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.

The authors present the preparation procedure and a computational model of a three-layered fibrous scaffold for prolonged drug release. The scaffold, produced by emulsion/sequential electrospinning, consists of a poly(d,l-lactic-co-glycolic acid) (PLGA) fiber layer sandwiched between two poly(εcaprolactone) (PCL) layers. Experimental results of drug release rates from the scaffold are compared with the results of the recently introduced computational finite element (FE) models for diffusive drug release from nanofibers to the three-dimensional (3D) surrounding medium. Two different FE models are used: (1) a 3D discretized continuum and fibers represented by a simple radial one-dimensional (1D) finite elements, and (2) a 3D continuum discretized by composite smeared finite elements (CSFEs) containing the fiber smeared and surrounding domains. Both models include the effects of polymer degradation and hydrophobicity (as partitioning) of the drug at the fiber/surrounding interface. The CSFE model includes a volumetric fraction of fibers and diameter distribution, and is additionally enhanced by using correction function to improve the accuracy of the model. The computational results are validated on Rhodamine B (fluorescent drug l) and other hydrophilic drugs. Agreement with experimental results proves that numerical models can serve as efficient tools for drug release to the surrounding porous medium or biological tissue. It is demonstrated that the introduced three-layered scaffold delays the drug release process and can be used for the time-controlled release of drugs in postoperative therapy. A promising approach in modern medicine for drug delivery over a long time period and with a desirable rate is the use of nano-scaffolds 1-3 , and specifically electrospun-made scaffolds composed of drug loaded nanofiber mats 4-8. Fibers are preferably prepared using a biodegradable polymer 7 , and their main function is targeted and cites specific drug delivery in human body 1-5 , without any burst release 7 , and with improved physicochemical properties 6. This kind of drug delivery systems have provided many mechanisms that improve the therapeutic efficacy of both new and already existing drugs 7 , and may be now used for various paramedical and medical applications such as wound healing and cancer therapy 1-5. The advantages of using biodegradable polymers for drug delivery are: no need for the second surgery to remove the scaffold once the drug is released 9 , their enhanced biocompatibility, degradability, bioactivity and resorbability 8,10-12. Among the most commonly used biodegradable synthetic polymers, poly(lactic-co-glycolide (PLGA) copolymer is well recognized for drug delivery processes 13. PLGA is known for good biocompatibility and ability to achieve complete drug release 14 , which is the result of its degradation and erosion properties 15,16. Many

Metastatic disease is a major cause of mortality in cancer patients. While many drug delivery strategies for anticancer therapeutics have been developed in preclinical studies of primary tumors, the drug delivery properties of metastatic tumors have not been sufficiently investigated. Therapeutic efficacy hinges on efficient drug permeation into the tumor microenvironment, which is known to be heterogeneous thus potentially making drug permeation heterogeneous, also. In this study, we have identified that 4T1 liver metastases, treated with pegylated liposomal doxorubicin, have unfavorable and heterogeneous transport of doxorubicin. Our drug extravasation results differ greatly from analogous studies with 4T1 tumors growing in the primary site. A probabilistic tumor population model was developed to estimate drug permeation efficiency and drug kinetics of liver metastases by integrating the transport and structural properties of tumors and delivered drugs. The results demonstrate significant heterogeneity in metastases with regard to transport properties of doxorubicin within the same animal model, and even within the same organ. These results also suggest that the degree of heterogeneity depends on the stage of tumor progression and that differences in transport properties can define transport-based tumor phenotypes. These findings may have valuable clinical implications by illustrating that therapeutic agents can permeate and eliminate metastases of “less resistant” transport phenotypes, while sparing tumors with more “resistant” transport properties. We anticipate that these results could challenge the current paradigm of drug delivery into metastases, highlight potential caveats for therapies that may alter tumor perfusion, and deepen our understanding of the emergence of drug transport-based therapeutic resistance.

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.

Modeling of drug transport within capillaries and tissue remains a challenge, especially in tumors and cancers where the capillary network exhibits extremely irregular geometry. Recently introduced Composite Smeared Finite Element (CSFE) provides a new methodology of modeling complex convective and diffusive transport in the capillary-tissue system. The basic idea in the formulation of CSFE is in dividing the FE into capillary and tissue domain, coupled by 1D connectivity elements at each node. Mass transport in capillaries is smeared into continuous fields of pressure and concentration by introducing the corresponding Darcy and diffusion tensors. Despite theoretically correct foundation, there are still differences in the overall mass transport to (and from) tissue when comparing smeared model and a true 3D model. The differences arise from the fact that the smeared model cannot take into account the detailed non-uniform pressure and concentration distribution in the vicinity of capillaries. We introduced a field of correction function for diffusivity through the capillary walls of smeared models, in order to have the same mass accumulation in tissue as in case of true 3D models. The parameters of the numerically determined correction function are: ratio of thickness and diameter of capillary wall, ratio of diffusion coefficient in capillary wall and surrounding tissue; and volume fraction of capillaries within tissue domain. Partitioning at the capillary wall – blood interface can also be included. It was shown that the correction function is applicable to complex configurations of capillary networks, providing improved accuracy of our robust smeared models in computer simulations of real transport problems, such as in tumors or human organs.