Fractal analysis of scatter imaging signatures to distinguish breast pathologies Alma Eguizabal a , Ashley M. Laughney bc , Venkataramanan Krishnaswamy c , Wendy A. Wells c , Keith D. Paulsen d , Brian W. Pogue c , Jose M. Lopez-Higuera a , Olga M. Conde a a Univ. de Cantabria (Spain); b Massachusetts General Hospital/Harvard Medical School (United States); c Thayer School of Engineering at Dartmouth (United States); d Dartmouth Hitchcock Medical Ctr. (United States); ABSTRACT Fractal analysis combined with a label-free scattering technique is proposed for describing the pathological architecture of tumors. Clinicians and pathologists are conventionally trained to classify abnormal features such as structural irregularities or high indices of mitosis. The potential of fractal analysis lies in the fact of being a morphometric measure of the irregular structures providing a measure of the object’s complexity and self-similarity. As cancer is characterized by disorder and irregularity in tissues, this measure could be related to tumor growth. Fractal analysis has been probed in the understanding of the tumor vasculature network. This work addresses the feasibility of applying fractal analysis to the scattering power map (as a physical modeling) and principal components (as a statistical modeling) provided by a localized reflectance spectroscopic system. Disorder, irregularity and cell size variation in tissue samples is translated into the scattering power and principal components magnitude and its fractal dimension is correlated with the pathologist assessment of the samples. The fractal dimension is computed applying the box-counting technique. Results show that fractal analysis of ex-vivo fresh tissue samples exhibits separated ranges of fractal dimension that could help classifier combining the fractal results with other morphological features. This contrast trend would help in the discrimination of tissues in the intraoperative context and may serve as a useful adjunct to surgeons. Keywords: breast tumor; localized backscattering; scattering parameters; principal component analysis; fractal dimension; box counting. 1. INTRODUCTION Tumor margin in breast conserving surgery continues being a handicap in operating rooms. Breast Conserving Therapy (BCT) is the standard of care for patients with early invasive breast cancers [1]. However, BCT requires a very accurate delineation of tumor, as residual disease decreases considerably the survival rate of patients. This is sometimes difficult to achieve with the current techniques [2]. Here, scatter-imaging signatures were used to detect and discriminate pathologies to improve the resection precision. Topological features related to image shape are then searched. To this aim fractal analysis has been considered being based on box-counting to evaluate its efficiency for malignancy detection. The fractal dimension is extracted on model-based parameters and statistical-based parameters and results are compared. Several studies show that fractal dimension can be an interesting feature for describing the pathological architecture of tumors, an even tumor growth and its irregular shape [3]. A fractal approach also could lead to a model of tissue that could help to extract optical properties, such as local refractive index variation and size distribution [4]; and it should also be possible to identify changes in size/volume concentration of the tissue from diffuse reflectance measurements employing a fractal model of tissue [5]. A higher fractal dimension is generally associated with malignancy [6], and fractal analysis improves automatic classification of histopathology H&E images of cancer [7] as tumor samples present higher cell disorder. However, this relation it is not definitive. Fractals of breast cancer carcinoma have also been used in classification on optical coherence tomography [8], whereas stroma had higher dimension than invasive carcinoma, while adipose tissue resulted to have the lowest fractal dimension. We propose fractal analysis of scatter imaging signatures to clarify the detection of malignancy regions. The potential of fractal analysis lies in the fact of being a morphometric measure of the irregular structures providing a measure of the