Mathematical Modeling of Sensitivity and Specificity for Basal Cell Carcinoma (BCC) Images

  • Sudhakar Singh
  • Shabana Urooj
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 701)


In this paper, mathematical modeling for malignant and non-malignant basal cell carcinoma is proposed. Image features are used for the modeling of growth rate, sensitivity, and specificity. Newton’s law and Hooke’s law play very important role in the modeling of growth, sensitivity, and specificity of basal carcinoma cell (BBC). Two features mean and entropy are used for two different positions. These two features are taken from the image data database of 550. Maximum growth rate of non-malignant and malignant BBC for the two different positions are 7.945, 10 and 19.76, 12, respectively. Maximum sensitivity and specificity calculated for malignant and non-malignant images are 0.8425, 0.3225 and 0.8512, 0.1992, respectively.


Growth of BCC Sensitivity Specificity Newton’s law 


  1. 1.
    Yerushalmy, J.: Statistical problems in assessing methods of medical diagnosis, with special reference to X-ray techniques. Public Health Rep. (1896–1970) 62, 1432–1449 (1947)Google Scholar
  2. 2.
    Greenberg, R.A., Jekel, J.F.: Some problems in the determination of the false positive and false negative rates of tuberculin tests. Am. Rev. Respir. Dis. 100(5), 645–650 (1969)Google Scholar
  3. 3.
    Goldberg, J.D.: The effects of misclassification on the bias in the difference between two proportions and the relative odds in the fourfold table. J. Am. Stat. Assoc. 70(351a), 561–567 (1975)CrossRefGoogle Scholar
  4. 4.
    Eves, P., Layton, C., Hedley, S., Dawson, R.A., Wagner, M., Morandini, R., Ghanem, G., Mac Neil, S.: Characterization of an in vitro model of human melanoma invasion based on reconstructed human skin. Brit. J. Dermatol. 142(2), 210–222 (2000)CrossRefGoogle Scholar
  5. 5.
    Nissen-Meyer, S.: Evaluation of screening tests in medical diagnosis. Biometrics 20, 730–755 (1964)CrossRefGoogle Scholar
  6. 6.
    DeLong, E.R., Vernon, W.B., Bollinger, R.R.: Sensitivity and specificity of a monitoring test. Biometrics 41, 947–958 (1985)Google Scholar
  7. 7.
    Ransohoff, D.F., Feinstein, A.R.: Problems of spectrum and bias in evaluating the efficacy of diagnostic tests. N. Engl. J. Med. 299(17), 926–930 (1978)CrossRefGoogle Scholar
  8. 8.
    Sudha, J., Aramudhan, M., Kannan, S.: Development of a mathematical model for skin disease prediction using response surface methodology. Biomed. Res. (2017)Google Scholar
  9. 9.
    Mendes, A.I., Nogueira, C., Pereira, J., Fonseca-Pinto, R.: On the geometric modulation of skin lesion growth: a mathematical model for melanoma. Rev. Bras. Eng. Biomed. 32(1), 44–54 (2016)Google Scholar
  10. 10.
    Diamond, G.A., Rozanski, A., Forrester, J.S., Morris, D., Pollock, B.H., Staniloff, H.M., Berman, D.S., Swan, H.J.C.: A model for assessing the sensitivity and specificity of tests subject to selection bias: application to exercise radionuclide ventriculography for diagnosis of coronary artery disease. J. Chronic Dis. 39(5), 343–355 (1986)CrossRefGoogle Scholar
  11. 11.
    Pereira, J.M., Mendes, A., Nogueira, C., Baptista, D., Fonseca-Pinto, R.: An adaptive approach for skin lesion segmentation in dermoscopy images using a multiscale Local Normalization. In: Bourguignon, J.P., Jeltsch, R., Pinto, A.A., Viana, M. (eds.) Dynamics, Games and Science DGS II (CIM Series in Mathematical Sciences; 1), pp. 537–45. Springer (2015)Google Scholar
  12. 12.
    Liu, Z., Sun, J., Smith, L., Smith, M., Warr, R.: Distribution quantification on dermoscopy images for computer-assisted diagnosis of cutaneous melanomas. Med. Biol. Eng. Comput. 50(5), 503–13 (2012). PMid: 22438064.

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of Electrical EngineeringGautam Buddha UniversityGreater NoidaIndia

Personalised recommendations