Mapping Blood Oxygen Saturation using a Multi-Spectral Imaging System

Transcription

1 Mapping Blood Oxygen Saturation using a Multi-Spectral Imaging System by Peter J. Dwyer, R. Rox Anderson, M.D. Massachusetts General Hospital Wellman Laboratories of Photomedicine Boston, Massachusetts Charles A. DiMarzio Center for Electromagnetics Research Northeastern University Boston, Massachusetts ABSTRACT Recent advances in imaging spectroscopy provide the opportunity for mapping the oxygen saturation of blood in skin with high accuracy, large spatial coverage, small spatial resolution, and high update rate. A four wavelength algorithm, specifically designed to compute the oxygen saturation of hemoglobin, in vivo, from a set of narrow-band visible images was used to analyze various skin tissue disorders. To illustrate the spatial capability of this algorithm, mapping of the oxygen saturation of normal skin, hypoxic tissue and various skin lesions was performed using reflectance spectroscopy, demonstrating the spatial resolution of the images of blood oxygen in the tissues. To explore the accuracy of the algorithm, Monte Carlo modeling was used to generate reflectivities of skin with known parameters. These reflectivities were used to evaluate the limiting effects of quantization error, photon noise, and finite filter bandwidth on the accuracy of the algorithm. In addition, a signal to noise (SNR) analysis was performed to determine the illumination requirements. It is shown that accurate maps of blood oxygen can be produced with good spatial resolution. 1. INTRODUCTION Reflectance spectroscopy is a common technique to determine the concentrations of chromophores, such as hemoglobin, in biological tissue. One common application is to calculate oxygen saturation in tissue using optical fiber probes in the reflectance or transmission modes.' The determination of the levels of light absorption by blood in tissue can be used to calculate the total oxygen saturation levels of the tissue. The feasibility of using imaging techniques to spectroscopically measure oxygen saturation in human dermis tissue phantoms and in vivo skin has been determined. This paper illustrates the results of an algorithm for computing oxygen saturation using four wavelengths.2 Spectral measurements on dermis phantoms were made using a multi-spectral imaging system and 270 SPIE Vol X/971$10.00

2 compared to existing published point measurement algorithms for determination of oxygen saturation. The imaging system consists of a 300 watt tungsten light source that directs linearly polarized light onto the target tissue.2 Reflectance is measured through a computer controlled birefringent, wavelength tunable filter (Cambridge Research Instrumentation, Cambridge, MA) with a full width half maximum 8 nm bandpass. Images are then taken with a standard black and white charged coupled device (CCD) camera, then digitized and stored in a personal computer using a video capture board. The images are later processed using the four wavelength algorithm to determine oxygen saturation. Spectral measurements were done in vivo on normal, ischemic and altered conditions of human skin. Monte Carlo simulation models were performed using properties of human skin3'4 to calculate reflectivities to verify the Lambertian nature of the reflectivity of skin, and to calculate the accuracy of the four wavelength algorithm. Photon noise and finite filter bandwidth effects have been analyzed using these reflectivities. Signal to noise ratio analysis quantified the performance of the multi spectral imaging system and camera/filter capabilities. 2.1 Measurement Configuration 2. REFLECTANCE FROM TISSUE Several optical configurations can be considered for reflectance measurements on biological tissue and different results are expected depending upon the configuration. The differences arise from tissue characteristics, the penetration depth of the light and the differences in collection areas and solid angles. The tissue considered is a two layer model appropriate for skin, consisting of a thin layer of blood less epidermis over the dermis which contains the chromophores oxygenated and deoxygenated hemoglobin. In the determination of oxygen saturation, the spectrum of reflected light is influenced by a combination of the two different spectra of the hemoglobin in the dermis. In using an imaging system for measurement, the reflectance is measured in the same manner as with a radiometer, which only detects the light in a small solid angle, and from a limited area of the sample. If the area is smaller than the incident beam, this technique determines the scattered radiance, divided by the incident irradiance: LR(X, y, 6, ) R1- (1) I where 6 and çb are angular coordinates measured from the point of incidence to the radiometer. 2.2 Simple Model Prediction of the behavior of light in a turbid medium has been the subject of many research efforts, both experimental and analytical.5'6 The goal here is not to predict 271

3 the reflectance quantitatively, but to postulate a functional form with sufficient degrees of freedom to fit actual measurements in a way that allows determination of the oxygen saturation. The simple concept of reflectance by a two layer model can be addressed with the aid of Figure 1. Light entering the medium is scattered along a random path involving many scatterers. Absorption may occur at any point along the path. In this model, light is incident on a layer (the epidermis) not containing significant amounts of chromophore. Some of this light passes through the layer to the underlying layer (dermis), containing scatterers and chromophores (oxygenated and deoxygenated hemoglobin, and perhaps others). It is assumed that the absorption processes in the dermis are linear, and that there is no fluorescence. The absorption and scattering is commonly characterized by an exponential decrease in flux density with distance along the path, so that for a particular path, the radiance can be represented by LRij=Sexp{ f. (s+a)d}, (2) path[j *z] where /i is the scattering coefficient, a 5 the absorption coefficient, and S is a constant that depends on all of the scattering processes involved along the path. However in an imaging format, incident and reflected light are not spatially separated and Equation 2 must be integrated over all possible paths. For strong scattering media, the direction of exiting light will be randomized thus leading to a Lambertian reflectivity. We assume that the total reflectance from a single layer of tissue is the transport albedo: R1=, (3) /28 +1-La where /i = (1 g),u is the reduced scattering coefficient, and g is the anisotropy, obtained by averaging the cosine of the scattering angle. 2.3 Blood Oxygen Saturation Determination A four wavelength algorithm was used to calculate oxygen saturation using the wavelengths of 570, 586, 600 and 610 nm. Our goal is to obtain absorption from measured reflectivities: it R1 The calculation of the absorption then leads to the solution of oxygen saturation s by modeling the dermal absorption as (4) = k0cs + kdoc(1 s) + /Lao (5) 272

4 where k0 and lcdeoxy are the molar extinction coefficients of oxygenated and deoxygenated hemoglobin, C is the total hemoglobin concentration,,uaq is absorption due to other chromophores in the dermis other than blood and s is the desired oxygen saturation fraction. The oxygen saturation is defined by s= [HbO] (6) [HbO]+[Hb] n IJIAI n//is' Figure 1 SYMBOLIC REPRESENTATION OF LIGHT INTER- ACTING WITH TWO-LAYER TISSUE. The left side shows scattering and absorption in the epidermis resulting in a signal independent of the dermis. The center shows scattering from and absorption in the dermis, which depends on blood concentration and oxygenation, but is attenuated by the epidermis. The right side shows a more complicated path. 273

5 In the two layer model shown in Figure 1, light may be absorbed or scattered in the epidermis. It may also pass through the epidermis where it is then absorbed or scattered. Light returned from the dermis in this way suffers absorption on transmission in both directions through the epidermis. More complicated scattering paths also exist, including those in which light is scattered into and out of the dermis more than once, but these will be neglected in establishing the simple model. The total reflectivity at a particular wavelength can therefore be described as R(A) = R0 + T2,. (7) The intervening layer reduces the measured albedo by T2, where T is a transmission coefficient, and also contributes it's own reflectivity, which will be called R0. For the present work, both R0 and T are assumed independent of wavelength. Any more complicated interactions are ignored in the model. There are four terms in this equation that are assumed to be unknown, including S which we seek and R0, C, and T21a' which are unrelated to the chromophores.2 The equations can not be solved in closed form for the four unknowns, and numerical techniques are required. 3. RESULTS 3.1 Monte Carlo Simulation A set of Monte Carlo simulations was undertaken to evaluate the algorithm described above. A well known Monte Carlo program7 was used, with input parameters including absorption coefficient, scattering coefficient, and anisotropy5 depending on wavelength. The first test was to determine the validity of the Lambertian assumption. Figure 2 shows the results for a two layer model. The solid line shows the total reflectance and the dotted line shows the reflectance per steradian, multiplied by it, added to the specular reflectance of about 2%. The structural dimensions of the tissue model were made similar to normal human skin with an epidermis of 65 microns and an optically thick dermis of 4 mm. The excellent agreement suggests that the tissue acts as a Lambertian scatterer. The second Monte Carlo simulation test was to validate the four-wavelength algorithm's estimate of oxygen saturation solving Equations 5 and 7 for oxygen saturation using reflectivity results from the Monte Carlo simulation. In Figure 3 the concentration of hemoglobin remains the same, but the oxygen saturation is varied over a wide range. The results show that a linear correlation exists between input s to the Monte Carlo model and estimated by the algorithm. This validates the four wavelength algorithm with proven tissue models. 274

6 Estimale from 15 deg Cone +2 % b r )\, Wavelength, nm Figure 2 MONTE-CARLO TEST OF THE ASSUMPTION OF LAMBERTIAN SCATTER. The close agreement between the total reflectance (solid line) and reflectance in a solid cone integrated over r steradians (dashed line) indicates that the Lambertian assumption is valid. 3.2 Signal to Noise Ratio Determination In any imaging sensor, but particularly one in which white light is filtered into narrow bandwidth channels, it is important to ensure that the signal is sufficiently above the noise to produce a good image. Given a light source of power, F, illuminating a target of area A, from an effective solid angle,, the spectral irradiance on the target is = 47r ii (8) where f,. is the fraction of the source power per unit bandwidth (expressed as wavelength) of the detector. For example, if the source is modeled as a 3000 K black body, at a 275

7 Cf 0 ci) Sat Figure 3 MONTE-CARLO MODEL and ALGORITHM COM- PARISON. The concentration of Hemoglobin is held constant and the oxygen saturation, s is varied. The estimate,., computed by the algorithm is plotted as a function of s. wavelength of 586 nanometers, fa is per nanometer. For a power of 300 Watts and a solid angle of 0.16 steradians, illuminating an area of 200 square centimeters, EA = 6.3 1uW/cm2/nm. The scattered spectral radiance is LA = R(A)EA1 (9) for a Lambertian target, where R(A) is the diffuse reflectivity of the target at the wavelength of interest. In the example above, for R(A) = 0.3, LA = 0.6 pw/sr/cm2/nm. 276

8 If the filter has a peak transmission, T0, and a bandwidth z\, the approximate radiance at the focal plane is L = LA T0 za, (10) or, in the example, for an 8 nanometer wide filter and a peak transmission of 60 percent, L = 2.9 W/sr/cm2. A CCD camera specification normally gives the required illumination in Lux to obtain a sufficient signal to noise ratio, assuming "normal" illumination. Because the camera response and the conversion from radiometric to photometric units both depend on wavelength, it is important to convert the radiance and the camera specification to units involving photoelectron count, which is the parameter measured by the camera. Thus, the photon radiance is (for small bandwidth) L Lh0t0 =, (11) where h is Planck's constant and i-i is the optical frequency. In the example, this is 8.6 x 10'6Photons/sec/sr/m2. For a pixel which is 10 micrometers square at f/i, this corresponds to N = Lh0t0 ()2 Apixei (sec) or 280,000 photons. The standard deviation of the Poisson distribution with this mean number is the square root of N, resulting in a quantum limited signal to noise ratio of 27 db. Assuming the camera is specified for viewing with 5000-K illumination, the conversion factor is 2.5 x 1016 photons per second per Lumen, so a camera sensitivity of 0.5 Lux corresponds to 1.25 x 1016 Photons/sec/sr/rn2. Thus the available light is about 7 times that required by the camera specification. This camera is marginally acceptable for these conditions, and some averaging of adjacent pixels is required. A camera having a sensitivity of 0.05 Lux would be more than adequate. 3.3 Tissue Imaging of Oxygen Saturation A number of patients with psoriasis were imaged using the imaging system described by Dwyer et. a].2 Psoriasis is a lesion of the skin where the epidermis proliferates 10 times faster than normal epidermis and the psoriatic plaque has increased dermal capillary density and infiltration into the epidermis. These lesions were of interest due to the known pathophysiology and interesting microangiography at the border between the lesion and 277

9 rft "ci 1 * Figure 4 OXYGEN SATURATION IMAGE OF A PSORIATIC PLAQUE. The horizontal line marks line 270, for which data is shown in Figure 5. normal skin. The growth and invasion of psoriasis into normal skin is poorly understood. Figure 4 is an image of s from a psoriatic plaque and normal skin on the lower extremity. 278

10 In this processed grayscale image, black corresponds to s = 0.4 and white to s = 0.9. The numerical value of s is plotted in Figure 5 for the line shown in Figure 4. As expected, the psoriatic plaque has increased oxygen saturation due the increase in capillary density, while the normal skin has sub-mean oxygen saturation. Interesting effects can be seen by analyzing the border of the psoriatic plaque and the distinct contrast in oxygenated hemoglobin. Further analysis of the images, with improved image processing could reveal the determination of psoriatic plaque growth progression C 0.7 cf C x, Column Figure 5 Oxygen Saturation on Line CONCLUSIONS The Monte Carlo simulation shows that it is possible to develop approximate forward models for imaging sensors using CCD cameras, and to numerically invert these models to obtain oxygen saturation. Monte Carlo results show that human dermis in vivo behaves like a Lambertian scattering surface, and that the estimate of oxygen saturation can be linearly correlated with actual oxygen saturation measurements. 279

11 Imaging and analysis of psoriatic plaque in patients using an imaging system and algorithm developed by Dwyer et. al. was performed and provided expected oxygen saturation values. The margins of the lesion were easily observed. Analysis of these images and other skin lesions can be important in determining the pathophysiology and microangiography of diseased skin. 5. REFERENCES 1. Knoefel, W.T., Kollias, N., Rattner, D.W., Nishioka, N.S., and Warshaw, A.L., "Reflectance Spectroscopy of Pancreatic Microcirculation," Journal of Applied Physiology, Jan page Dwyer, P.J., DiMarzio, C.A., Tearney, G.J., and Anderson, R.R., Publication Pending. 3. Wan, S., Anderson, R.R., Parrish, J.A., "Analytical modeling for the optical properties of the skin with in vitro and in vivo applications," Photochem. Photobiol., 1981 v 34 page Anderson, R.R., Parrish, J.A., "The optics of human skin," J. Invest. Dermatol., 1981 v 77 page Van Gemert, M.J.C., Jacques, Steven L., Sterenborg, H.J.C.M., Star, W.M., "Skin Optics," IEEE Transactions on Biomedical Engineering, Dec 1989 v 36 n 12, page Patterson, Michael S., Ephraim Schwartz, and Brian C. Wilson, "Quantitative Reflectance Spectrophotometry for the Noninvasive Measurement of Photosensitizer Concentration in Tissue During Photodynamic Therapy," Photodynamic Therapy Mechanisms, SPIE Volume 1065, Pp Jacques, Steven L., and Lihong Wang, Monte Carlo Modeling of Light Transport in Multi Layered Tissues in Standard C, M. D. Anderson Cancer Center, University of Texas, 1992, Pages. 280