On the generality of the finite element modeling physical fields in biological systems by the multiscale smeared concept (Kojic transport model).

The biomechanical and biochemical processes in the biological systems of living organisms are extremely complex. Advances in understanding these processes are mainly achieved by laboratory and clinical investigations, but in recent decades they are supported by computational modeling. Besides enormous efforts and achievements in this modeling, there still is a need for new methods that can be used in everyday research and medical practice. In this report, we give a view of the generality of the finite element methodology introduced by the first author and supported by his collaborators. It is based on the multiscale smeared physical fields, termed as Kojic Transport Model (KTM), published in several journal papers and summarized in a recent book (Kojic et al., 2022) [1]. We review relevant literature to demonstrate the distinctions and advantages of our methodology and indicate possible further applications. We refer to our published results by a selection of a few examples which include modeling of partitioning, blood flow, molecular transport within the pancreas, multiscale-multiphysics model of coupling electrical field and ion concentration, and a model of convective-diffusive transport within the lung parenchyma. Two new examples include a model of convective-diffusive transport within a growing tumor, and drug release from nanofibers with fiber degradation.

Machine learning and physical based modeling for cardiac hypertrophy.

Background and objective: Predicting the long-term expansion and remodeling of the left ventricle in patients is challenging task but it has the potential to be clinically very useful. Methods: In our study, we present machine learning models based on random forests, gradient boosting, and neural networks, used to track cardiac hypertrophy. We collected data from multiple patients, and then the model was trained using the patient's medical history and present level of cardiac health. We also demonstrate a physical-based model, using the finite element procedure to simulate the development of cardiac hypertrophy. Results: Our models were used to forecast the evolution of hypertrophy over six years. The machine learning model and finite element model provided similar results. Conclusions: The finite element model is much slower, but it's more accurate compared to the machine learning model since it's based on physical laws guiding the hypertrophy process. On the other hand, the machine learning model is fast but the results can be less trustworthy in some cases. Both of our models, enable us to monitor the development of the disease. Because of its speed machine learning model is more likely to be used in clinical practice. Further improvements to our machine learning model could be achieved by collecting data from finite element simulations, adding them to the dataset, and retraining the model. This can result in a fast and more accurate model combining the advantages of physical-based and machine learning modeling.

Cardiac hypertrophy simulations using parametric and echocardiography-based left ventricle model with shell finite elements.

In our paper, we simulated cardiac hypertrophy with the use of shell elements in parametric and echocardiography-based left ventricle (LV) models. The hypertrophy has an impact on the change in the wall thickness, displacement field and the overall functioning of the heart. We computed both eccentric and concentric hypertrophy effects and tracked changes in the ventricle shape and wall thickness. Thickening of the wall was developed under the influence of concentric hypertrophy, while the eccentric hypertrophy produces wall thinning. To model passive stresses we used the recently developed material modal based on the Holzapfel experiments. Also, our specific shell composite finite element models for heart mechanics are much smaller and simpler to use with respect to conventional 3D models. Furthermore, the presented modeling approach of the echocardiography-based LV can serve as the basis for practical applications since it relies on the true patient-specific geometry and experimental constitutive relationships. Our model gives an insight into hypertrophy development in realistic heart geometries, and it has the potential to test medical hypotheses regarding hypertrophy evolution in a healthy and heart with a disease, under the influence of different conditions and parameters.

Computational Modeling on Drugs Effects for Left Ventricle in Cardiomyopathy Disease.

Cardiomyopathy is associated with structural and functional abnormalities of the ventricular myocardium and can be classified in two major groups: hypertrophic (HCM) and dilated (DCM) cardiomyopathy. Computational modeling and drug design approaches can speed up the drug discovery and significantly reduce expenses aiming to improve the treatment of cardiomyopathy. In the SILICOFCM project, a multiscale platform is developed using coupled macro- and microsimulation through finite element (FE) modeling of fluid-structure interactions (FSI) and molecular drug interactions with the cardiac cells. FSI was used for modeling the left ventricle (LV) with a nonlinear material model of the heart wall. Simulations of the drugs' influence on the electro-mechanics LV coupling were separated in two scenarios, defined by the principal action of specific drugs. We examined the effects of Disopyramide and Dygoxin which modulate Ca2+ transients (first scenario), and Mavacamten and 2-deoxy adenosine triphosphate (dATP) which affect changes of kinetic parameters (second scenario). Changes of pressures, displacements, and velocity distributions, as well as pressure-volume (P-V) loops in the LV models of HCM and DCM patients were presented. Additionally, the results obtained from the SILICOFCM Risk Stratification Tool and PAK software for high-risk HCM patients closely followed the clinical observations. This approach can give much more information on risk prediction of cardiac disease to specific patients and better insight into estimated effects of drug therapy, leading to improved patient monitoring and treatment.

SILICOFCM platform, multiscale modeling of left ventricle from echocardiographic images and drug influence for cardiomyopathy disease.

BACKGROUND AND OBJECTIVE: In silico clinical trials are the future of medicine and virtual testing and simulation are the future of medical engineering. The use of a computational platform can reduce costs and time required for developing new models of medical devices and drugs. The computational platform, which is one of the main results of the SILICOFCM project, was developed using state-of-the-art finite element modeling for macro simulation of fluid-structure interaction with micro modeling at the molecular level for drug interaction with the cardiac cells. SILICOFCM platform is using for risk prediction and optimal drug therapy of familial cardiomyopathy in a specific patient. METHODS: In order to obtain 3D image reconstruction, the U-net architecture was used to determine geometric parameters for the left ventricle which were extracted from the echocardiographic apical and M-mode views. A micro-mechanics cellular model which includes three kinetic processes of sarcomeric proteins interactions was developed. It allows simulation of the drugs which are divided into three major groups defined by the principal action of each drug. Fluid-solid coupling for the left ventricle was presented. A nonlinear material model of the heart wall that was developed by using constitutive curves which include the stress-strain relationship was used. RESULTS: The results obtained with the parametric model of the left ventricle where pressure-volume (PV) diagrams depend on the change of Ca2+ were presented. It directly affects the ejection fraction. The presented approach with the variation of the left ventricle (LV) geometry and simulations which include the influence of different parameters on the PV diagrams are directly interlinked with drug effects on the heart function. It includes different drugs such as Entresto and Digoxin that directly affect the cardiac PV diagrams and ejection fraction. CONCLUSIONS: Computational platforms such as the SILICOFCM platform are novel tools for risk prediction of cardiac disease in a specific patient that will certainly open a new avenue for in silico clinical trials in the future.

InSilc Computational Tool for In Silico Optimization of Drug-Eluting Bioresorbable Vascular Scaffolds.

Stents made by different manufacturers must meet the requirements of standard in vitro mechanical tests performed under different physiological conditions in order to be validated. In addition to in vitro research, there is a need for in silico numerical simulations that can help during the stent prototyping phase. In silico simulations have the ability to give the same stent responses as well as the potential to reduce costs and time needed to carry out experimental tests. The goal of this paper is to show the achievements of the computational platform created as a result of the EU-funded project InSilc, used for numerical testing of most standard tests for validation of preproduction bioresorbable vascular scaffolds (BVSs). Within the platform, an ad hoc simulation protocol has been developed based on the finite element (FE) analysis program PAK and user interface software CAD Field and Solid. Two different designs of two different stents have been numerically simulated using this integrated tool, and the results have been demonstrated. The following standard tests have been performed: longitudinal tensile strength, local compression, kinking, and flex 1-3. Strut thickness and additional pocket holes (slots) in two different scaffolds have been used as representative parameters for comparing the mechanical characteristics of the stents (AB-BVS vs. AB-BVS-thinner and PLLA-prot vs. PLLA-plot-slot). The AB-BVS-thinner prototype shows better overall stress distribution than the AB-BVS, while the PLLA-prot shows better overall stress distribution in comparison to the PLLA-plot-slot. In all cases, the values of the maximum effective stresses are below 220 MPa-the value obtained by in vitro experiment. Despite the presented results, additional considerations should be included before the proposed software can be used as a validation tool for stent prototyping.

Huxley muscle model surrogates for high-speed multi-scale simulations of cardiac contraction.

The computational requirements of the Huxley-type muscle models are substantially higher than those of Hill-type models, making large-scale simulations impractical or even impossible to use. We constructed a data-driven surrogate model that operates similarly to the original Huxley muscle model but consumes less computational time and memory to enable efficient usage in multiscale simulations of the cardiac cycle. The data was collected from numerical simulations to train deep neural networks so that the neural networks' behavior resembles that of the Huxley model. Since the Huxley muscle model is history-dependent, time series analysis is required to take the previous states of the muscle model into account. Recurrent and temporal convolutional neural networks are typically used for time series analysis. These networks were trained to produce stress and instantaneous stiffness. Once the networks have been trained, we compared the similarity of the produced stresses and achieved speed-up to the original Huxley model, which indicates the potential of the surrogate model to replace the model efficiently. We presented the creation procedure of the surrogate model and integration of the surrogate model into the finite element solver. Based on similarities between the surrogate model and the original model in several types of numerical experiments, and also achieved speed-up of an order of magnitude, it can be concluded that the surrogate model has the potential to replace the original model within multiscale simulations. Finally, we used our surrogate model to simulate a full cardiac cycle in order to demonstrate the application of the surrogate model in larger-scale problems.

Integration of Surrogate Huxley Muscle Model into Finite Element Solver for Simulation of the Cardiac Cycle.

Clinicians can use biomechanical simulations of cardiac functioning to evaluate various real and fictional events. Our present understanding of the molecular processes behind muscle contraction has inspired Huxley-like muscle models. Huxley-type muscle models, unlike Hill-type muscle models, are capable of modeling non-uniform and unstable contractions. Huxley's computational requirements, on the other hand, are substantially higher than those of Hill-type models, making large-scale simulations impractical to use. We created a data-driven surrogate model that acts similarly to the original Huxley muscle model but requires substantially less processing power in order to make the Huxley muscle models easier to use in computer simulations. We gathered data from multiple numerical simulations and trained a deep neural network based on gated-recurrent units. Once we accomplished satisfying precision, we integrated the surrogate model into our finite element solver and simulated a full cardiac cycle. Clinical Relevance- This enables clinicians to track the effects of changes in muscles at the microscale to the cardiac contraction (macroscale).

In Silico Clinical Trials for Cardiovascular Disease.

The SILICOFCM project mainly aims to develop a computational platform for in silico clinical trials of familial cardiomyopathies (FCMs). The unique characteristic of the platform is the integration of patient-specific biological, genetic, and clinical imaging data. The platform allows the testing and optimization of medical treatment to maximize positive therapeutic outcomes. Thus, adverse effects and drug interactions can be avoided, sudden cardiac death can be prevented, and the time between the commencement of drug treatment and the desired result can be shortened. This article presents a parametric model of the left ventricle automatically generated from patient-specific ultrasound images by applying an electromechanical model of the heart. Drug effects were prescribed through specific boundary conditions for inlet and outlet flow, ECG measurements, and calcium function for heart muscle properties. Genetic data from patients were incorporated through the material property of the ventricle wall. Apical view analysis involves segmenting the left ventricle using a previously trained U-net framework and calculating the bordering rectangle based on the length of the left ventricle in the diastolic and systolic cycle. M-mode view analysis includes bordering of the characteristic areas of the left ventricle in the M-mode view. After extracting the dimensions of the left ventricle, a finite elements mesh was generated based on mesh options, and a finite element analysis simulation was run with user-provided inlet and outlet velocities. Users can directly visualize on the platform various simulation results such as pressure-volume, pressure-strain, and myocardial work-time diagrams, as well as animations of different fields such as displacements, pressures, velocity, and shear stresses.

Improved predictive performance of prostate biopsy collaborative group risk calculator when based on automated machine learning.

BACKGROUND: The Prostate Biopsy Collaborative Group risk calculator (PBCG RC) has a moderate discriminatory capability. This study aimed to create automated machine learning (AutoML) PBCG RC for predicting the probability of any-grade and high-grade prostate cancer (PCa). METHODS: This retrospective, single-center study was carried out using the database with 832 patients who were subject to transrectal ultrasound-guided prostate biopsy with prostate-specific antigen (PSA) values from 2 to 50 ng/ml. Information about PBCG RC predictors was gathered for all patients. We used H2O, as an open-source platform for AutoML, where the set of 20 base learning algorithms were trained. The AutoML PBCG RC was compared in terms of discrimination, calibration, and clinical utility with the original PBCG RC. RESULTS: PCa was detected in 341 (41%) men, and 159 (19.1%) of them had high-grade PCa. Our AutoML models demonstrated better discriminative ability than the original PBCG RC for detection of PCa (area under the curve [AUC]: 0.703 vs 0.628; P = 0.023) and high-grade PCa (AUC: 0.990 vs 0.717; P < 0.001). The decision curve analyses showed that AutoML models performed better. For high-grade PCa the PSA was the most important feature. CONCLUSIONS: We applied ensemble techniques to create a freely available online PCa risk tool based on PBCG RC predictors and AutoML algorithms. The AutoML models drastically improved original model performance and the predictions of high-grade PCa were nearly perfect. However, new models should be used with a reserve, because external validation has not been performed yet.

Application of in silico Platform for the Development and Optimization of Fully Bioresorbable Vascular Scaffold Designs.

Bioresorbable vascular scaffolds (BVS), made either from polymers or from metals, are promising materials for treating coronary artery disease through the processes of percutaneous transluminal coronary angioplasty. Despite the opinion that bioresorbable polymers are more promising for coronary stents, their long-term advantages over metallic alloys have not yet been demonstrated. The development of new polymer-based BVS or optimization of the existing ones requires engineers to perform many very expensive mechanical tests to identify optimal structural geometry and material characteristics. in silico mechanical testing opens the possibility for a fast and low-cost process of analysis of all the mechanical characteristics and also provides the possibility to compare two or more competing designs. In this study, we used a recently introduced material model of poly-l-lactic acid (PLLA) fully bioresorbable vascular scaffold and recently empowered numerical InSilc platform to perform in silico mechanicals tests of two different stent designs with different material and geometrical characteristics. The result of inflation, radial compression, three-point bending, and two-plate crush tests shows that numerical procedures with true experimental constitutive relationships could provide reliable conclusions and a significant contribution to the optimization and design of bioresorbable polymer-based stents.

Coupling tumor growth and bio distribution models.

We couple a tumor growth model embedded in a microenvironment, with a bio distribution model able to simulate a whole organ. The growth model yields the evolution of tumor cell population, of the differential pressure between cell populations, of porosity of ECM, of consumption of nutrients due to tumor growth, of angiogenesis, and related growth factors as function of the locally available nutrient. The bio distribution model on the other hand operates on a frozen geometry but yields a much refined distribution of nutrient and other molecules. The combination of both models will enable simulating the growth of a tumor in a whole organ, including a realistic distribution of therapeutic agents and allow hence to evaluate the efficacy of these agents.

Smeared Multiscale Finite Element Models for Mass Transport and Electrophysiology Coupled to Muscle Mechanics.

Mass transport represents the most fundamental process in living organisms. It includes delivery of nutrients, oxygen, drugs, and other substances from the vascular system to tissue and transport of waste and other products from cells back to vascular and lymphatic network and organs. Furthermore, movement is achieved by mechanical forces generated by muscles in coordination with the nervous system. The signals coming from the brain, which have the character of electrical waves, produce activation within muscle cells. Therefore, from a physics perspective, there exist a number of physical fields within the body, such as velocities of transport, pressures, concentrations of substances, and electrical potential, which is directly coupled to biochemical processes of transforming the chemical into mechanical energy and further internal forces for motion. The overall problems of mass transport and electrophysiology coupled to mechanics can be investigated theoretically by developing appropriate computational models. Due to the enormous complexity of the biological system, it would be almost impossible to establish a detailed computational model for the physical fields related to mass transport, electrophysiology, and coupled fields. To make computational models feasible for applications, we here summarize a concept of smeared physical fields, with coupling among them, and muscle mechanics, which includes dependence on the electrical potential. Accuracy of the smeared computational models, also with coupling to muscle mechanics, is illustrated with simple example, while their applicability is demonstrated on a liver model with tumors present. The last example shows that the introduced methodology is applicable to large biological systems.

A Computational Model for Drug Release from PLGA Implant.

Due to the relative ease of producing nanofibers with a core⁻shell structure, emulsion electrospinning has been investigated intensively in making nanofibrous drug delivery systems for controlled and sustained release. Predictions of drug release rates from the poly (d,l-lactic-co-glycolic acid) (PLGA) produced via emulsion electrospinning can be a very difficult task due to the complexity of the system. A computational finite element methodology was used to calculate the diffusion mass transport of Rhodamine B (fluorescent drug model). Degradation effects and hydrophobicity (partitioning phenomenon) at the fiber/surrounding interface were included in the models. The results are validated by experiments where electrospun PLGA nanofiber mats with different contents were used. A new approach to three-dimensional (3D) modeling of nanofibers is presented in this work. The authors have introduced two original models for diffusive drug release from nanofibers to the 3D surrounding medium discretized by continuum 3D finite elements: (1) A model with simple radial one-dimensional (1D) finite elements, and (2) a model consisting of composite smeared finite elements (CSFEs). Numerical solutions, compared to experiments, demonstrate that both computational models provide accurate predictions of the diffusion process and can therefore serve as efficient tools for describing transport inside a polymer fiber network and drug release to the surrounding porous medium.