Smeared multiscale finite element model for electrophysiology and ionic transport in biological tissue

Basic functions of living organisms are governed by the nervous system through bidirectional signals transmitted from the brain to neural networks. These signals are similar to electrical waves. In electrophysiology the goal is to study the electrical properties of biological cells and tissues, and the transmission of signals. From a physics perspective, there exists a field of electrical potential within the living body, the nervous system, extracellular space and cells. Electrophysiological problems can be investigated experimentally and also theoretically by developing appropriate mathematical or computational models. Due to the enormous complexity of biological systems, it would be almost impossible to establish a detailed computational model of the electrical field, even for only a single organ (e.g. heart), including the entirety of cells comprising the neural network. In order to make computational models feasible for practical applications, we here introduce the concept of smeared fields, which represents a generalization of the previously formulated multiscale smeared methodology for mass transport in blood vessels, lymph, and tissue. We demonstrate the accuracy of the smeared finite element computational models for the electric field in numerical examples. The electrical field is further coupled with ionic mass transport within tissue composed of interstitial spaces extracellularly and by cytoplasm and organelles intracellularly. The proposed methodology, which couples electrophysiology and molecular ionic transport, is applicable to a variety of biological systems.

Coupling tumor growth and bio distribution models

We couple a tumor growth model embedded in a microenvironment, with a bio distribution model able to simulate a whole organ. The growth model yields the evolution of tumor cell population, of the differential pressure between cell populations, of porosity of ECM, of consumption of nutrients due to tumor growth, of angiogenesis, and related growth factors as function of the locally available nutrient. The bio distribution model on the other hand operates on a frozen geometry but yields a much refined distribution of nutrient and other molecules. The combination of both models will enable simulating the growth of a tumor in a whole organ, including a realistic distribution of therapeutic agents and allow hence to evaluate the efficacy of these agents.

A Computational Model for Drug Release from PLGA Implant

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.

Progression-dependent transport heterogeneity of breast cancer liver metastases as a factor in therapeutic resistance

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 4 T1 liver metastases, treated with pegylated liposomal doxorubicin, have unfavorable and heterogeneous transport of doxorubicin. Our drug extravasation results differ greatly from analogous studies with 4 T1 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.

Correction function for accuracy improvement of the Composite Smeared Finite Element for diffusive transport in biological tissue systems

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.

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.

Strategic planning in an academic radiation medicine program

Background

In this paper, we report on the process of strategic planning in the Radiation Medicine Program (rmp) at the Princess Margaret Cancer Centre. The rmp conducted a strategic planning exercise to ensure that program priorities reflect the current health care environment, enable nimble responses to the increasing burden of cancer, and guide program operations until 2020.

Methods

Data collection was guided by a project charter that outlined the project goal and the roles and responsibilities of all participants. The process was managed by a multidisciplinary steering committee under the guidance of an external consultant and consisted of reviewing strategic planning documents from close collaborators and institutional partners, conducting interviews with key stakeholders, deploying a program-wide survey, facilitating an anonymous and confidential e-mail feedback box, and collecting information from group deliberations.

Results

The process of strategic planning took place from December 2014 to December 2015. Mission and vision statements were developed, and core values were defined. A final document, Strategic Roadmap to 2020, was established to guide programmatic pursuits during the ensuing 5 years, and an implementation plan was developed to guide the first year of operations.

Conclusions

The strategic planning process provided an opportunity to mobilize staff talents and identify environmental opportunities, and helped to enable more effective use of resources in a rapidly changing health care environment. The process was valuable in allowing staff to consider and discuss the future, and in identifying strategic issues of the greatest importance to the program. Academic programs with similar mandates might find our report useful in guiding similar processes in their own organizations.

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.

Tumor progression effects on drug vector access to tumor-associated capillary bed

Over the last decade, the benefits of drug vectors to treat cancer have been well recognized. However, drug delivery and vector distribution differences in tumor-associated capillary bed at different stages of disease progression are not well understood. To obtain further insights into drug vector distribution changes in vasculature during tumor progression, we combined intra-vital imaging of metastatic tumors in mice, microfluidics-based artificial tumor capillary models, and Computational Fluid Dynamics (CFD) modeling. Microfluidic and CFD circulation models were designed to mimic tumor progression by escalating flow complexity and chaoticity. We examined flow of 0.5 and 2μm spherical particles, and tested the effects of hematocrit on particle local accessibility to flow area of capillary beds by co-circulating red blood cells (RBC). Results showed that tumor progression modulated drug vector distribution in tumor-associated capillaries. Both particles shared 80-90% common flow area, while 0.5 and 2μm particles had 2-9% and 1-2% specific flow area, respectively. Interestingly, the effects of hematocrit on specific circulation area was opposite for 0.5 and 2μm particles. Dysfunctional capillaries with no flow, a result of tumor progression, limited access to all particles, while diffusion was shown to be the only prevailing transport mechanism. In view of drug vector distribution in tumors, independent of formulation and other pharmacokinetic aspects, our results suggest that the evolution of tumor vasculature during progression may influence drug delivery efficiency. Therefore, optimized drug vectors will need to consider primary vs metastatic tumor setting, or early vs late stage metastatic disease, when undergoing vector design.

Extension of the composite smeared finite element (CSFE) to include lymphatic system in modeling mass transport in capillary systems and biological tissue

We have recently introduced a composite smeared finite element (CSFE) to model gradient-driven mass transport in biological tissue. The transport from capillary system is smeared in a way to transform 1D transport to a continuum, while the tissue is considered as a continuum. Coupling between the smeared pressure and concentration field is achieved through 1D connectivity elements assigned at each FE node. Here we extend our smeared model to include the lymphatic system. The lymphatic vessels are treated in a way analogous to the capillaries, by introducing the corresponding Darcy and diffusion tensors. New connectivity elements are added. In the numerical examples we demonstrate accuracy of the smeared model and the effects of the lymph on the pressure and concentration within extracellular space are evaluated, assuming that there is no transport to the cell space.