Igor Saveljic

Computer simulation of three-dimensional plaque formation and progression in the carotid artery

Atherosclerosis is becoming the number one cause of death worldwide. In this study, three-dimensional computer model of plaque formation and development for human carotid artery is developed. The three-dimensional blood flow is described by the Navier–Stokes equation, together with the continuity equation. Mass transfer within the blood lumen and through the arterial wall is coupled with the blood flow and is modeled by a convection–diffusion equation. The low-density lipoproteins transports in lumen of the vessel and through the vessel tissue are coupled by Kedem–Katchalsky equations. The inflammatory process is modeled using three additional reaction–diffusion partial differential equations. Fluid–structure interaction is used to estimate effective wall stress analysis. Plaque growth functions for volume progression are correlated with shear stress and effective wall stress distribution. We choose two specific patients from MRI study with significant plaque progression. Plaque volume progression using three time points for baseline, 3- and 12-month follow up is fitted. Our results for plaque localization correspond to low shear stress zone and we fitted parameters from our model using nonlinear least-square method. Determination of plaque location and composition, and computer simulation of progression in time for a specific patient shows a potential benefit for the prediction of disease progression. The proof of validity of three-dimensional computer modeling in the evaluation of atherosclerotic plaque burden may shift the clinical information of MRI from morphological assessment toward a functional tool. Understanding and prediction of the evolution of atherosclerotic plaques either into vulnerable or stable plaques are major tasks for the medical community.

Impact of the lower third molar presence and position on the fragility of mandibular angle and condyle: A Three-dimensional finite element study.

The aim of the present study was to investigate the influences of the presence and position of a lower third molar (M3) on the fragility of mandibular angle and condyle, using finite element analysis. From computed tomographic scans of a human mandible with normally erupted M3, two additional virtual models were generated: a mandibular model with partially impacted M3 and a model without M3. Two cases of impact were considered: a frontal and a lateral blow. The results are based on the chromatic analysis of the distributed von Mises and principal stresses, and calculation of their failure indices. In the frontal blow, the angle region showed the highest stress in the case with partially impacted M3, and the condylar region in the case without M3. Compressive stresses were dominant but caused no failure. Tensile stresses were recorded in the retromolar areas, but caused failure only in the case with partially impacted M3. In the lateral blow, the stress concentrated at the point of impact, in the ipsilateral and contralateral angle and condylar regions. The highest stresses were recorded in the case with partially impacted M3. Tensile stresses caused the failure on the ipsilateral side, whereas compressive stresses on the contralateral side.

Occlusal load distribution through the cortical and trabecular bone of the human mid-facial skeleton in natural dentition: A three-dimensional finite element study

Understanding of the occlusal load distribution through the mid-facial skeleton in natural dentition is essential because alterations in magnitude and/or direction of occlusal forces may cause remarkable changes in cortical and trabecular bone structure. Previous analyses by strain gauge technique, photoelastic and, more recently, finite element (FE) methods provided no direct evidence for occlusal load distribution through the cortical and trabecular bone compartments individually. Therefore, we developed an improved three-dimensional FE model of the human skull in order to clarify the distribution of occlusal forces through the cortical and trabecular bone during habitual masticatory activities. Particular focus was placed on the load transfer through the anterior and posterior maxilla. The results were presented in von Mises stress (VMS) and the maximum principal stress, and compared to the reported FE and strain gauge data. Our qualitative stress analysis indicates that occlusal forces distribute through the mid-facial skeleton along five vertical and two horizontal buttresses. We demonstrated that cortical bone has a priority in the transfer of occlusal load in the anterior maxilla, whereas both cortical and trabecular bone in the posterior maxilla are equally involved in performing this task. Observed site dependence of the occlusal load distribution may help clinicians in creating strategies for implantology and orthodontic treatments. Additionally, the magnitude of VMS in our model was significantly lower in comparison to previous FE models composed only of cortical bone. This finding suggests that both cortical and trabecular bone should be modeled whenever stress will be quantitatively analyzed.

Microstructural properties of the mid-facial bones in relation to the distribution of occlusal loading

Although the concept of the occlusal load transfer through the facial skeleton along the buttresses has been extensively studied, there has been no study to link microarchitecture of the mid-facial bones to the occlusal load distribution. The aim of this study was to analyze micro-structural properties of the mid-facial bones in relation to occlusal stress. The study was performed by combining the three-dimensional finite element analysis (3D FEA) and micro-computed tomography analysis (micro-CT). Clenching was simulated on the computer model of the adult male human skull which was also used as a source of bone specimens. After the FEA was run, stress was measured at the specific sites in cortical shell and trabecular bone of the model along and between the buttresses. From the corresponding sites on the skull, twenty-five cortical and thirteen cancellous bone specimens were harvested. The specimens were classified into high stress or low stress group based on the stress levels measured via the FEA. Micro-architecture of each specimen was assessed by micro-CT. In the high stress group, cortical bone showed a tendency toward greater thickness and density, lower porosity, and greater pore separation. Stress-related differences in microstructure between the groups were more pronounced in trabecular bone, which showed significantly greater bone volume fraction (BV/TV) and trabecular thickness (Tb.Th) in the high stress group. Our results suggest that the mid-facial bones in the adult dentate male skull exhibit regional variations in cortical and trabecular bone micro-architecture that could be a consequence of different occlusal stress.

SIFEM project: Finite element modeling of the cochlea

The cochlea is a very interesting part of the body. There are several investigations of experiments on the real cochlea and mathematical models. The cochlea works on the basis of a vibrating system. SIFEM project focuses on the development the multi-scale modelling of the inner-ear with regard to the sensorineural hearing loss. In this study we focused on the finite element model of the cochlea. The first approximation is straight box model where both domain basilar membrane and surrounding fluid are modeled. Fluid-structure interaction problem was implemented. The basilar membrane was modeled as structural plate with 3D brick finite element and fluid domain around the basilar membrane was modeled as full 3D Navier-Stokes equations. ALE formulation was employed for fluid domain and mesh moving algorithm for motion of the membrane and fluid mesh. The results for different frequencies for 3D box and spiral model are presented. It can be observed that viscous fluid allow a sharper response of the membrane, because the viscous fluid would quickly damp out the vibratory motion.

Computational modeling of shear forces and experimental validation of endothelial cell responses in an orbital well shaker system

Vascular endothelial cells are continuously exposed to hemodynamic shear stress. Intensity and type of shear stress are highly relevant to vascular physiology and pathology. Here, we modeled shear stress distribution in a tissue culture well (R = 17.5 mm, fill volume 2 ml) under orbital translation using computational fluid dynamics with the finite element method. Free surface distribution, wall shear stress, inclination angle, drag force, and oscillatory index on the bottom surface were modeled. Obtained results predict nonuniform shear stress distribution during cycle, with higher oscillatory shear index, higher drag force values, higher circular component, and larger inclination angle of the shear stress at the periphery of the well compared with the center of the well. The oscillatory index, inclination angle, and drag force are new quantitative parameters modeled in this system, which provide a better understanding of the hydrodynamic conditions experienced and reflect the pulsatile character of blood flow in vivo. Validation experiments revealed that endothelial cells at the well periphery aligned under flow and increased Kruppel-like Factor 4 (KLF-4), cyclooxygenase-2 (COX-2) expression and endothelial nitric oxide synthase (eNOS) phosphorylation. In contrast, endothelial cells at the center of the well did not show clear directional alignment, did not induce the expression of KLF-4 and COX-2 nor increased eNOS phosphorylation. In conclusion, this improved computational modeling predicts that the orbital shaker model generates different hydrodynamic conditions at the periphery versus the center of the well eliciting divergent endothelial cell responses. The possibility of generating different hydrodynamic conditions in the same well makes this model highly attractive to study responses of distinct regions of the same endothelial monolayer to different types of shear stresses thereby better reflecting in vivo conditions.

Computer simulation of thromboexclusion of the complete aorta in the treatment of chronic type B aneurysm.

The purpose of this computational study was to examine the hemodynamic parameters of the velocity fields, shear stress, pressure and drag force field in the complex aorta system, based on a case of type B aortic dissection. The extra-anatomic reconstruction of the complete aorta and bipolar exclusion of the aneurysm was investigated by computational fluid dynamics. Three different cases of the same patient were analyzed: the existing preoperative condition and two alternative surgical treatment options, cases A and B, involving different distal aorto-aortic anastomosis sites. The three-dimensional Navier-Stokes equations and the continuity equation were solved with an unsteady stabilized finite element method. The aorta and large tube graft geometries were reconstructed based on CT angiography images to generate a patient-specific 3D finite element mesh. The computed results showed velocity profiles with smaller intensity in the aorta than in the graft tube in the postoperative case. The shear stress distribution showed low zones around 0.5 Pa in the aneurysm part of the aorta for all three cases. Pressure distribution and, particularly, drag force had much higher values in the preoperative aneurysm zones (7.37 N) than postoperatively (2.45 N), which provides strong evidence of the hemodynamic and biomechanical benefits of this type of intervention in this specific patient. After assessing the outcome obtained with each of the two alternatives A and B, for which we found no significant difference, it was decided to use option A to treat the patient. In summary, computational studies could complement surgical preoperative risk assessment and provide significant insight into the benefits of different treatment alternatives.

Pharmacological Modulation of Hemodynamics in Adult Zebrafish In Vivo.

Introduction Hemodynamic parameters in zebrafish receive increasing attention because of their important role in cardiovascular processes such as atherosclerosis, hematopoiesis, sprouting and intussusceptive angiogenesis. To study underlying mechanisms, the precise modulation of parameters like blood flow velocity or shear stress is centrally important. Questions related to blood flow have been addressed in the past in either embryonic or ex vivo-zebrafish models but little information is available for adult animals. Here we describe a pharmacological approach to modulate cardiac and hemodynamic parameters in adult zebrafish in vivo. Materials and Methods Adult zebrafish were paralyzed and orally perfused with salt water. The drugs isoprenaline and sodium nitroprusside were directly applied with the perfusate, thus closely resembling the preferred method for drug delivery in zebrafish, namely within the water. Drug effects on the heart and on blood flow in the submental vein were studied using electrocardiograms, in vivo-microscopy and mathematical flow simulations. Results Under control conditions, heart rate, blood flow velocity and shear stress varied less than ± 5%. Maximal chronotropic effects of isoprenaline were achieved at a concentration of 50 μmol/L, where it increased the heart rate by 22.6 ± 1.3% (n = 4; p < 0.0001). Blood flow velocity and shear stress in the submental vein were not significantly increased. Sodium nitroprusside at 1 mmol/L did not alter the heart rate but increased blood flow velocity by 110.46 ± 19.64% (p = 0.01) and shear stress by 117.96 ± 23.65% (n = 9; p = 0.03). Discussion In this study, we demonstrate that cardiac and hemodynamic parameters in adult zebrafish can be efficiently modulated by isoprenaline and sodium nitroprusside. Together with the suitability of the zebrafish for in vivo-microscopy and genetic modifications, the methodology described permits studying biological processes that are dependent on hemodynamic alterations.

Modeling of liver metastatic disease with applied drug therapy.

Colorectal carcinoma is acknowledged as the second leading cause of total cancer-related death in the European Region. The majority of deaths related to colorectal carcinoma are connected with liver metastatic disease. Approximately, in 25% of all patients, liver metastatic disease is diagnosed at the same time as the primary diagnosis, while up to a quarter of others would develop liver metastases in the course of the illness. In this study, we developed reaction-diffusion model and analyzed the effect of drug therapy on liver metastatic disease for a specific patient. Tumor volumes in specific time points were obtained using CT scan images. The nonlinear function for cell proliferation rate as well as data about clinically applied drug therapy was included in the model. Fitting procedure was used for parameter estimation. Good agreement of numerical and experimental results shows the feasibility and efficacy of the proposed system.

Trauma of the Frontal Region Is Influenced by the Volume of Frontal Sinuses. A Finite Element Study

Anatomy of frontal sinuses varies individually, from differences in volume and shape to a rare case when the sinuses are absent. However, there are scarce data related to influence of these variations on impact generated fracture pattern. Therefore, the aim of this study was to analyse the influence of frontal sinus volume on the stress distribution and fracture pattern in the frontal region. The study included four representative Finite Element models of the skull. Reference model was built on the basis of computed tomography scans of a human head with normally developed frontal sinuses. By modifying the reference model, three additional models were generated: a model without sinuses, with hypoplasic, and with hyperplasic sinuses. A 7.7 kN force was applied perpendicularly to the forehead of each model, in order to simulate a frontal impact. The results demonstrated that the distribution of impact stress in frontal region depends on the frontal sinus volume. The anterior sinus wall showed the highest fragility in case with hyperplasic sinuses, whereas posterior wall/inner plate showed more fragility in cases with hypoplasic and undeveloped sinuses. Well-developed frontal sinuses might, through absorption of the impact energy by anterior wall, protect the posterior wall and intracranial contents.