Preface

The 10th International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) due to the international conditions regarding the pandemic Covid-19 was held online and in addition to the lectures and presentations that took place in real time, it also had a large collection of pre-recorded presentations that were available to the participants through the conference website. The Conference was attended by more than 180 participants and hosted about 250 oral and virtual presentations while counted more than 600 pre-registered authors. The 10th IC-MSQUARE consisted of different and diverging workshops and thus covered various research fields where Mathematical Modeling is used, such as Theoretical/Mathematical Physics, Neutrino Physics, Non-Integrable Systems, Dynamical Systems, Computational Nanoscience, Biological Physics, Computational Biomechanics, Complex Networks, Stochastic Modeling, Fractional Statistics, DNA Dynamics, Macroeconomics etc. The scientific program was rather heavy, however, according to all attendees, the program was excellent with high level of talks and the scientific environment was fruitful, thus all attendees had a creative time. The Conference Chairman Dimitrios Vlachos University of Peloponnese List of International Scientific Committee, Organizing Committee are available in the pdf.

Symmetry of the Human Head—Are Symmetrical Models More Applicable in Numerical Analysis?

The study of symmetrical and non-symmetrical effects in physics, mathematics, mechanics, medicine, and numerical methods is a current topic due to the complexity of the experiments, calculations, and virtual simulations. However, there is a limited number of research publications in computational biomechanics focusing on the symmetry of numerical head models. The majority of the models in the researched literature are symmetrical. Thus, we stated a hypothesis wherever the symmetrical models might be more applicable in numerical analysis. We carried out in-depth studies about head symmetry through clinical data, medical images, materials models, and computer analysis. We concluded that the mapping of the entire geometry of the skull and brain is essential due to the significant differences that affect the results of numerical analyses and the possibility of misinterpretation of the tissue deformation under mechanical load results.

The Biomechanics of the Fibrocystic Breasts at Finite Compressive Deformation

The deformation of the human breast, especially that of the female, under variable pressure conditions, has been a recent focus for researchers, both in the computational biomechanics, computational biology and the health sector. When the deformation of the breast is large, it hampers suitable cyst tracing as a mammographic biopsy precontrive data. Finite element methods (FEM) has been instrumental in the currently studied practices to trail nodules dislocation. However, the effect of breast material constitution, especially that of a fibrocystic composition, on the biomechanical response of these nodules has gained less attention. The present study is aimed at developing a finite element fibrocystic breast model within the frame of biosolid mechanics and material hyperelasticity to model the breast deformation at finite strain. The geometry of a healthy stress‐free breast is modelled from a magnetic resonance image (MRI) using tissues deformations measurements and solid modelling technology. Results show that the incompressible Neo-Hookean and Mooney-Rivlin constitutive models can approximate large deformation of a stressed breast. In addition to the areola (i.e. nipple base), the surrounding area of the cyst together with its interface with the breast tissue is the maximum stressed region when the breast is subjected to compressive pressure. This effect can lead to an internal tear of the breast that could degenerate to malignant tissue.

Simulation of atherosclerotic plaque growth using computational biomechanics and patient-specific data

Atherosclerosis is the one of the major causes of mortality worldwide, urging the need for prevention strategies. In this work, a novel computational model is developed, which is used for simulation of plaque growth to 94 realistic 3D reconstructed coronary arteries. This model considers several factors of the atherosclerotic process even mechanical factors such as the effect of endothelial shear stress, responsible for the initiation of atherosclerosis, and biological factors such as the accumulation of low and high density lipoproteins (LDL and HDL), monocytes, macrophages, cytokines, nitric oxide and formation of foams cells or proliferation of contractile and synthetic smooth muscle cells (SMCs). The model is validated using the serial imaging of CTCA comparing the simulated geometries with the real follow-up arteries. Additionally, we examine the predictive capability of the model to identify regions prone of disease progression. The results presented good correlation between the simulated lumen area (P < 0.0001), plaque area (P < 0.0001) and plaque burden (P < 0.0001) with the realistic ones. Finally, disease progression is achieved with 80% accuracy with many of the computational results being independent predictors.

Mechano-chemo-biological computational models for arteries in health, disease and healing: from tissue remodelling to drug-eluting devices

: This review aims to highlight urgent priorities for the computational biomechanics community in the framework of mechano-chemo-biological models. Recent approaches, promising directions and open challenges on the computational modelling of arterial tissues in health and disease are introduced and investigated, together with in silico approaches for the analysis of drug-eluting stents that promote a pharmacological-induced healing. The paper addresses a number of chemo-biological phenomena that are generally neglected in biomechanical engineering models but are most likely instrumental for the onset and the progression of arterial diseases. An interdisciplinary effort is thus encouraged for providing the tools for an effective in silico insight into medical problems. An integrated mechano-chemo-biological perspective is believed to be a fundamental missing piece for crossing the bridge between computational engineering and life sciences, and for bringing computational biomechanics into medical research and clinical practice.