Fractal structures in stenoses and aneurysms in blood vessels

Abstract

Recent advances in the field of chaotic advection provide the impetus to revisit the dynamics of particles transported by blood flow in the presence of vessel wall irregularities. The irregularity, being either a narrowing or expansion of the vessel, mimicking stenoses or aneurysms, generates abnormal flow patterns that lead to a peculiar filamentary distribution of advected particles, which, in the blood, would include platelets. Using a simple model, we show how the filamentary distribution depends on the size of the vessel wall irregularity, and how it varies under resting or exercise conditions. The particles transported by blood flow that spend a long time around a disturbance either stick to the vessel wall or reside on fractal filaments. We show that the faster flow associated with exercise creates widespread filaments where particles can get trapped for a longer time, thus allowing for the possible activation of such particles. We argue, based on previous results in the field of active processes in flows, that the non-trivial long-time distribution of transported particles has the potential to have major effects on biochemical processes occurring in blood flow, including the activation and deposition of platelets. One aspect of the generality of our approach is that it also applies to other relevant biological processes, an example being the coexistence of plankton species investigated previously.

Emerging fractal patterns in a real 3D cerebral aneurysm

“…It is possible that this chaotic behaviour or even some of its statistical description (like D 1 ) could be linked to the formation or rupture process of the aneurysms. For example, the increased residence times, efficient mixing and exponential outflow of the particles in the diseased blood vessel segment can have direct effects on the biochemical reactions taking place in blood [21,22,23]. It would also be meaningful to collect statistical information about the relation of pathological vessel malformations, and the fractal properties they enforce upon the flow.…”

“…Numerous biological and chemical processes take place in fluid flows, ranging from environmental processes (plankton blooming [1,2,3] or ozone hole formation [4,5]), through chemistry [6,7,8], cavitation processes [9], valve flows [10], and combustion [11,12], to microfluidics [13,14]. It has been shown [15] that mixing in fluids has an important influence on the biological or chemical activity that takes place in the fluid.…”

Alteration of chaotic advection in blood flow around partial blockage zone: Role of hematocrit concentration

“…1-3 Therefore, most of the complex spatial distribution of the particles can be found around the shape anomaly zone. [1][2][3] The above-mentioned qualitative description of the essential physics, although indicative in nature, may represent the quantitative details of the underlying chaos in a grossly incomplete manner, as attributable to negligence in capturing the role played by the HCT concentration of the blood sample. Towards dictating the consequent alterations in chaotic dynamics, the time constant in the constitutive model of blood, with its sensitive dependence on the HCT, acts notionally analogous to that of a relaxation time.…”

“…13 In the study of chaotic advection in blood flow, the zone of paramount interest is the chaotic mixing zone; it is this zone where the spatial distribution of the advected particles displays the nontrivial features. [1][2][3]13 One of the most visible effects in this regard is the distribution of particles along complex filamentary pathways; such filamentary structures are indeed fractal in nature. The dimensions of those fractal structures not only describe the complexity of the system but also decisive towards the rate equation of biological activities.…”

Complex dynamics of life at different scales: from genomic to global environmental issues

“…Schelin et al (2010) study the dynamics of particles transported by blood flow in the presence of irregularities in the vessel walls. This mimics stenoses or aneurysms, which generate abnormal flow patterns.…”