1. SPECTROPHOTOMETRIC DIFFERENTIATION OF HUMAN SKIN MELANOMA II. DIAGNOSTIC CHARACTERISTICS V.G. PETRUCK 1, A.P. IVANOV 2, S.M. KVATERNYUK 1, V.V. BARUN 2 1 Vinnica National Technical University, Vinnica, Ukraine 2 B.I. Stepanov Institute of Physics, Belarus National Academy of Sciences, Minsk, Belarus petrukvg@gmail.com barun@dragon.bas-net.by

2. Our goal is to design an objective, non-invasive optical tool for discriminating melanoma skin of a person from intact (healthy) or benign nevus (non-dangerous) skin and to evaluate its diagnostic characteristics. ABSTRACT. Experimental data on the spectral light diffuse reflectances (DR) of skin of different persons with melanoma or nevus are represented as the DR probability densities of the respective pigment formations. A non-invasive technique for differentiating the malignant and benign tumors is proposed, which is based on the measurement of a DR value for a specific patient and its comparison with a prior threshold DR. When the experimental result is lower than the threshold, the conclusion on melanoma of the patient is made. When the opposite situation occurs, one assumes that there is no melanoma. A wavelength of 870 nm is considered as an example. The risk of malignant nevus (formation of melanoma) is calculated for various measured DR values. The errors of the method, its operational and probabilistic characteristics are investigated at the varying threshold. The reliability, sensitivity, specificity, and efficiency of the method are derived to be maximal and to exceed 0.82 at the threshold of 0.45 – 0.47. The operational characteristics of the proposed technique are shown to be higher, in principle, than the respective performances of other optical approaches to diagnose melanoma known from the published data. The technique features in the operation at a single wavelength and, as a consequence, in the simple and cheap experimental device for its implementation. The ways for further investigations and development of the obtained results are outlined.

3. Content 1. Introduction 2. Probability density of R for melanoma and nevus skin Spectrophotometric method of differentiation3. Spectrophotometric method of differentiation 4. Probabilistic characteristics of the method 5. Statistical testing 6. Errors and operational characteristics of the method 7. Results 8. Comparison with published data 9. Conclusion

4. 1. Introduction It is known from numerous publications that early detection of melanoma essentially enhances the long-term survivability of patients. For example, 10-year survival rate is 80 – 95 % at early stages of the disease and drops to 8 – 15 % at latest ones. Currently, the main technique of the detection of a malignant tumor state is visual inspection of skin, making the preliminary decision by using the ABCDE rule, surgical intervention, and final diagnose on the base of histological evaluation of a tissue sample. There have been proposed optical means [1 – 3] for exposing the melanoma and its differentiating with respect to other oncologic and benign tumors on the base of light characteristics backscattered by tissue at several wavelengths (540, 650, 950 nm [1] and 560, 650, 700, 760 nm [2, 3]). But usage a number wavelengths complicates the experimental equipment and will be shown below leads to the error increase due to the growth of the variance of random observations. The physical basis of our method is an experimentally established fact that probability densities f M (R) and f N (R) of observations of diffuse reflectance R for melanoma (M) and nevus (N) are different to overlap within only narrow range of R. This enables one to construct a procedure for preliminary diagnostics and differentiation of melanoma and nevus. It is understood that the method is probabilistic and cannot replace the final decision of a physician. The probabilistic and operational characteristics of the method will be evaluated below by comparison of the non- invasive measurements with histological analysis of tissue samples in clinical conditions.

5. 2. Probability density of R for melanoma and nevus skin Fig. 1. Histograms of R values at wavelength 870 nm for nevus (left) and melanoma (right). Left ordinate – number of cases, right ordinate – normalized probability density. Curves – approximation by normal distribution

6. Fig. 2. R values for intact skin (Int), skin with melanoma (M) and nevus (N) at 870 nm. Boxes show interquartile range, point inside them – medians, vertical bars – minimal and maximal values One can see from Figs. 1 and 2 that the R distributions for melanoma and nevus overlap. This prevents from unambiguous expose of the corresponding pigment formation.

7. 3. Spectrophotometric method of differentiation We will use a threshold method for differentiation and diagnostics of melanoma. It consists of the measurement of diffuse reflectance of skin with pigment formation and the comparison of the result with a selected threshold R* that divides all observations onto two regions of “melanoma” and “no melanoma”. If R < R*, one concludes that there is melanoma, Otherwise, melanoma is absent. The data of Fig. 1 will be used to evaluate the characteristics of the method. Note that these data are obtained after skin diagnostics on the base of the histological analysis by a physician. Any measurement result can be insert in the below Table. PhotometryHistological analysis sickhealthy sick (positive result of test) Number of true positives, a Number of false positives, b healthy (negative result of test) Number of false negatives, с Number of true negatives, d

8. 4. Probabilistic characteristics of the method Write down numbers a, b, c, and d via probabilities of Fig. 1: There participated a + c = N M = 35 and b + d = N N = 35 persons in experiments. Naturally, all the numbers a, b, c, and d are random.

9. 5. Statistical testing Is the null hypothesis on the same densities F M (R) and F N (R) true? Evaluate this by using the Kramer – Welch’s T-test. Mean diffuse reflectance values and their variance were taken from our Internet presentation 1 for sample sizes N M = 31 and N N = 20. Experiments performed later for N M = 70 and N N = 84 showed that these values did not change essentially. The test gave that the significance level of the hypothesis is less than 0.0035. In other words, one can conclude that functions F M (R) and F N (R) are different with probability more than 0.996. This creates the statistical substantiation of the threshold method on the base of probability densities F M (R) and F N (R).

10. Let k = N N /N M. One usually introduce errors of the first (  ) and second (  ) kinds  = b/(a + b + c + d) = kp b /(1 + k) (1) and  = с/(a + b + c + d) = p c /(1 + k),(2) that characterize a fraction of wrongly diagnosed persons in the total number of volunteers. The reliability of the method is assumed to be  = 1 – (  +  ). Besides, the following operational characteristics are used: - sensitivity, D 1 = a/(a + c) = p a, (3) – specificity, D 2 = d/(b + d) = p b,(4) – efficiency, D e = (D 1 + D 2 )/2,(5) – positive predictive value), P 1 = a/(a + b) = p a /(p a + kp b ),(6) – negative predictive value, P 2 = c/(c + d) = p c /(p c + kp d ).(7) Quantities (1, 2) and (6, 7) are obviously to depend both on threshold R* and ratio k. So, having the distributions of Fig. 1, one can easily recalculate the characteristics of Eqs. (1, 2) and (6, 7) for any k. 6. Errors and operational characteristics of the method

11. 7. Results Consider first the malignant transformation risk, which is r M (R) = n M /(n M + n N ) = N M F M (R)/[N M F M (R) + N N F N (R)] Fig. 3. Malignant transformation risk as a function of measured R at k = 0.1 (curves 1), 1 (2), 3 (3), and 20 (4) One can see that at R 0.51 it is absent. For R=0.44 – 0.51, the both situations are possible.

12. Fig. 4. Errors  (left) and  (right) as a function of threshold reflectance There is arisen a question: what threshold should one select? The answer is understood to depend on what characteristic should be minimize or maximize. Apparently, the most dangerous is error , when the method tells on “no melanoma”, but it occurs really. One should select R*>0.51 to minimize . However, this leads to increasing false diagnoses and reducing the reliability of the method. Note that the reliability is maximal (0.96 – 0.98) at R*= 0.42 – 0.44, когда  ≈  ≈ 0.01 – 0.02.

13. Fig. 5. Operational characteristics D 1 (curve 1), D 2 (2), D e (3), Р 1 (4), and Р 2 (5) as a function of threshold reflectance at k = 1 Threshold R*= 0.42 – 0.44 provides the sensitivity, the specificity, and the efficiency of the method larger than 0.85.

14. 8. Comparison with published data Paper [2] proposed the criterion of K = W 760 /W 560 to differentiate melanoma (W 760 and W 560 are backscattered light power values at = 760 and 560 nm). When K>1.2, the pigment formation is melanoma, otherwise it is absent. Calculate variance V K of ratio K. Assume that values independent. This assumption is rather reasonable because fluxes W 760 and W 560 are mainly determined by the absorption of different tissue chromophores, namely by melanin and blood, respectively. Then, where the bar means averaging over observations. Compare V K with variance V 760 of the flux at a single wavelength of 760 nm. Consider difference  V = V K – V 760. It is It is easily to show that  V >0. In other words, the overlapping range for ration K is larger for melanoma and nevus than that of R at 760 nm. Note that V 760 ≈ V 870. used in this work. Hence, the operational characteristics at a single = 870 nm will be better than the same at the two wavelengths. Apparently, large values of D 1 = 0.83 – 0.89 and D 2 0.8 – 0.96 [2, 3] are due to small sample sizes N = 5 – 12. The similar estimations can be made for the variance of criterion [1] logQ M > logQ N or Q M > Q N, where Q M, Q N = W 540 /(W 650 W 950 ) are determined at = 540, 650, and 950 nm for melanoma and nevus (or healthy skin). Our data give Q M = 1.99 and Q N = 1.86 or the criterion for melanoma is fulfilled.

15. 9. CONCLUSION We considered here a threshold method for differentiating skin melanoma and nevus implemented at a single wavelength of 870 nm. One can use other wavelengths, where the probability of different random values of diffuse reflectance is high. The usage of the method enables one to select an optimal procedure for surgical intervention. We are planning to make additional experiments to increase the sample sizes N N and N M, to evaluate the operational characteristics at other wavelengths, and to find optimal. Full texts of our presentations will be published in Journal of Applied Spectroscopy at the end of the year or at the beginning of the next year.

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