pure backscattering yields p = - 1 and pure forward scattering yields p = + l . Diffusive sources can occur within the medium when unscattered photons enter and are then scattered beneath the surface. In the analytic model presented here, the scattering sources occur beneath the surface plane within a hemisphere (diffusor) of radius ro located at the origin in the coordinate system. This hemisphere becomes part of the boundary for the medium, so that S(r, 4 , 0) = 0 within the infinite half-space of the medium. The photon flux at each point on the hemisphere surface is dependent upon
0018-9294/92$03.00 0 1992 IEEE
~
'
111
I
I
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CUI AND OSTRANDER: RELATIONSHIP OF SURFACE REFLECTANCE MEASUREMENTS
source intensity Io and is chosen to vary with the angle 6 and to be independent of 4 so that the boundary condition is represented by =
-Io
COS
10 9 8
(e),
0
I8 I~
/ 2 . 7
(4)
6
In this representation, the angle 0 is measured with respect to the normal to the surface of the medium such that e = 0 for a vector directed into the medium. The medium surface outside the diffusing hemisphere ( r Iro, 0 I0 I r / 2 ) is represented as an ideal absorber, or in other words, the diffuse photon intensity at the boundary is zero ~141.
5
+(r, + n / 2 ) = 0,
e) = 0,
*(a,
(5)
for r 2 ro foro
e5
I
~ / 2 .
(6)
The distribution of photon intensity within the medium for the above boundary conditions is amenable to solution by separation of variables, yielding the following closedform solution [15]: e P pCOS (8)
where p
=
rk and the constant
(Y
3
2 1
0 0
2
4
6
8
10
Depth into tissue (kr) Fig. 1 . Computed diffuse intensity contours and maximum flux paths for a homogenous medium (separation and depth in normalized coordinates p = r k ) . The values of q,,(W/cm2) are 0.5/i5, i = 1, 2, 3, . . . , 15, for the contours from the innermost to the outermost.
(7)
is given by
and where po = r&. The reflectance on the surface for r > ro is
Diffuse Intensity Contours and Diffuse Flux Paths I ) Diffuse Intensity Contours: Let 9, = * / a be the normalized function dependent upon only p and 8 and which has a value of 2e-' at p = 1 and 8 = 0. Fig. 1 shows the isointensity contours (solid lines) of 9,.The values of 9, are 0 . 5 / i 5 , i = 1, 2 , 3, , 15, for the contours from the inner most to the outer most. The scattering of photons causes them to migrate along random paths in the medium before being absorbed or escaping from the medium through any point (i.e., target) on the boundary. At any point in the medium, the direction for maximum migration occurs normal to the isointensity contours such that the concentration gradient is largest. The dotted lines, referred to in the following discussion as maximum flux paths, are drawn in the gradient directions of the diffuse intensity. 2) Maximum Flux Paths: As is evident in Fig. 1, the reaching depths of different maximum flux paths depends upon the distance between the two ends on the surface (or the source-target separation). Weiss et al. [ 161 studied the statistics of penetration depth for a photon reemitted from
-
4
a diffusive medium. Their results demonstrated that the maximum depth attained by a photon exiting from the surface at any given source-target separation follows a distribution with maximum probability density at a calculated depth below the surface [ 161. This distribution and its maximum are affected by the separation between the source and detector and by the photon absorption within the medium. Given the statistical nature of the process, there is a path between source and target of maximum probability density. Since any departure from the maximum flux path (which is defined by the concentration gradients) reduces the probability of reaching the target, the path of maximum probability density must be coincident with the maximum flux path. 3) Simulation Study: For the layered medium, finite difference methods provide a solution to the diffuse intensity and yield isoconcentration contours and maximum flux paths shown in Fig. 2 . The model coefficients (i.e., the k values) of the medium layers were chosen based upon the values obtained by Amfield et al. [ 171, and are given in Table I. Due to symmetry of the three-dimensional medium, the solution of (1) is independent of the angular variable 4, producing a two-dimensional equation to be solved. In this two-dimensional mathematical system, the cylindrical coordinates are the vertical depth z into the medium and the radial distance r ' out from the z axis. The two-dimensional system was discretized and finite difference methods used. A single point in the solution grid, located at the origin, served as a source [15]. Thus, the source differed from the analytic solution, although in both cases the injection site was confined to a small area relative to the source-target separations. A comparison of the finite difference and analytic solutions to the problem of
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properties in a medium can be assessed by measuring the reflectance at different source-detector separations. 4) S u ~ a c eRejlectance Measurements: Surface reflectance measurements decay with distance from the source in approximately exponential fashion. To interpret variations in reflectance with structure and optical properties of a test medium, it is convenient to define an index which contrasts the reflectance R(r) from the test medium with that from a reference medium Rref(r).
Bottom layer
'6'
0"
10
8
Index(r) = In [R(r)/Rr&].
I 4
2
0
0
2
4
8
6
10
Dbtanw from lbM sourw (mm) Fig. 2. Computed diffuse intensity contours and maximum flux paths for a layered medium (medium I in Table I). The diffuse intensity q,, (in microwatts per cm2) for these contours, proceeding outward from the contour nearest thesource, are 1540, 308, 1 0 8 , 4 6 . 6 , 2 2 . 4 , 1 1 . 5 , 6 . 1 5 , 3 . 3 9 , 1.91, 1.10, 0.683, 0.375, 0.222, and 0.133, respectively.
TABLE I
k COEFFICIENTS AND DIMENSION OF THE LAYERS FOR THE FINITE DIFFERENCE REFLECTANCE SIMULATION Simulation Case Medium I (Homo.) Medium 2 (Homo.) Medium 3 (Layered) Medium 4 (Layered)
k, (I/") 0.43 0.33 0.23 0.23
kb (1 /mm)
0.43 0.33 0.43 0.43
d (mm)
-
-
1.0 2.0
Media 1 and 2 are homogeneous and are used as references. Subscripts t and b refer to top and bottom layers respectively.
the homogeneous medium showed that the differences became negligible as the radial distance from the source increased beyond 1/ k . Fig. 2 suggests that an increase in the source-target separation results in an increased portion of the flux path being imbedded within the lower layer. This, in turn, suggests that the lower layer will exert an increased influence on the reflectance, relative to that of top layer, as the source-target separation increases. From the nonintersecting property of the maximum flux paths in Fig. 1 and 2, it is observed that the maximum flux paths ending at larger source-target separations reach deeper into a medium, even for a nonhomogeneous medium. This analysis agrees with Takatani's conclusion [ 121 that to increase the influence from deeper tissue on the measured signal, large source-detector separation should be selected. This analysis also suggests that the depth distribution of optical
(10)
If both the reference medium and the test medium are homogeneous, it follows from (9) that Index@, when plotted against r, approaches a straight line of slope (kref k) for large r (curve 1 in Fig. 3) [15], where kEf and k refer to the k values for the reference and the test media, respectively. Fig. 3 uses a homogeneous reference medium for all curves with the kEf given at the top of the figure. In Fig. 3(a), curves 2 and 3, the k value of the bottom layer (kb) in the test medium is the same as the kEf. The index approaches a constant for large r, the magnitude of which depends upon the thickness of the top layer. The reflectance for large separation is proportional to that for the reference, but increased by 65 and 20%, respectively, as a result of the smaller attenuation of light in the top layer. It is also noted that the final index value is approached more rapidly as the thickness of the upper layer is reduced. The index curve slope for large sourcetarget separation is equivalent to the index curve slope for a homogeneous medium which has optical properties to match those of the deeper layer. The value of the index at large separations for the layered medium is shifted due to passage of light through the top layer. In Fig. 3(b), curves 2 and 3, the deeper layer has a different k value from that of the reference. Again, the index slope approaches that which would be expected for a homogenous medium with the same k value as the deeper layer. Since the reference k value is less than that of the deeper layer (kEf Ikb), the index has negative values corresponding at large r to a reduced reflectance for the two layer mediums as compared with the reference medium. Since the shape of the index curves for larger separations are controlled by the bottom layer, this suggests that the index curve pattern may be used to obtain the optical properties of the deeper tissue layers, while the effect from the top layer is eliminated.
EXPERIMENTAL STUDY The purpose of the experimental study was to determine whether the functionality observed in the indexes for layered media bore resemblance to behavior observed ex vivo and in vivo. Since the available reported studies of photon diffusion through biological media do not lend themselves to calculating and plotting the above described index, experimental data was collected. An ex vivo study provided conditions for directly relating the index to known structure of biological tissue. 'In vivo studies pro-
-
CUI AND OSTRANDER: RELATIONSHIP OF SURFACE REFLECTANCE MEASUREMENTS
a). Reference k
2
I97
0.43 /mm.
1.6
0.6
0 0
3
6 10 15 20 25 30 Sourcedetector separatlon (mm)
b). Reference k
-
0.33 /mm.
. - (8:+=a2U",~=a4Mnm. lyrulldmu = mm
Fig. 4. Probe design for measuring the surface reflectance at different source-detector separations and the photodetector response.
1
illumination intensity at the opening of the cylinder. As seen from the detector response curve in Fig. 4,the light wavelengths for this study fall in the passband of the detector. Since reflectances are analyzed as ratios at each wavelength (i.e., the index curve values), differences in detector sensitivity with wavelength cancel. The open face of the cylinder was in the same plane as the surface of the 32 concentric detector strips. Each strip consisted of an annular photosensitive segment of 0.9 mm width at a fixed distance from the light source, with 0.1 mm spacing between the strips. To attenuate inherent detector noise and the effect of stray light, the illumination was electrically modulated at 2000 Hz, and the received signal at the detector was amplitude demodulated. 0
5
10
16
20
25
30
Sourcedetector separatlon (mm) . (h\ ,-,
Fig. 3 . Simulation results in which the layered medium differs from the homoneneous reference medium. In (a) ~,the bottom laver has the same value for k i s the homogeneous medium, while in (b) boih top and deep layers have values of k which differ from that o f the reference. In (b), negative indexes are plotted for krCf < kb.
vided the correlation of index curves with expected physiologic changes associated with heat-induced hyperemia. Rejectance Probe and Measurement System High-intensity light emitting diodes (660 and 880 nm with an average source current of 50 mA) were held in place with clear epoxy in a stainless steel cylinder of 4 mm inner diameter (see Fig. 4) so as to provide equal
Ex Vivo Experiments A biological model was constructed from muscle, subcutaneous fat, and dermis which were sectioned from pork shoulder- The was cm across, cm thick* The dermal layer and the fat layer, of similar length and width, were 3-4 mm thick. The test models were constructed by covering the muscle with the dermal layer, or the fat layer, or both. Transmittance at 880 nm was measured separately for the dermis, fat, and muscle to determine their optical light transmission differences at this wavelength. The samples were each sandwiched between two pieces of plexiglass, and diffusively illuminated on one side using translucent plexiglass. The transmitted light intensity was measured at the opposite surface. The ratio of the transmitted light with and without the sample present was calculated, pro-
~
I 8
-
,
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 39, NO. 2, FEBRUARY 1992
198
TABLE I1 THETRANSMITTANCE OF THE EX vivo DERMIS, SUBCUTANEOUS FATAND MUSCLE (MEANf STD) AT 880 nm FOR Two SAMPLE THICKNESS (n = 5) Thickness
3.45 mm
4.95 mm
1.2
1 -
Dennis
Fat
Muscle
0.48 0.031 0.35 f 0.019
0.46 f 0.029 0.39 f 0.024
0.64 k 0.011 0.54 f 0.019
0.8
e 0.6
5 A
viding averaged (n = 5 ) transmittance values in Table I1 for each material. The results show that at 880 nm, the transmittances of the dermis and fat were relatively close to each other, but differed significantly from that for the muscle. To calculate an index for the experimental models using (1O), reflectance from the muscle was taken as the reference. Given in Fig. 5 are the resulting indexes which compare the reflectance from each assembled test model with the reflectance from the muscle by itself. The indexes show the differences in reflectance which occur due to the presence of a top layer or layers over the muscle. The initial increase of the negative index for these models is consistent with the higher attenuation of light in fat and dermis than in muscle (Table 11), which has a dominating effect at small separation of source and detector. The flat segment of these curves is consistent with an index reading from the deeper muscle layer. The combination of “dermis fat muscle” also suggests only a two-layer structure. This is consistent with the similarity of transmittance at 880 nm for fat and dermis such that the two materials together act optically as one thicker top layer. As a result of the greater top layer thickness in the threelayer combination, the knee of the curve occurs at a larger source-detector separation. The ex vivo experiment corroborates the simulation study results by showing a dependence of the index upon the layered structure. The index segments below and above the knee are influenced by the differences in optical properties of the upper and lower layers from the reference medium. The slope of the index curve at larger separation was representative of the dominant influence of the bottom layer of the layered model and the photons fat arriving therefrom. In the case of the “dermis muscle,” the muscle was approximately 7 mm beneath the surface from which measurements were taken.
+
+
+
Reference:’Muscle
I
+
In Vivo Experiments For in vivo studies, the surface of the skin was heated with a hot water bag at 40°C for 5 min so as to produce a change in circulation. The dermal circulation is significantly influenced by the environmental temperature so as to balance the heat generation and dissipation. Under the physiological condition, the dermal blood flow is about 20-30 times the blood flow necessary for supplying the oxygen requirement and this factor can be over 100 times in a hot environment [18]. The response of the skin to the local heating thus would result in a layered blood volume change through thermal regulation mechanisms in the dermis, which in turn results in a layered optical property
-
0.4
0.2
-
0 -
4.2’ 0
’
’
10
’
’
20
’
’
30
‘
40
Separation (mm) Fig. 5. Ex vivo index curves at 880 nm comparing the reflectance from the muscle only with that from the muscle covered by dermis and/or fat. Negative index is plotted.
change. The reflectance data prior to the heat application provided the reference for the reflectances during the period of approximately 20 min in which hyperemia was observed following heat application. Reflectance data, before and after hyperemia, were collected from eight subjects, with informed consent, so as to obtain examples of eleven index curves. The reflectances were measured at a selected site on the anterior surface of the lower leg, the calf, the anterior or lateral surface of the thigh, or on the surface of the forearm. During the ten minute test, the subject sat with the leg or arm slightly elevated depending upon the site of measurement. The source-detector probe was held lightly in place with tape and reflectances measured at both 660 nm and 880 nm. Fig. 6 is representative of these index measurements, showing an initial rapid rise of the negative index, followed by a region at larger source-detector separations of lesser slope. Inference from the simulation and ex vivo studies suggest that the initial increase below the knee of the curve represents a significant absorption increase in the top layers for the hyperemic states. The apparent changes in top layer absorption is consistent with increased blood volume and flow in the dermis, in response to the local heating. Fig. 7 shows the index curve slopes for the first segment of the index below the knee of the curve and the second segment above the knee, from the eleven measurements. In the data collected in the first segment of the curve, the hypothesis that the index curve slopes at 660 and 880 nm were the same could not be rejected by student’s paired t-test ( p I0.05). Since the blood absorption is different at the red and infrared wavelengths, the similarity of the slopes in the first segment at 660 and at 880 nm suggests that no significant change in oxygenation took place in the shallow thermoregulating layers during the hyperemic response. This is possible when the blood
199
CUI AND OSTRANDER: RELATIONSHIP OF SURFACE REFLECTANCE MEASUREMENTS
Reference: Normal Reflectance 1.6 ,-
1.2 -
1.4
h
e
1 -
-
5 0.8 -
5 0.6
0
5
10
15
20
25
30 35
40
separauon Fig. 6. An example of in vivo index curves at 660 and 880 nm. In this case, measurements were taken on the lateral side of the thigh. Negative index is plotted.
0.3 0.25
0.2
E
0.15
i
0.1
0.05 0 -0.05
A1
Bl
82
C1
D1
El
F1
F2
F3
F4
01
AL
LT
AT
LT
LC
Subject I.D. LC
FA
LC
LT
LC
LC
Sample Site
(a) Fig. 7. The linear regression slopes for (a) the first segment (below the knee at smaller source-detector separations) and (b) the second segment (above the knee) of eleven in vivo negative index curves from eight subjects. Measurement Site: AL-anterior surface of lower leg; AT-anterior surface of thigh; FA-forearm; LC-lateral surface of calf; LT-lateral surface of thigh.
is highly oxygen saturated and remains so with the increased blood volume and flow of hyperemia. The oxygen saturation is normally expected to be high due to excessive flow in the thermoregulating region [ 181. The separation between the first and second segments for the red and infrared curves may indicate the depth of the thermoregulating vascular beds in which blood flow exceeds that necessary to meet the metabolic demand for oxygen. The smaller index slope in the second segment suggests a less significant change in deep tissue optical properties with hyperemia. The negative second segment slope for
subjects C 1 and D 1 suggests a decrease in blood volume in the deeper tissue after the local heating for these subjects. The difference in the red and infrared responses in the second segment can be attributed to the differences in photon absorption at the two wavelengths associated with changes in blood volume and oxygenation in the deeper tissue. An increased dermal circulation outflow with high oxygenation could increase the mean blood oxygenation in the venous network in the deeper tissue. Given the effect of oxygenation upon light absorption, the increased
0.03 0.02
E 5
O.O1
! L o
m
4.01 4.02 -0.03
A1
B1
82
C1
D1
El
F1
F2
F3
F4
Ql
AL
LT
AT
LT
LC
Subject I.D. LC
FA
LC
LT
LC
LC
Sample site (b) Fig. 7. (Continued)
oxygenation would provide additional absorption to the light at 880 nm and lesser absorption at 660 nm [ 191. The effect on light absorption of both increased volume and increased oxygenation at the infrared wavelength would be additive, but at the red wavelength would be expected to partially cancel, resulting in a lesser slope of the red index curve when compared with infrared. This effect is seen in Fig. 7 where in all data collected beyond the knee, the slope of the index curve was larger for 880 nm than for 660 nm. The hypothesis for the second segment that the slope was smaller at 880 nm or equal to that at 660 nm was rejected by student’s paired t-test (p 5 0.005). DISCUSSION AND CONCLUSION Diffusion theory has been used to relate the optical properties of a layered turbid material to the reflectance on the surface. Our theoretical study has introduced the concept of photon flux paths to describe, in an averaged statistical sense, the escape of photons following their propagation through a diffusive medium. The study suggests that the internal optically differentiable structure can be assessed by photon flux measurements on the surface of the medium. A closed-form three-dimensional photon diffusion model was developed to describe the photon density distribution in the diffusing medium. With this model and with additional results of simulation methods and ex vivo experiments, the layered optical property distribution in a medium and its relation to reflectance were studied. The simulation suggests that photons measured at larger source-target separations have penetrated more deeply even when the medium is heterogenous. The modeling and finite difference simulation approximate the experimental conditions with some differences in boundary conditions and in source specifications. Reflections at the surface of the medium are not included in the theoretical analysis, and are assumed to be negligible,
based on previous studies [ 141. Agreement of the theory and experiment in the present study supports this approx. imation. The different light source specifications used in the modeling and finite difference simulation resulted in a difference in diffuse intensity distribution only in the immediate vicinity of the light source. In the experimental studies, the tissue beneath the light source acted as a light diffusor. The anisotropic scattering property of tissue can result in a stronger photon flux for small 6 in the immediate vicinity of the source. Beyond the immediate vicinity of the source, the illumination is effectively diffusive such that deeper penetration of the photons is measured at larger separations. In addition, since the index defined in (10) compares the reflectances measured by the same source at the same location, the effect of the differences among illumination sources is minimized. The index of (10) assesses the layered optical property differences of two media by comparing their reflectances. The corroborating results of the simulation and of the ex vivo studies demonstrate the capability for assessing layered differences using the index. The shape of the in vivo index curves is consistent with a significant blood fractional volume change in the dermal layer for hyperemic skin, and the slope for the later segment of the index curve corresponds to the optical property changes for the tissue beneath dermis, as analyzed in the simulation study. The index response with layering, as inferred by the modeling study, changes with differences in the k value, which can be a combined effect of E,, E,, and p . Thus, the index profile measured on the surface should be interpreted as a layered k distribution rather than layered distribution in E,, E,, or p. Both the thickness of the upper layer and the difference between the k values of the upper and lower layer affect the shape of the index curve. A thicker upper layer or a larger difference in the k values results in larger initial slope changes. This study suggests that surface measurements are sensitive to deeper tissue
CUI AND OSTRANDER: RELATIONSHIP OF SURFACE REFLECTANCE MEASUREMENTS
optical properties and that features of the measurements at larger source-detector separation tend to be independent of upper layer effects. In general, the Sensitivity Of surface measurements to the optical properties of the unat different depths is derlying biological tissue governed by (1). The method of analysis utilizing an index requires a reference medium for comparison. The reference may be selected to have an optical constant, or k , value close to the range of values of the tested medium so as to yield good resolution of the layering since biological tissues have different diffusive behavior and therefore different Optical constants at different wavelengths, it may be to use the Same tissue for both test and reference purposes, but with different wavelengths. Also, a reference may be provided by the reflectance prior to a physiological perturbation as was done for the in vivo study in this paper. The studies described in this paper demonstrate the assessment of intemal optical properties by measurement on the surface, so as to separate the effect of the top layer from the effect of the bottom layer of tissue on the measured photons. The studies of this paper utilizing the maximum flux path concept have relied upon the statistical behavior of photons and upon the context of photon diffusion theory. In general, the photon paths are affected by physical properties such as the scattering and absorption coefficients of the medium and by the anisotropy of the medium. The diffusion theory is based on the assumption of weak anisotropy and the assumption of much stronger scattering than absorption, drawn from more general but less easily applicable theories of radiative transfer [20]. Weak anisotropy is not always the case for biological tissue ( p can be higher than 0.9 [21]). Consequently, the reaching depth of the maximum flux paths may be affected by the different anisotropy of biological tissue. The heterogeneity of biological tissue will also contribute to the variation in the location of the maximum flux paths. By developing methods which distinguish properties at depth within the diffusive medium, the study also suggests the possibility in the future of imaging the layered and other structural patterns of optical properties for in vivo tissue by the use of surface measurements.
REFERENCES [ I ] L. Duteil, J. C. Bemengo, and W. Schalla, “A double wavelength laser Doppler system to investigate skin microcirculation,” IEEE Trans. Biomed. Eng., vol. BME-32, pp. 439-447, June 1985. [2] P. A . Oberg and D. A. Saab, “Gingival blood flow studies using laser Doppler flowmetry,” in Proc. Annu. Internat. Con$ IEEE Eng. Med. Biol. Soc., Seattle, WA, 1989, vol. 1 1 , no. 5, pp. 1647-1649. [3] H. Petterson, P. A . Oberg, H. Rohamn, B. Gazelius, and L. Olgart, “Vitality assessment in human teeth by laser Doppler flowmeter,” in Proc. Annu. Internat. Con$ IEEE Eng. Med. Biol. Soc., Seattle, WA, 1989, vol. 1 1 , pp. 1650-1651. [4] D. J . Smith, P. J. Bendick, and S. A. Madison, “Evaluation of vascular compromise in the injured extremity: A photoplethysmographic technique,” Hand Surg., vol. 9A, no. 3, 1984. [SI Y. Mendelson, J. C. Kent, B. L., Yocum, and M. J. Birle, “Design and evaluation of a new reflectance pulse oximeter sensor,” Med. Instrument., vol. 22, no. 4 , pp. 167-173, 1988.
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[6] Y. Mendelson and B. D. Ochs, “Noninvasive pulse oximetry utilizing skin reflectance photoplethysmography ,” IEEE Trans. Biomed. Eng., vol. 35, pp. 798-805, Oct. 1988. 171 s. Takatani, P. W. Cheung, and E. A. Emst, “A noninvasive tissue reflectance oximeter,” Ann. Biomed. Eng., vol. 8, pp. 1-15, 1980. [8] G. E. Nilsson, A Jakobsson, and K. Wirdell, “Image of tissue blood flow by coherent light scattering,” in Proc. Annu. Internal. Con$ IEEE Eng. Med. Biol. Soc., Seattle, WA, 1989, vol. 1 1 , no. 2, pp. 391-392. [91 B. Chance, S . Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, and G. Holtom, “Time-resolved spectroscopy of hemoglobin in resting and ischemic muscle,” Anal. Biochem., vol. 174, pp. 698707, 1988. [lo] B. Chance, J. S. Leigh, H. W a k e . et al., “Comparison of timeresolved and -unresolved measurement of deoxyhemoglobin in brain,” in Proc. Nat. Acad. Sci.. 1988. vol. 85, PP. 4971-4875. [ I 11 J. Giltvedt and A. Sira, “Pulsed multifrequency photoplethysmograph,” Med. Biol. Eng. Comput., vol. 22, pp. 212-215, 1984. [I21 S. Takatani, “Toward absolute reflectance oximetry: I. Theoretical consideration for noninvasive tissue reflectance oximetry,” Adv. Exp. Med. Biol., vol. 248, pp. 91-102, 1989. [13] J. M. Steinke and A. P. Stepherd, “Diffusion Model of the Optical Absorbance of Whole Blood,” J . Opt. Soc. Amer. A, vol. 5 , no. 6, pp. 813-822, June 1988. [I41 S. Takatani and M. D. Graham, “Theoretical analysis of diffuse reflectance from a two-layer tissue model,” IEEE Trans. Biomed. Eng., vol. BME-26, pp. 656-664, Dec. 1979. [15] W. Cui, “Photon diffusion theory and noninvasive tissue optical measurement,” Ph.D. thesis, Dep. Biomed. Eng. Rensselaer Polytechnic Institute, Troy, NY, 1990, pp. 126-127. [16] G. H. Weiss, R. Nossal, and R. F. Bonner, “Statistics of penetration depth of photons re-emitted from irradiated tissue,” J . Modern Opt., vol. 36, pp. 349-359, 1989. [ 17) M. R. Amfield, J. Tulip, and M. S. McPhee, “Optical propagation in tissue with anisotropic scattering,” IEEE Trans. Biomed. Eng., vol. 35, pp. 372-380, May, 1988. [18] D. I. Abramson, Circulation in the Extremities. New York: Academic, 1967, ch. VI, pp. 126-134. [ 191 0. W. Van Assendelft, Spectrophotometry of Haemoglobin Derivatives. Springfield, IL: Charles C. Thomas, 1970, ch. 3, pp. 55-57. [20] A. Ishimaru, Wave Propagation and Scattering in Random Media. New York: Academic, vol. 1, 1978, ch. 9, pp. 175-190. [21] M. J. C. Van Gemert, S. L. Jacques, H. J. C. M. Sterenborg, and W. M. Star, “Skin optics,” IEEE Trans. Biomed. Eng., vol. 36, pp. 1146-1 154, Dec. 1989.
Weijia Cui received the B.S. degree in electrical engineering from Xi’an Jiaotong University, China, in 1982; the M.S.degrees in biomedical engineering and electrical engineering in 1987 and 1989, respectively; and the Ph.D. degree in biomedical engineering in 1990, all from Rensselaer Polytechnic Institute, Troy, NY, in 1990. His research interests focus on the tissue optical modeling and noninvasive measurement with light. He did his postdoctorate research at the Department of Biochemistry and Biophysics, University of Pennsylvania. Currently, he is a senior engineer in the BOC Technical Center, Murray Hill, NJ 07974.
Lee E. Ostrander (S’61-M’66-SM’77) received the A.B. degree from Hamilton College, Clinton, NY, in 1961, and the M.S. and Ph.D. degrees in electrical engineering in 1963 and 1966, respectively. He is currently Associate Professor of Biomedical Engineering and Executive Officer of the Biomedical Engineering Department at Rensselaer Polytechnic Institute, Troy, NY. His research interests include the optical properties of soft tissue and the noninvasive and in vivo measurement of blood flow and mechanical properties of soft tissue. Dr. Ostrander is a former President of the IEEE Engineering in Medicine and Biology Society.
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 39, NO. 2, FEBRUARY 1992
The Relationship of Surface Reflectance Measurements to Optical Properties of Layered Biological Media Weijia Cui and Lee E. Ostrander, Senior Member, IEEE
Abstract-Reflectance from a turbid biological tissue is discussed for a diffusive light source illuminating the surface of the medium, and is related to the optical property distribution within the medium and to photon propagation through the medium. A three-dimensional photon diffusion model with closed form is developed to describe the photon diffuse intensity in a homogeneous medium. The solution is extended by numerical methods to the medium with layered structure. The concepts of photon flux paths and of reflectance indexes are utilized, together with reflectance data, to extract information about the internal optical properties of a medium. The flux path concept was corroborated by successfully detecting in vivo and ex vivo layered differences in optical properties within the biological medium. These studies suggest that the optical properties of subdermal tissue can be measured from light reflectance and that the effect of the upper skin layers can be eliminated.
INTRODUCTION EASUREMENT of the influences exerted upon light by biological media as the light travels through the media is key to several noninvasive measurements of physiological variables, such as arterial blood flow and of microcirculation [ 11-[3], blood volume concentration [4], and blood oxygen concentration [5]-[7]. Noninvasive imaging of blood flow beneath the surface of in vivo skin [8] has also been suggested as an application. In recent years, techniques have been extended in efforts to extract information about light absorption of in vivo muscle and brain from light which has travelled through the upper layers of skin and bone [9], [lo]. The optical properties in each layer-epidermis, dermis, subcutaneous tissue, muscle, and bone-contribute to the reflectance at the surface [lo], [ 1 11. The effect of each layer depends upon its optical properties and upon measurement conditions such as the source-detector separation [ 121. However, determining the contributions of
M
Manuscript received April 2, 1990; revised August 1, 1991. This paper was based upon a thesis by W. Cui submitted in partial fulfillment for the degree of Doctor of Philosophy in the Department of Biomedical Engineering at Rensselaer, with support from NSF Grant BCS-9008533. W. Cui was with the Department of Biomedical Engineering, Rensselaer Polytechnique Institute, Troy, NY 12180. He is now with the BOC Technical Center, Murray Hill, NJ 07974. L. E. Ostrander is with the Department of Biomedical Engineering, Rensselaer Polytechnique Institute, Troy, NY 12280. IEEE Log Number 9104917.
the different layers to surface reflectance measurements has remained a frustration. This paper relates surface photon flux to the photon propagation within a layered turbid medium using photon diffusion theory. Methods are discussed for extracting layering information from surface measurements and these methods are corroborated through ex vivo and in vivo experiments with biological tissue. THEORETICAL STUDY Difision Equation Modeling While numerical solution is generally necessary for models of photon diffusion in layered media, a closedform solution illustrates the simple case in which the medium is a uniform homogeneous diffusing material in a half space. The photon diffuse intensity, or space irradiance, \k (W/cm2) and the photon flux @at location ( r , 4 , 0) in the medium can be described as [ 131
v 2 w - , 4, 0)
-
k2wI-, 4,
e)
= ~ ( r4, ,
e)
(1)
4
F = -DV\k
(2)
where (I-,4, 0) are coordinates in a spherical system, S(r, 4 , 0) is the source term for diffused photons, and d is the diffusion coefficient (mm). The inverse of k is diffusion length (in mm); and furthermore, k2 is computed as k2 = E,/D = 3C,[Cs(1
- p)
+ E,]
(3)
where C, is the absorption coefficient (mm-I), E, is the scattering coefficient (mm-I) and p is the anisotropy parameter of the medium with values between - l and l . Isotropic scattering yields a value of p = 0, while pure backscattering yields p = - 1 and pure forward scattering yields p = + l . Diffusive sources can occur within the medium when unscattered photons enter and are then scattered beneath the surface. In the analytic model presented here, the scattering sources occur beneath the surface plane within a hemisphere (diffusor) of radius ro located at the origin in the coordinate system. This hemisphere becomes part of the boundary for the medium, so that S(r, 4 , 0) = 0 within the infinite half-space of the medium. The photon flux at each point on the hemisphere surface is dependent upon
0018-9294/92$03.00 0 1992 IEEE
~
'
111
I
I
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CUI AND OSTRANDER: RELATIONSHIP OF SURFACE REFLECTANCE MEASUREMENTS
source intensity Io and is chosen to vary with the angle 6 and to be independent of 4 so that the boundary condition is represented by =
-Io
COS
10 9 8
(e),
0
I8 I~
/ 2 . 7
(4)
6
In this representation, the angle 0 is measured with respect to the normal to the surface of the medium such that e = 0 for a vector directed into the medium. The medium surface outside the diffusing hemisphere ( r Iro, 0 I0 I r / 2 ) is represented as an ideal absorber, or in other words, the diffuse photon intensity at the boundary is zero ~141.
5
+(r, + n / 2 ) = 0,
e) = 0,
*(a,
(5)
for r 2 ro foro
e5
I
~ / 2 .
(6)
The distribution of photon intensity within the medium for the above boundary conditions is amenable to solution by separation of variables, yielding the following closedform solution [15]: e P pCOS (8)
where p
=
rk and the constant
(Y
3
2 1
0 0
2
4
6
8
10
Depth into tissue (kr) Fig. 1 . Computed diffuse intensity contours and maximum flux paths for a homogenous medium (separation and depth in normalized coordinates p = r k ) . The values of q,,(W/cm2) are 0.5/i5, i = 1, 2, 3, . . . , 15, for the contours from the innermost to the outermost.
(7)
is given by
and where po = r&. The reflectance on the surface for r > ro is
Diffuse Intensity Contours and Diffuse Flux Paths I ) Diffuse Intensity Contours: Let 9, = * / a be the normalized function dependent upon only p and 8 and which has a value of 2e-' at p = 1 and 8 = 0. Fig. 1 shows the isointensity contours (solid lines) of 9,.The values of 9, are 0 . 5 / i 5 , i = 1, 2 , 3, , 15, for the contours from the inner most to the outer most. The scattering of photons causes them to migrate along random paths in the medium before being absorbed or escaping from the medium through any point (i.e., target) on the boundary. At any point in the medium, the direction for maximum migration occurs normal to the isointensity contours such that the concentration gradient is largest. The dotted lines, referred to in the following discussion as maximum flux paths, are drawn in the gradient directions of the diffuse intensity. 2) Maximum Flux Paths: As is evident in Fig. 1, the reaching depths of different maximum flux paths depends upon the distance between the two ends on the surface (or the source-target separation). Weiss et al. [ 161 studied the statistics of penetration depth for a photon reemitted from
-
4
a diffusive medium. Their results demonstrated that the maximum depth attained by a photon exiting from the surface at any given source-target separation follows a distribution with maximum probability density at a calculated depth below the surface [ 161. This distribution and its maximum are affected by the separation between the source and detector and by the photon absorption within the medium. Given the statistical nature of the process, there is a path between source and target of maximum probability density. Since any departure from the maximum flux path (which is defined by the concentration gradients) reduces the probability of reaching the target, the path of maximum probability density must be coincident with the maximum flux path. 3) Simulation Study: For the layered medium, finite difference methods provide a solution to the diffuse intensity and yield isoconcentration contours and maximum flux paths shown in Fig. 2 . The model coefficients (i.e., the k values) of the medium layers were chosen based upon the values obtained by Amfield et al. [ 171, and are given in Table I. Due to symmetry of the three-dimensional medium, the solution of (1) is independent of the angular variable 4, producing a two-dimensional equation to be solved. In this two-dimensional mathematical system, the cylindrical coordinates are the vertical depth z into the medium and the radial distance r ' out from the z axis. The two-dimensional system was discretized and finite difference methods used. A single point in the solution grid, located at the origin, served as a source [15]. Thus, the source differed from the analytic solution, although in both cases the injection site was confined to a small area relative to the source-target separations. A comparison of the finite difference and analytic solutions to the problem of
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properties in a medium can be assessed by measuring the reflectance at different source-detector separations. 4) S u ~ a c eRejlectance Measurements: Surface reflectance measurements decay with distance from the source in approximately exponential fashion. To interpret variations in reflectance with structure and optical properties of a test medium, it is convenient to define an index which contrasts the reflectance R(r) from the test medium with that from a reference medium Rref(r).
Bottom layer
'6'
0"
10
8
Index(r) = In [R(r)/Rr&].
I 4
2
0
0
2
4
8
6
10
Dbtanw from lbM sourw (mm) Fig. 2. Computed diffuse intensity contours and maximum flux paths for a layered medium (medium I in Table I). The diffuse intensity q,, (in microwatts per cm2) for these contours, proceeding outward from the contour nearest thesource, are 1540, 308, 1 0 8 , 4 6 . 6 , 2 2 . 4 , 1 1 . 5 , 6 . 1 5 , 3 . 3 9 , 1.91, 1.10, 0.683, 0.375, 0.222, and 0.133, respectively.
TABLE I
k COEFFICIENTS AND DIMENSION OF THE LAYERS FOR THE FINITE DIFFERENCE REFLECTANCE SIMULATION Simulation Case Medium I (Homo.) Medium 2 (Homo.) Medium 3 (Layered) Medium 4 (Layered)
k, (I/") 0.43 0.33 0.23 0.23
kb (1 /mm)
0.43 0.33 0.43 0.43
d (mm)
-
-
1.0 2.0
Media 1 and 2 are homogeneous and are used as references. Subscripts t and b refer to top and bottom layers respectively.
the homogeneous medium showed that the differences became negligible as the radial distance from the source increased beyond 1/ k . Fig. 2 suggests that an increase in the source-target separation results in an increased portion of the flux path being imbedded within the lower layer. This, in turn, suggests that the lower layer will exert an increased influence on the reflectance, relative to that of top layer, as the source-target separation increases. From the nonintersecting property of the maximum flux paths in Fig. 1 and 2, it is observed that the maximum flux paths ending at larger source-target separations reach deeper into a medium, even for a nonhomogeneous medium. This analysis agrees with Takatani's conclusion [ 121 that to increase the influence from deeper tissue on the measured signal, large source-detector separation should be selected. This analysis also suggests that the depth distribution of optical
(10)
If both the reference medium and the test medium are homogeneous, it follows from (9) that Index@, when plotted against r, approaches a straight line of slope (kref k) for large r (curve 1 in Fig. 3) [15], where kEf and k refer to the k values for the reference and the test media, respectively. Fig. 3 uses a homogeneous reference medium for all curves with the kEf given at the top of the figure. In Fig. 3(a), curves 2 and 3, the k value of the bottom layer (kb) in the test medium is the same as the kEf. The index approaches a constant for large r, the magnitude of which depends upon the thickness of the top layer. The reflectance for large separation is proportional to that for the reference, but increased by 65 and 20%, respectively, as a result of the smaller attenuation of light in the top layer. It is also noted that the final index value is approached more rapidly as the thickness of the upper layer is reduced. The index curve slope for large sourcetarget separation is equivalent to the index curve slope for a homogeneous medium which has optical properties to match those of the deeper layer. The value of the index at large separations for the layered medium is shifted due to passage of light through the top layer. In Fig. 3(b), curves 2 and 3, the deeper layer has a different k value from that of the reference. Again, the index slope approaches that which would be expected for a homogenous medium with the same k value as the deeper layer. Since the reference k value is less than that of the deeper layer (kEf Ikb), the index has negative values corresponding at large r to a reduced reflectance for the two layer mediums as compared with the reference medium. Since the shape of the index curves for larger separations are controlled by the bottom layer, this suggests that the index curve pattern may be used to obtain the optical properties of the deeper tissue layers, while the effect from the top layer is eliminated.
EXPERIMENTAL STUDY The purpose of the experimental study was to determine whether the functionality observed in the indexes for layered media bore resemblance to behavior observed ex vivo and in vivo. Since the available reported studies of photon diffusion through biological media do not lend themselves to calculating and plotting the above described index, experimental data was collected. An ex vivo study provided conditions for directly relating the index to known structure of biological tissue. 'In vivo studies pro-
-
CUI AND OSTRANDER: RELATIONSHIP OF SURFACE REFLECTANCE MEASUREMENTS
a). Reference k
2
I97
0.43 /mm.
1.6
0.6
0 0
3
6 10 15 20 25 30 Sourcedetector separatlon (mm)
b). Reference k
-
0.33 /mm.
. - (8:+=a2U",~=a4Mnm. lyrulldmu = mm
Fig. 4. Probe design for measuring the surface reflectance at different source-detector separations and the photodetector response.
1
illumination intensity at the opening of the cylinder. As seen from the detector response curve in Fig. 4,the light wavelengths for this study fall in the passband of the detector. Since reflectances are analyzed as ratios at each wavelength (i.e., the index curve values), differences in detector sensitivity with wavelength cancel. The open face of the cylinder was in the same plane as the surface of the 32 concentric detector strips. Each strip consisted of an annular photosensitive segment of 0.9 mm width at a fixed distance from the light source, with 0.1 mm spacing between the strips. To attenuate inherent detector noise and the effect of stray light, the illumination was electrically modulated at 2000 Hz, and the received signal at the detector was amplitude demodulated. 0
5
10
16
20
25
30
Sourcedetector separatlon (mm) . (h\ ,-,
Fig. 3 . Simulation results in which the layered medium differs from the homoneneous reference medium. In (a) ~,the bottom laver has the same value for k i s the homogeneous medium, while in (b) boih top and deep layers have values of k which differ from that o f the reference. In (b), negative indexes are plotted for krCf < kb.
vided the correlation of index curves with expected physiologic changes associated with heat-induced hyperemia. Rejectance Probe and Measurement System High-intensity light emitting diodes (660 and 880 nm with an average source current of 50 mA) were held in place with clear epoxy in a stainless steel cylinder of 4 mm inner diameter (see Fig. 4) so as to provide equal
Ex Vivo Experiments A biological model was constructed from muscle, subcutaneous fat, and dermis which were sectioned from pork shoulder- The was cm across, cm thick* The dermal layer and the fat layer, of similar length and width, were 3-4 mm thick. The test models were constructed by covering the muscle with the dermal layer, or the fat layer, or both. Transmittance at 880 nm was measured separately for the dermis, fat, and muscle to determine their optical light transmission differences at this wavelength. The samples were each sandwiched between two pieces of plexiglass, and diffusively illuminated on one side using translucent plexiglass. The transmitted light intensity was measured at the opposite surface. The ratio of the transmitted light with and without the sample present was calculated, pro-
~
I 8
-
,
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 39, NO. 2, FEBRUARY 1992
198
TABLE I1 THETRANSMITTANCE OF THE EX vivo DERMIS, SUBCUTANEOUS FATAND MUSCLE (MEANf STD) AT 880 nm FOR Two SAMPLE THICKNESS (n = 5) Thickness
3.45 mm
4.95 mm
1.2
1 -
Dennis
Fat
Muscle
0.48 0.031 0.35 f 0.019
0.46 f 0.029 0.39 f 0.024
0.64 k 0.011 0.54 f 0.019
0.8
e 0.6
5 A
viding averaged (n = 5 ) transmittance values in Table I1 for each material. The results show that at 880 nm, the transmittances of the dermis and fat were relatively close to each other, but differed significantly from that for the muscle. To calculate an index for the experimental models using (1O), reflectance from the muscle was taken as the reference. Given in Fig. 5 are the resulting indexes which compare the reflectance from each assembled test model with the reflectance from the muscle by itself. The indexes show the differences in reflectance which occur due to the presence of a top layer or layers over the muscle. The initial increase of the negative index for these models is consistent with the higher attenuation of light in fat and dermis than in muscle (Table 11), which has a dominating effect at small separation of source and detector. The flat segment of these curves is consistent with an index reading from the deeper muscle layer. The combination of “dermis fat muscle” also suggests only a two-layer structure. This is consistent with the similarity of transmittance at 880 nm for fat and dermis such that the two materials together act optically as one thicker top layer. As a result of the greater top layer thickness in the threelayer combination, the knee of the curve occurs at a larger source-detector separation. The ex vivo experiment corroborates the simulation study results by showing a dependence of the index upon the layered structure. The index segments below and above the knee are influenced by the differences in optical properties of the upper and lower layers from the reference medium. The slope of the index curve at larger separation was representative of the dominant influence of the bottom layer of the layered model and the photons fat arriving therefrom. In the case of the “dermis muscle,” the muscle was approximately 7 mm beneath the surface from which measurements were taken.
+
+
+
Reference:’Muscle
I
+
In Vivo Experiments For in vivo studies, the surface of the skin was heated with a hot water bag at 40°C for 5 min so as to produce a change in circulation. The dermal circulation is significantly influenced by the environmental temperature so as to balance the heat generation and dissipation. Under the physiological condition, the dermal blood flow is about 20-30 times the blood flow necessary for supplying the oxygen requirement and this factor can be over 100 times in a hot environment [18]. The response of the skin to the local heating thus would result in a layered blood volume change through thermal regulation mechanisms in the dermis, which in turn results in a layered optical property
-
0.4
0.2
-
0 -
4.2’ 0
’
’
10
’
’
20
’
’
30
‘
40
Separation (mm) Fig. 5. Ex vivo index curves at 880 nm comparing the reflectance from the muscle only with that from the muscle covered by dermis and/or fat. Negative index is plotted.
change. The reflectance data prior to the heat application provided the reference for the reflectances during the period of approximately 20 min in which hyperemia was observed following heat application. Reflectance data, before and after hyperemia, were collected from eight subjects, with informed consent, so as to obtain examples of eleven index curves. The reflectances were measured at a selected site on the anterior surface of the lower leg, the calf, the anterior or lateral surface of the thigh, or on the surface of the forearm. During the ten minute test, the subject sat with the leg or arm slightly elevated depending upon the site of measurement. The source-detector probe was held lightly in place with tape and reflectances measured at both 660 nm and 880 nm. Fig. 6 is representative of these index measurements, showing an initial rapid rise of the negative index, followed by a region at larger source-detector separations of lesser slope. Inference from the simulation and ex vivo studies suggest that the initial increase below the knee of the curve represents a significant absorption increase in the top layers for the hyperemic states. The apparent changes in top layer absorption is consistent with increased blood volume and flow in the dermis, in response to the local heating. Fig. 7 shows the index curve slopes for the first segment of the index below the knee of the curve and the second segment above the knee, from the eleven measurements. In the data collected in the first segment of the curve, the hypothesis that the index curve slopes at 660 and 880 nm were the same could not be rejected by student’s paired t-test ( p I0.05). Since the blood absorption is different at the red and infrared wavelengths, the similarity of the slopes in the first segment at 660 and at 880 nm suggests that no significant change in oxygenation took place in the shallow thermoregulating layers during the hyperemic response. This is possible when the blood
199
CUI AND OSTRANDER: RELATIONSHIP OF SURFACE REFLECTANCE MEASUREMENTS
Reference: Normal Reflectance 1.6 ,-
1.2 -
1.4
h
e
1 -
-
5 0.8 -
5 0.6
0
5
10
15
20
25
30 35
40
separauon Fig. 6. An example of in vivo index curves at 660 and 880 nm. In this case, measurements were taken on the lateral side of the thigh. Negative index is plotted.
0.3 0.25
0.2
E
0.15
i
0.1
0.05 0 -0.05
A1
Bl
82
C1
D1
El
F1
F2
F3
F4
01
AL
LT
AT
LT
LC
Subject I.D. LC
FA
LC
LT
LC
LC
Sample Site
(a) Fig. 7. The linear regression slopes for (a) the first segment (below the knee at smaller source-detector separations) and (b) the second segment (above the knee) of eleven in vivo negative index curves from eight subjects. Measurement Site: AL-anterior surface of lower leg; AT-anterior surface of thigh; FA-forearm; LC-lateral surface of calf; LT-lateral surface of thigh.
is highly oxygen saturated and remains so with the increased blood volume and flow of hyperemia. The oxygen saturation is normally expected to be high due to excessive flow in the thermoregulating region [ 181. The separation between the first and second segments for the red and infrared curves may indicate the depth of the thermoregulating vascular beds in which blood flow exceeds that necessary to meet the metabolic demand for oxygen. The smaller index slope in the second segment suggests a less significant change in deep tissue optical properties with hyperemia. The negative second segment slope for
subjects C 1 and D 1 suggests a decrease in blood volume in the deeper tissue after the local heating for these subjects. The difference in the red and infrared responses in the second segment can be attributed to the differences in photon absorption at the two wavelengths associated with changes in blood volume and oxygenation in the deeper tissue. An increased dermal circulation outflow with high oxygenation could increase the mean blood oxygenation in the venous network in the deeper tissue. Given the effect of oxygenation upon light absorption, the increased
0.03 0.02
E 5
O.O1
! L o
m
4.01 4.02 -0.03
A1
B1
82
C1
D1
El
F1
F2
F3
F4
Ql
AL
LT
AT
LT
LC
Subject I.D. LC
FA
LC
LT
LC
LC
Sample site (b) Fig. 7. (Continued)
oxygenation would provide additional absorption to the light at 880 nm and lesser absorption at 660 nm [ 191. The effect on light absorption of both increased volume and increased oxygenation at the infrared wavelength would be additive, but at the red wavelength would be expected to partially cancel, resulting in a lesser slope of the red index curve when compared with infrared. This effect is seen in Fig. 7 where in all data collected beyond the knee, the slope of the index curve was larger for 880 nm than for 660 nm. The hypothesis for the second segment that the slope was smaller at 880 nm or equal to that at 660 nm was rejected by student’s paired t-test (p 5 0.005). DISCUSSION AND CONCLUSION Diffusion theory has been used to relate the optical properties of a layered turbid material to the reflectance on the surface. Our theoretical study has introduced the concept of photon flux paths to describe, in an averaged statistical sense, the escape of photons following their propagation through a diffusive medium. The study suggests that the internal optically differentiable structure can be assessed by photon flux measurements on the surface of the medium. A closed-form three-dimensional photon diffusion model was developed to describe the photon density distribution in the diffusing medium. With this model and with additional results of simulation methods and ex vivo experiments, the layered optical property distribution in a medium and its relation to reflectance were studied. The simulation suggests that photons measured at larger source-target separations have penetrated more deeply even when the medium is heterogenous. The modeling and finite difference simulation approximate the experimental conditions with some differences in boundary conditions and in source specifications. Reflections at the surface of the medium are not included in the theoretical analysis, and are assumed to be negligible,
based on previous studies [ 141. Agreement of the theory and experiment in the present study supports this approx. imation. The different light source specifications used in the modeling and finite difference simulation resulted in a difference in diffuse intensity distribution only in the immediate vicinity of the light source. In the experimental studies, the tissue beneath the light source acted as a light diffusor. The anisotropic scattering property of tissue can result in a stronger photon flux for small 6 in the immediate vicinity of the source. Beyond the immediate vicinity of the source, the illumination is effectively diffusive such that deeper penetration of the photons is measured at larger separations. In addition, since the index defined in (10) compares the reflectances measured by the same source at the same location, the effect of the differences among illumination sources is minimized. The index of (10) assesses the layered optical property differences of two media by comparing their reflectances. The corroborating results of the simulation and of the ex vivo studies demonstrate the capability for assessing layered differences using the index. The shape of the in vivo index curves is consistent with a significant blood fractional volume change in the dermal layer for hyperemic skin, and the slope for the later segment of the index curve corresponds to the optical property changes for the tissue beneath dermis, as analyzed in the simulation study. The index response with layering, as inferred by the modeling study, changes with differences in the k value, which can be a combined effect of E,, E,, and p . Thus, the index profile measured on the surface should be interpreted as a layered k distribution rather than layered distribution in E,, E,, or p. Both the thickness of the upper layer and the difference between the k values of the upper and lower layer affect the shape of the index curve. A thicker upper layer or a larger difference in the k values results in larger initial slope changes. This study suggests that surface measurements are sensitive to deeper tissue
CUI AND OSTRANDER: RELATIONSHIP OF SURFACE REFLECTANCE MEASUREMENTS
optical properties and that features of the measurements at larger source-detector separation tend to be independent of upper layer effects. In general, the Sensitivity Of surface measurements to the optical properties of the unat different depths is derlying biological tissue governed by (1). The method of analysis utilizing an index requires a reference medium for comparison. The reference may be selected to have an optical constant, or k , value close to the range of values of the tested medium so as to yield good resolution of the layering since biological tissues have different diffusive behavior and therefore different Optical constants at different wavelengths, it may be to use the Same tissue for both test and reference purposes, but with different wavelengths. Also, a reference may be provided by the reflectance prior to a physiological perturbation as was done for the in vivo study in this paper. The studies described in this paper demonstrate the assessment of intemal optical properties by measurement on the surface, so as to separate the effect of the top layer from the effect of the bottom layer of tissue on the measured photons. The studies of this paper utilizing the maximum flux path concept have relied upon the statistical behavior of photons and upon the context of photon diffusion theory. In general, the photon paths are affected by physical properties such as the scattering and absorption coefficients of the medium and by the anisotropy of the medium. The diffusion theory is based on the assumption of weak anisotropy and the assumption of much stronger scattering than absorption, drawn from more general but less easily applicable theories of radiative transfer [20]. Weak anisotropy is not always the case for biological tissue ( p can be higher than 0.9 [21]). Consequently, the reaching depth of the maximum flux paths may be affected by the different anisotropy of biological tissue. The heterogeneity of biological tissue will also contribute to the variation in the location of the maximum flux paths. By developing methods which distinguish properties at depth within the diffusive medium, the study also suggests the possibility in the future of imaging the layered and other structural patterns of optical properties for in vivo tissue by the use of surface measurements.
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Weijia Cui received the B.S. degree in electrical engineering from Xi’an Jiaotong University, China, in 1982; the M.S.degrees in biomedical engineering and electrical engineering in 1987 and 1989, respectively; and the Ph.D. degree in biomedical engineering in 1990, all from Rensselaer Polytechnic Institute, Troy, NY, in 1990. His research interests focus on the tissue optical modeling and noninvasive measurement with light. He did his postdoctorate research at the Department of Biochemistry and Biophysics, University of Pennsylvania. Currently, he is a senior engineer in the BOC Technical Center, Murray Hill, NJ 07974.
Lee E. Ostrander (S’61-M’66-SM’77) received the A.B. degree from Hamilton College, Clinton, NY, in 1961, and the M.S. and Ph.D. degrees in electrical engineering in 1963 and 1966, respectively. He is currently Associate Professor of Biomedical Engineering and Executive Officer of the Biomedical Engineering Department at Rensselaer Polytechnic Institute, Troy, NY. His research interests include the optical properties of soft tissue and the noninvasive and in vivo measurement of blood flow and mechanical properties of soft tissue. Dr. Ostrander is a former President of the IEEE Engineering in Medicine and Biology Society.
