Restenosis refers to the uncontrolled growth of tissue in vessel walls as part of an inflammatory response that follows cardiovascular interventional procedures including balloon angioplasty and stent implantation. Although the risk of restenosis has reduced with the advent of drug-eluting stents, it is not completely eliminated. An in silico replication of neointimal hyperplasia, the mechanism behind restenosis, shall therefore provide the necessary means to derive insights about the biochemical and cellular interactions within the vessel wall, and eventually address the risks of restenosis in a patient-specific manner. In this regard, six important biochemical species in the vessel wall are modeled within the scope of this work: platelet-derived growth factor (PDGF), transforming growth factor (TGF)-β, extracellular matrix (ECM), endothelial cells (ECs), drug (rapamycin) and smooth muscle cells (SMCs). This is considered an extension of the work presented by the authors in [1]. The intricate interactions between these species are then coupled to a continuum mechanical finite growth theory, where the local SMC density drives the growth process and the local ECM (hence collagen) concentration controls the compliance of the vessel wall. Multiphysics-based frameworks for modeling damage-driven growth and remodeling have been presented in several earlier works (e.g. [2]), but the presented model specifically addresses the inflammatory response due to endothelium denudation in addition to the pharmacological influences of the rapamycin-based drugs embedded in modern drug-eluting stents.

[1] Manjunatha, K., Behr, M., Vogt, F., Reese, S., “A multiphysics modeling approach for in-stent restenosis: Theoretical aspects and finite element implementation”, Computers in Biology and Medicine, 150:106166, (2022).

[2] Escuer, J., Martinez, M. A., McGinty, S., and Pena, E., “Mathematical modelling of the restenosis process after stent implantation”, J. R. Soc. Interface, 16:20190313, (2019).

Aortic Dissection is a severe medical condition that can lead to fatality if not treated early. Aortic Dissection begins when a tear occurs in the aortic wall's inner layer (intima). Moreover, a second blood-filled channel called a false lumen is created where thrombosis most probably will happen. In type B Aortic Dissection, severe complications, such as malperfusion or rupture in the aorta, can occur in the first seven days, resulting in high mortality rates. The optimal treatment for type B Aortic Dissection remains a topic of debate, leading to an interest in computational methods to aid in decision-making for treatment.
To obtain a macroscopic model the Theory of Porous Media is chosen to modell the multiphasic structure of the thrombus. The whole aggregate is divided into solid, liquid, and nutrient constituents. As usual in the theory of porous media, all three phases occupy each material point simultaneously. The constituents are assumed to be materially incompressible, under isothermal conditions, and the entire aggregate is fully saturated. Darcy's law is used to describe the flow of fluid phases, i.e., the liquid and the nutrient phase. The constituents' balance equations have coupling terms that account for the interactions between the different phases. The essential coupling term for the growth process is the mass exchange term in the volume balances. Due to the incompressibility assumption the volume fractions can be used to define the constituents. Therefore, the regions with thrombus are determined using the solid volume fraction.
Initially, a set of equations for thrombosis in type B Aortic Dissection is presented. The respective variational form is approximated with finite elements and implemented in PANDAS, a finite element package used for solving strongly coupled multiphase porous media problems. However, the model's description is challenging due to the need for detailed knowledge and parameters to quantify the influence of different factors. Nevertheless, the effects of blood velocity and nutrients on thrombus growth are well researched. Therefore, a velocity and nutrient concentration induced growth model is proposed within the Theory of Porous Media. The effects of various parameters are studied using a realistic 2D geometry of the false lumen, and reasonable parameters for thrombus growth are selected. We present the model's features in agreement with the Virchow triad and its usefulness in actual cases. The simulations show that the thrombus grows in the low-velocity regions of the blood. The proposed model provides a reasonable approach for the numerical simulation of thrombosis.

Endovascular coil embolization is one of the primary methods for the treatment of a ruptured or unruptured cerebral aneurysm. Though being a well accepted and minimally invasive method, it bears the risk of suboptimal coil placement, which can lead to incomplete occlusion of the aneurysm, causing a degenerate healing process or in the worst case even aneurysm recurrence.

Our study investigates factors that lead to a suboptimal placement when a coil is deployed in an aneurysm. To this end, we use a mathematical model that simulates the embolization process of the coil in patient specific three-dimensional aneurysm geometries. One of the key features of coils is that they have an imprinted rest shape, which helps to safely fix them inside aneurysms. We consider the latter property by introducing bending and torsional forces into our model of the coil. In order to differentiate optimal from suboptimal placements, we use measures like the local packing density, which is connected to the quality of the subsequent healing process.

We model the coil as a one dimensional discrete space curve with the dynamics of a mass spring system. For this purpose, we include stretching, bending and torsional springs. The aimed for deflected rest shape is accounted for by penalizing deviations from it within the individual spring energies. To obtain the forces that act on the coil, we differentiate the total elastic energy of the spring mass system by algorithmic differentiation with respect to the material points. Collisions between coil segments and the aneurysm-wall are taken into account by an efficient contact algorithm, such that only a fraction of the possible contact partners have to be evaluated. The numerical solution of the model is obtained by a first order accurate time stepping scheme.

We then carry out a sensitivity study that shows how process parameters like the insertion point or the angle of insertion affect the shape of the deployed coil in the aneurysm. We further show how other medical tools such as, for example, stents or hyper-elastic balloons can support the coil-placement process. Finally, we investigate the sensitivity of our model with respect to the material parameters and rest shape of the coil.

Our model can be easily incorporated into blood-flow simulations of embolized aneurysms. It is our goal to eventually provide a simulation tool that will provide new insight into the behavior of coils and allow medical professionals to better plan coil embolization procedures and hence assist them in their practice.

Left ventricular (LV) hemodynamics are hypothesized to serve as an early indicator for the manifestation of cardiovascular diseases. In the analysis of hemodynamics, computational fluid dynamics (CFD) can complement medical imaging methods for in-depth flow investigations. To obtain information about individual conditions, a high level of patient-specific input into the model is required. Considering the variety of data sources, medical imaging modalities, and the range of data quality, this leads to demanding case processing with a lot of manual effort.

To target this issue, we standardized the workflow by coupling the patient-individual anatomical representation in form of a statistical shape model (SSM) with a fluid structure interaction (FSI) workflow. Thereby, we obtain a high degree of individuality in our simulations while keeping the case-specific effort involved at an acceptable level. Furthermore, the workflow allows usage of all common cardiac imaging modalities, namely computed tomography (CT), magnetic resonance imaging (MRI), and ultrasound (US).
To test the simulation pipeline, we processed data of healthy volunteers by comparing the FSI-computed flow results to measured velocity fields from 4D flow MRI. Further applications of the workflow were tested with simulations of patients showing isolated or combined aortic stenosis and mitral regurgitation. For patients with ventricle aneurysms after myocardial infarction, we compared pre- and post-treatment situations.

Imaging data of the healthy volunteers included 4D flow MRI and cine MRI sequences. While the latter served as model input, the flow data was used to check the results of computed hemodynamics for plausibility. Simulations of mitral regurgitation patients revealed characteristics of altered kinetic energy and specific energy dissipation during diastole. These results correspond well with findings of previous clinical MRI studies. Simulations of the pre- and post-surgical hemodynamics of left ventricular aneurysms showed significantly improved flow conditions after surgery. Although, the flow results cannot quantitatively be compared to clinical data because no MRI was acquired, results show improved flow patterns and align well with the improvement of the medical conditions patients showed after surgery.

To conclude, we could prove that our workflow is robust and easy to use while including a lot of patient-specific details. This allows for representation of individual flow features, which can perspectively be used in the clinical routine to support diagnostics, therapy planning, and outcome prediction. A profound validation study must be performed to test the approach on a sufficient amount of data. However, the availability of such comprehensive data is rare and prospective studies are very costly.