Fractal dimension of tumor microvasculature by dynamic contrast-enhanced ultrasound Massimo Mischi 1 , Carola Heneweer 2 , Julian von Broich-Oppert 2 , Tamerlan Saidov 1 , and Hessel Wijkstra 1,3 1 Lab. of Biomedical Diagnostics, Eindhoven University of Technology, the Netherlands 2 Department of Radiology, University Hospital Schleswig-Holstein, Kiel, Germany 3 Department of Urology, Academic Medical Center University of Amsterdam, the Netherlands Abstract—Angiogenesis plays a fundamental role in the growth of several types of cancer. Characterization of the microvascular architecture has therefore gained attention as a possible tool for cancer localization. However, the available options to assess the main features characterizing the microvascular architecture require immunohistological analysis of the resected tumors. Contrast-enhanced ultrasound (CEUS) provides new options for minimally-invasive investigation of the microvasculature by spatiotemporal analysis of the ultrasound-contrast-agent (UCA) transport kinetics. In this work, we propose a novel method to analyze CEUS data. The fractal dimension (FD) of the flow distribution is employed as a geometrical feature to characterize the microvascular architecture. To this end, the fractal dimension of parametric maps reflecting blood flow, such as UCA wash-in rate and peak enhancement, is derived for areas representing different microvascular architectures. Subcutaneous xenograft models of DU-145 and PC-3 prostate-cancer lines in mice were employed as they show marked differences in the spatial distribution of the microvascular density (MVD) inside the tumor. The ability of the method to differentiate between these models was therefore evaluated. For validation purposes, comparison with immunohistological MVD and FD assessment, as well as with UCA dispersion maps, was also performed. The results show good agreement between FD and MVD assessment, with the proposed method able to differentiate between the two cancer lines. I. I NTRODUCTION Angiogenesis is an essential process for the growth and devel- opment of many types of solid tumors. It leads to the formation of a chaotic, dense network of irregular microvessels, and it is often a good indicator of cancer aggressiveness [1]. Thereby, angiogenesis is a relevant imaging marker and promising prognostic indicator for cancer localization and diagnosis [2]. Currently, the characterization of an angiogenic network requires an invasive procedure, being performed by analysis of the microvascular density (MVD) from immunohistolog- ical sections of resected tumors [2], [3]. Methods enabling a non-invasive characterization of angiogenic structures can therefore provide an asset to cancer diagnostics, monitoring of treatment, and evaluation of new drugs. Contrast-enhanced ultrasound (CEUS), making use of gas- shelled microbubbles that can pass through all the capillaries, is a promising option for non-invasive cancer localization by analysis of the microvasculature [2], [4], [5]. To this end, several approaches have been proposed in the literature that are based on the analysis of features related to the evolution of the UCA concentration over time, referred to as time- intensity curve (TIC). All these methods are based on a linear (or linearized) relation between UCA concentration and the measured acoustic intensity [6]. The estimated TIC features relate to either blood perfusion or UCA dispersion kinetics, reflecting those changes in the microvasculature due to cancer angiogenesis [4], [5]. For perfusion estimation, temporal fea- tures like wash-in rate or peak enhancement are extracted from the measured TIC. Contrast ultrasound dispersion imaging (CUDI) has recently been proposed as an alternative method for non-invasive cancer localization by assessment of the UCA dispersion coefficient [4], [7]. In its most promising implemen- tation, the similarity among neighbor TICs is estimated as an indirect measure of dispersion [7], [8]. Several key properties of the microvascular architecture, such as microvascular density, vessel tortuosity, and multipath trajectories, influence not only the dispersion kinetics of a diluted agent [9], but also the regional blood flow distribution [10]. Therefore, the regional blood flow distribution, defined by the geometry of the vascular network, is also affected by the presence of cancer angiogenic processes [11]. The well-known concept of Mandelbrot suggests fractal bifurcating networks to mimic the vascular tree [12], enabling the characterization of angiogenic networks in terms of fractal theory. This concept has been applied to immunohistological samples, where the vascular networks, highlighted by specific tracers binding to the epithelial cells of blood vessels, were represented by the fractal dimension (FD) [10], [13], [14]. In this paper, we evaluate the potential of FD for the char- acterization of microvascular networks by CEUS. To this end, ad hoc TIC parameters are defined that reflect blood flow. The method was tested on two subcutaneous (SC) xenograft mouse models of human prostate cancer, namely, DU-145 and PC- 3. These models are characterized by a marked difference in MVD distribution; SC PC-3 develops a spatially homogenous vascular network, whereas SC DU-145 forms a core with higher MVD compared to the periphery [3], [15]. The method was also compared with immunohistological MVD and FD assessment, as well as with CUDI, based on the coherence between neighbor TICs [7], [15], [8]. II. METHODOLOGY A. Data acquisition Data acquisition was performed at the University Hospital Schleswig-Holstein (Kiel, Germany), in compliance with the Institutional Animal Care and Use Committee guidelines. Two 978-1-4799-8182-3/15/$31.00 ©2015 IEEE 2015 IEEE International Ultrasonics Symposium Proceedings 10.1109/ULTSYM.2015.0269