Multiscale smeared finite element model for mass transport in biological tissue: From blood vessels to cells and cellular organelles.

One of the basic and vital processes in living organisms is mass exchange, which occurs on several levels: it goes from blood vessels to cells and organelles within cells. On that path, molecules, as oxygen, metabolic products, drugs, etc. Traverse different macro and micro environments - blood, extracellular/intracellular space, and interior of organelles; and also biological barriers such as walls of blood vessels and membranes of cells and organelles. Many aspects of this mass transport remain unknown, particularly the biophysical mechanisms governing drug delivery. The main research approach relies on laboratory and clinical investigations. In parallel, considerable efforts have been directed to develop computational tools for additional insight into the intricate process of mass exchange and transport. Along these lines, we have recently formulated a composite smeared finite element (CSFE) which is composed of the smeared continuum pressure and concentration fields of the capillary and lymphatic system, and of these fields within tissue. The element offers an elegant and simple procedure which opens up new lines of inquiry and can be applied to large systems such as organs and tumors models. Here, we extend this concept to a multiscale scheme which concurrently couples domains that span from large blood vessels, capillaries and lymph, to cell cytosol and further to organelles of nanometer size. These spatial physical domains are coupled by the appropriate connectivity elements representing biological barriers. The composite finite element has "degrees of freedom" which include pressures and concentrations of all compartments of the vessels-tissue assemblage. The overall model uses the standard, measurable material properties of the continuum biological environments and biological barriers. It can be considered as a framework into which we can incorporate various additional effects (such as electrical or biochemical) for transport through membranes or within cells. This concept and the developed FE software within our package PAK offers a computational tool that can be applied to whole-organ systems, while also including specific domains such as tumors. The solved examples demonstrate the accuracy of this model and its applicability to large biological systems.

Mass release curves as the constitutive curves for modeling diffusive transport within biological tissue.

In diffusion governed by Fick's law, the diffusion coefficient represents the phenomenological material parameter and is, in general, a constant. In certain cases of diffusion through porous media, the diffusion coefficient can be variable (i.e. non-constant) due to the complex process of solute displacements within microstructure, since these displacements depend on porosity, internal microstructural geometry, size of the transported particles, chemical nature, and physical interactions between the diffusing substance and the microstructural surroundings. In order to provide a simple and general approach of determining the diffusion coefficient for diffusion through porous media, we have introduced mass release curves as the constitutive curves of diffusion. The mass release curve for a selected direction represents cumulative mass (per surface area) passed in that direction through a small reference volume, in terms of time. We have developed a methodology, based on numerical Finite Element (FE) and Molecular Dynamics (MD) methods, to determine simple mass release curves of solutes through complex media from which we calculate the diffusion coefficient. The diffusion models take into account interactions between solute particles and microstructural surfaces, as well as hydrophobicity (partitioning). We illustrate the effectiveness of our approach on several examples of complex composite media, including an imaging-based analysis of diffusion through pancreatic cancer tissue. The presented work offers an insight into the role of mass release curves in describing diffusion through porous media in general, and further in case of complex composite media such as biological tissue.

Assessment of hepatic steatosis algorithms in non-alcoholic fatty liver disease.

BACKGROUND: In order to optimize the identification of persons with non-alcoholic fatty liver disease (NAFLD), several algorithms for hepatic steatosis were developed. These available algorithms, as well as an algorithm, derived using biochemical and anthropometric data of our participants, are compared in a cross-sectional pilot study. MATERIAL AND METHODS: We included 77 participants with abdominal obesity: 43 with NAFLD and 33 without NAFLD. Body mass index (BMI), waist circumference (WC) and hip circumference (HC), systolic and diastolic blood pressure were assessed. Fibrinogen, high sensitive C-reactive protein (hsCRP), aspartate aminotransferase (AST), alanine transaminase (ALT), gamma-glutamyl transferase (GGT), uric acid, ferritin, glucose, insulin, homocysteine, lipid status parameters, apolipoprotein A-I, apolipoprotein B and Lp(a)-lipoprotein were measured. Fatty liver was assessed by ultrasound with the presence or absence of hepatic steatosis. Discovering the most significant factor in the presence of NAFLD is assessed through logistic regression modeling. The predictor variables were chosen according to an algorithm derived from conducted factor analysis and other available algorithms for hepatic steatosis. RESULTS: Participants with NAFLD had significantly higher BMI (34.38 ± 9.73 vs 28.05 ± 4.79 kg/m2, p =0.001), WC (108.05 ± 11.47 vs 96.15 ± 14.27 cm, p =0.001), HC (114.93 ± 11.01 vs 108.21 ± 9.82 cm, p =0.050), systolic (128.98 ± 8.67 vs 122.42 ± 10.62 mmHg, p =0.010) and diastolic blood pressure (83.64 ± 5.94 vs 78.33 ± 7.57 mmHg, p =0.001), AST (23.93 ± 6.91 vs 21.70 ± 5.21 U/L, p =0.014), ALT (30.50 ± 13.70 vs 23.00 ± 11.75 U/L, p =0.007), hsCRP (4.34 ± 5.56 vs 2.98 ± 2.34mg/l, p =0.004) and uric acid (358.02 ± 83.29 vs 296.78 ± 84.54µmol/l, p =0.001), in comparison non NAFLD. Logistic regression model with algorithm derived from factor analysis showed the best performance. From other available algorithms, only fatty liver index (FLI) and hepatic steatosis index (HSI) had statistically significant discriminatory power.   Conclusions: Elevation of WC, HC, BMI, DBP, SBP, Fbg, hsCRP, glucose, and uric acid, incorporated in our hepatic steatosis prediction model, had the best predictive power among all assessed algorithms. HIPPOKRATIA 2018, 22(1): 10-16.

A composite smeared finite element for mass transport in capillary systems and biological tissue.

One of the key processes in living organisms is mass transport occurring from blood vessels to tissues for supplying tissues with oxygen, nutrients, drugs, immune cells, and - in the reverse direction - transport of waste products of cell metabolism to blood vessels. The mass exchange from blood vessels to tissue and vice versa occurs through blood vessel walls. This vital process has been investigated experimentally over centuries, and also in the last decades by the use of computational methods. Due to geometrical and functional complexity and heterogeneity of capillary systems, it is however not feasible to model in silico individual capillaries (including transport through the walls and coupling to tissue) within whole organ models. Hence, there is a need for simplified and robust computational models that address mass transport in capillary-tissue systems. We here introduce a smeared modeling concept for gradient-driven mass transport and formulate a new composite smeared finite element (CSFE). The transport from capillary system is first smeared to continuous mass sources within tissue, under the assumption of uniform concentration within capillaries. Here, the fundamental relation between capillary surface area and volumetric fraction is derived as the basis for modeling transport through capillary walls. Further, we formulate the CSFE which relies on the transformation of the one-dimensional (1D) constitutive relations (for transport within capillaries) into the continuum form expressed by Darcy's and diffusion tensors. The introduced CSFE is composed of two volumetric parts - capillary and tissue domains, and has four nodal degrees of freedom (DOF): pressure and concentration for each of the two domains. The domains are coupled by connectivity elements at each node. The fictitious connectivity elements take into account the surface area of capillary walls which belongs to each node, as well as the wall material properties (permeability and partitioning). The overall FE model contains geometrical and material characteristics of the entire capillary-tissue system, with physiologically measurable parameters assigned to each FE node within the model. The smeared concept is implemented into our implicit-iterative FE scheme and into FE package PAK. The first three examples illustrate accuracy of the CSFE element, while the liver and pancreas models demonstrate robustness of the introduced methodology and its applicability to real physiological conditions.

A multiscale MD-FE model of diffusion in composite media with internal surface interaction based on numerical homogenization procedure.

Mass transport by diffusion within composite materials may depend not only on internal microstructural geometry, but also on the chemical interactions between the transported substance and the material of the microstructure. Retrospectively, there is a gap in methods and theory to connect material microstructure properties with macroscale continuum diffusion characteristics. Here we present a new hierarchical multiscale model for diffusion within composite materials that couples material microstructural geometry and interactions between diffusing particles and the material matrix. This model, which bridges molecular dynamics (MD) and the finite element (FE) method, is employed to construct a continuum diffusion model based on a novel numerical homogenization procedure. The procedure is general and robust for evaluating constitutive material parameters of the continuum model. These parameters include the traditional bulk diffusion coefficients and, additionally, the distances from the solid surface accounting for surface interaction effects. We implemented our models to glucose diffusion through the following two geometrical/material configurations: tightly packed silica nanospheres, and a complex fibrous structure surrounding nanospheres. Then, rhodamine 6G diffusion analysis through an aga-rose gel network was performed, followed by a model validation using our experimental results. The microstructural model, numerical homogenization and continuum model offer a new platform for modeling and predicting mass diffusion through complex biological environment and within composite materials that are used in a wide range of applications, like drug delivery and nanoporous catalysts.

Ex vivo rheology of spider silk.

We investigate the rheological properties of microliter quantities of the spinning material extracted ex vivo from the major ampullate gland of a Nephila clavipes spider using two new micro-rheometric devices. A sliding plate micro-rheometer is employed to measure the steady-state shear viscosity of approximately 1 microl samples of silk dope from individual biological specimens. The steady shear viscosity of the spinning solution is found to be highly shear-thinning, with a power-law index consistent with values expected for liquid crystalline solutions. Calculations show that the viscosity of the fluid decreases 10-fold as it flows through the narrow spinning canals of the spider. By contrast, measurements in a microcapillary extensional rheometer show that the transient extensional viscosity (i.e. the viscoelastic resistance to stretching) of the spinning fluid increases more than 100-fold during the spinning process. Quantifying the properties of native spinning solutions provides new guidance for adjusting the spinning processes of synthetic or genetically engineered silks to match those of the spider.

Contribution to the history of plastic and reconstructive surgery from Dubrovnik and split during the fourteenth to sixteenth centuries.

Medieval contracts for medical treatment are, without doubt, evidence of proper and adequate insight into the quality of operations performed centuries ago. Historical archives in Dalmatian cities have preserved a certain number of such contracts. Their contents assist in better understanding our historical heritage. This paper submits contracts, kept in Dubrovnik and Split, for the operation of inguinal hernia. A case depicting a defective palate treated by Amatus Lusitanus, who lived in Dubrovnik from 1555 to 1558, is also presented.