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