Modelling perfusion in the human heart

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Heart tissue is perfused by thousands of very small arteries and capillaries branching off the coronary arteries. Obtaining truthful representations of the exact geometries of the perfusion circulation using state-of-the-art imaging techniques is virtually impossible. Despite being the most fundamental process in maintaining organ health and the major pathway for drug delivery, perfusion has, from a computational point of view, received very little attention. Thanks to the work done by SIMULA in CUPIDO, a computationally efficient and accurate model is now available and provides a framework for the simulation of experimentally relevant time frames for pre-clinical research.

In CUPIDO, SIMULA has developed a novel particle tracking-based method to simulate the distribution of nanoparticles in the heart mediated by perfusion. To model blood flow through perfused tissue they follow the approach of others and treat the tissue as a porous medium in a continuum model [Michler et al. – 2013]. Perfused heart tissue is modelled as a superposition of three porous materials that represent perfusion at the artery, arteriole, and capillary level.

However, the main problem to solve for the distribution of nanoparticles was the discrepancy of scales between advection in arteries and diffusion. Classically, solutes are modelled using reaction-advection-diffusion kinetics. When advective forces dominate much over diffusion this method becomes, practically speaking, numerically unstable and too computationally expensive. SIMULA proposed a method that splits the issue: in arteries, it tracks a bolus of nanoparticles by particle tracking based purely on advection, while in capillaries it utilizes an effective diffusion coefficient that mimics capillary blood flow to track the distribution of nanoparticles.

The study, now published in the Biophysical Journal , demonstrates that, as opposed to advection-diffusion kinetics, SIMULA’s method is numerically stable for advection-dominated problems like blood flow, as well as computationally much more efficient . Using this method allows for the simulation of multiple cardiac cycles of a left ventricle using a conventional laptop, enabling simulations over experimentally relevant time frames.

Nanoparticle distribution in the left ventricle geometry over three cardiac cycles at t = 1.0, 2.0, 3.0 s (left to right). Values are shown as a fraction of the maximum concentration.

In CUPIDO, the method has been used to compare the distributions in the left ventricle of CaP- and FeCaP-nanoparticles, demonstrating that distribution patterns are influenced by the presence of magnetic forces. The model shows that the difference in distribution grows with a quadratic function over time, and full perfusion is much faster using FeCaP nanoparticles, compared to CaP ones. These results indicate that the use of magnetic forces to manipulate nanoparticle distribution and deposition is viable.