Dalibor Nikolic

ARTreat project: Three-dimensional numerical simulation of plaque formation and development in the arteries

Atherosclerosis is a progressive disease characterized by the accumulation of lipids and fibrous elements in arteries. It is characterized by dysfunction of endothelium and vasculitis, and accumulation of lipid, cholesterol, and cell elements inside blood vessel wall. In this study, a continuum-based approach for plaque formation and development in 3-D is presented. The blood flow is simulated by the 3-D Navier-Stokes equations, together with the continuity equation while low-density lipoprotein (LDL) transport in lumen of the vessel is coupled with Kedem-Katchalsky equations. The inflammatory process was solved using three additional reaction-diffusion partial differential equations. Transport of labeled LDL was fitted with our experiment on the rabbit animal model. Matching with histological data for LDL localization was achieved. Also, 3-D model of the straight artery with initial mild constriction of 30% plaque for formation and development is presented.

Patient-Specific Prediction of Coronary Plaque Growth From CTA Angiography: A Multiscale Model for Plaque Formation and Progression

Computational fluid dynamics methods based on in vivo 3-D vessel reconstructions have recently been identified the influence of wall shear stress on endothelial cells as well as on vascular smooth muscle cells, resulting in different events such as flow mediated vasodilatation, atherosclerosis, and vascular remodeling. Development of image-based modeling technologies for simulating patient-specific local blood flows is introducing a novel approach to risk prediction for coronary plaque growth and progression. In this study, we developed 3-D model of plaque formation and progression that was tested in a set of patients who underwent coronary computed tomography angiography (CTA) for anginal symptoms. The 3-D blood flow is described by the Navier-Stokes equations, 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 lipoprotein (LDL) transports in lumen of the vessel and through the vessel tissue (which has a mass consumption term) are coupled by Kedem-Katchalsky equations. The inflammatory process is modeled using three additional reaction-diffusion partial differential equations. A full 3-D model was created. It includes blood flow and LDL concentration, as well as plaque formation and progression. Furthermore, features potentially affecting plaque growth, such as patient risk score, circulating biomarkers, localization and composition of the initial plaque, and coronary vasodilating capability were also investigated. The proof of concept of the model effectiveness was assessed by repetition of CTA, six months after the baseline evaluation. Besides the low values of local shear stress, plaque characteristics, risk profile, pattern of circulating adhesion molecules, and reduced coronary flow reserve at baseline appeared to affect plaque progression toward flow-limiting lesions at follow-up evaluation. Although preliminary, our multidisciplinary approach to a “personalized” prediction of coronary plaque progression suggests that incorporation in atherosclerotic models of systemic and local hemodynamic features may better predict evolution of plaques in coronary artery disease stable patients.

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.

Computational analysis of lung deformation after murine pneumonectomy. [corrected].

In many mammalian species, the removal of one lung (pneumonectomy) is associated with the compensatory growth of the remaining lung. To investigate the hypothesis that parenchymal deformation may trigger lung regeneration, we used microCT scanning to create 3D finite element geometric models of the murine lung pre- and post-pneumonectomy (24 h). The structural correspondence between models was established using anatomic landmarks and an iterative computational algorithm. When compared with the pre-pneumonectomy lung, the post-pneumonectomy models demonstrated significant translation and rotation of the cardiac lobe into the post-pneumonectomy pleural space. 2D maps of lung deformation demonstrated significant heterogeneity; the areas of greatest deformation were present in the subpleural regions of the lobe. Consistent with the previously identified growth patterns, subpleural regions of enhanced deformation are compatible with a mechanical signal – likely involving parenchymal stretch – triggering lung growth.

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.

Mapping cyclic stretch in the postpneumonectomy murine lung

In many mammalian species, the removal of one lung [pneumonectomy (PNX)] is associated with the compensatory growth of the remaining lung. To investigate the hypothesis that parenchymal deformation may trigger lung regeneration, we used respiratory-gated micro-computed tomography scanning to create three-dimensional finite-element geometric models of the murine cardiac lobe with cyclic breathing. Models were constructed of respiratory-gated micro-computed tomography scans pre-PNX and 24 h post-PNX. The computational models demonstrated that the maximum stretch ratio map was patchy and heterogeneous, particularly in subpleural, juxta-diaphragmatic, and cephalad regions of the lobe. In these parenchymal regions, the material line segments at peak inspiration were frequently two- to fourfold greater after PNX; some regions of the post-PNX cardiac lobe demonstrated parenchymal compression at peak inspiration. Similarly, analyses of parenchymal maximum shear strain demonstrated heterogeneous regions of mechanical stress with focal regions demonstrating a threefold increase in shear strain after PNX. Consistent with previously identified growth patterns, these subpleural regions of enhanced stretch and shear strain are compatible with a mechanical signal, likely involving cyclic parenchymal stretch, triggering lung growth.

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.

Finite element coiled cochlea model

Cochlea is important part of the hearing system, and thanks to special structure converts external sound waves into neural impulses which go to the brain. Shape of the cochlea is like snail, so geometry of the cochlea model is complex. The simplified cochlea coiled model was developed using finite element method inside SIFEM FP7 project. Software application is created on the way that user can prescribe set of the parameters for spiral cochlea, as well as material properties and boundary conditions to the model. Several mathematical models were tested. The acoustic wave equation for describing fluid in the cochlea chambers – scala vestibuli and scala timpani, and Newtonian dynamics for describing vibrations of the basilar membrane are used. The mechanical behavior of the coiled cochlea was analyzed and the third chamber, scala media, was not modeled because it does not have a significant impact on the mechanical vibrations of the basilar membrane. The obtained results are in good agreement with experiment...

Patient specific multiscale modelling for plaque formation and progression

We present a three-dimensional model of plaque formation and progression that was tested in a set of patients who underwent coronary Computed Tomography angiography (CTA) for anginal symptoms. The 3D blood flow is described by the Navier-Stokes equations, 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 Lipoprotein (LDL) transports in lumen of the vessel and through the vessel tissue (which has a mass consumption term) are coupled by Kedem-Katchalsky equations. The inflammatory process is modeled using three additional reaction-diffusion partial differential equations. A full three-dimensional model was created. Furthermore, features potentially affecting plaque growth, such as patient risk score, circulating biomarkers, localization and composition of the initial plaque, and coronary vasodilating capability were also investigated. The proof of concept of the model effectiveness was assessed 6 months after the baseline evaluation.