Freezing Response of Mammary Tissue: A Mathematical Study

Abstract

Abstract Cryosurgery, the use of low temperatures to devitalize neoplastic tissue, has become an accepted treatment modality for many cancers such as those of the liver and prostate. Recently, the application of cryosurgery to human breast malignancies has been explored (Staren et. al, 1997, Pham and Rubinsky, 1998). Breast cancer will affect 1 in 9 women over the course of their lifetime (American Cancer Society, 1997). Although there are a wide variety of therapies available to treat this disease, the broad pathological spectrum of patients with breast cancer necessitates newer and better treatments before these numbers will decline. The composition of human mammary tissue is highly varied (age, body mass, and hormone dependent) making the application of cryosurgery to this tissue complex. Although the preponderance of breast cancer lesions occur in post-menopausal patients, women of all ages are affected by this disease. More importantly, lesions persist in all types of breast tissue. If cryosurgery is to become a viable therapy for breast cancer, it is important to understand the range of responses expected from the different tissue compositions, and, if relevant, identify the tissue types most suited to cryo-based therapies. To this end, an understanding of the response of these various classes of breast tissue to freezing can be accomplished using accurate heat and mass transfer models. Based on a review of basic human breast histology during all stages of mammary gland development, several different categories of human breast tissue were chosen for constitutional analysis. The volumetric dominance of each of the different tissue constituents was determined and then using this information, the volume-averaged thermal properties for each category calculated. A preliminary analysis, utilizing basic heat conduction equations and effective heat transfer properties, was performed to understand if, in a pure conduction sense, the various categories of breast tissue would respond differently to the same applied freezing protocol, and if so, which components were thermally most relevant. This analysis, although not completely descriptive of the physical situation occurring during an actual cryosurgery protocol, represents the first steps in determining the morphological features of mammary tissue which must be taken into consideration in future modeling efforts.