A mixture theory model of fluid and solute transport in the microvasculature of normal and malignant tissues. II: Factor sensitivity analysis, calibration, and validation

Lymphatic uptake of biotherapeutics through a 3D hybrid discrete-continuum vessel network in the skin tissue

Subcutaneous administration is a common approach for the delivery of biotherapeutics, which is achieved mainly through the absorption across lymphatic vessels. In this paper, the drug transport and lymphatic uptake through a three-dimensional hybrid discrete-continuum vessel network in the skin tissue are investigated through high-fidelity numerical simulations. We find that the local lymphatic uptake through the explicit vessels significantly affects macroscopic drug absorption. The diffusion of drug solute through the explicit vessel network affects the lymphatic uptake after the injection. This effect, however, cannot be captured using previously developed continuum models. The lymphatic uptake is dominated by the convection due to lymphatic drainage driven by the pressure difference, which is rarely studied in experiments and simulations. Furthermore, the effects of injection volume and depth on the lymphatic uptake are investigated in a multi-layered domain. We find that the injection volume significantly affects the rate of lymphatic uptake through the heterogeneous vessel network, while the injection depth has little influence, which is consistent with the experimental results. At last, the binding and metabolism of drug molecules are studied to bridge the simulations to the drug clearance experients. We provide a new approach to study the diffusion and convection of drug molecules into the lymphatic system through the hybrid vessel network.

A model for designing intraocular pressure-regulating glaucoma implants

Glaucoma is a group of eye conditions that damage the optic nerve, the health of which is vital for vision. The key risk factor for the development and progression of this disease is increased intraocular pressure (IOP). Implantable glaucoma drainage devices have been developed to divert aqueous humor from the glaucomatous eye as a means of reducing IOP. The artificial drainage pathway created by these devices drives the fluid into a filtering bleb. The long-term success of filtration surgery is dictated by the proper functioning of the bleb and overlying Tenon’s and conjunctival tissue. To better understand the influence of the health condition of these tissues on IOP, we have developed a mathematical model of fluid production in the eye, its removal from the anterior chamber by a particular glaucoma implant–the PRESERFLO^® MicroShunt–, drainage into the bleb and absorption by the subconjunctival vasculature. The mathematical model was numerically solved by commercial FEM package COMSOL. Our numerical results of IOP for different postoperative conditions are consistent with the available evidence on IOP outcomes after the implantation of this device. To obtain insight into the adjustments in the implant’s hydrodynamic resistance that are required for IOP control when hypotony or bleb scarring due to tissue fibrosis take place, we have simulated the flow through a microshunt with an adjustable lumen diameter. Our findings show that increasing the hydrodynamic resistance of the microshunt by reducing the lumen diameter, can effectively help to prevent hypotony. However, decreasing the hydrodynamic resistance of the implant will not sufficiently decrease the IOP to acceptable levels when the bleb is encapsulated due to tissue fibrosis. Therefore, to effectively reduce IOP, the adjustable glaucoma implant should be combined with a means of reducing fibrosis. The results reported herein may provide guidelines to support the design of future glaucoma implants with adjustable hydrodynamic resistances.

Effect of Particle Size and Surface Charge on Nanoparticles Diffusion in the Brain White Matter

Purpose

Brain disorders have become a serious problem for healthcare worldwide. Nanoparticle-based drugs are one of the emerging therapies and have shown great promise to treat brain diseases. Modifications on particle size and surface charge are two efficient ways to increase the transport efficiency of nanoparticles through brain-blood barrier; however, partly due to the high complexity of brain microstructure and limited visibility of Nanoparticles (NPs), our understanding of how these two modifications can affect the transport of NPs in the brain is insufficient.

Methods

In this study, a framework, which contains a stochastic geometric model of brain white matter (WM) and a mathematical particle tracing model, was developed to investigate the relationship between particle size/surface charge of the NPs and their effective diffusion coefficients (D) in WM.

Results

The predictive capabilities of this method have been validated using published experimental tests. For negatively charged NPs, both particle size and surface charge are positively correlated with D before reaching a size threshold. When Zeta potential (Zp) is less negative than -10 mV, the difference between NPs’ D in WM and pure interstitial fluid (IF) is limited.

Conclusion

A deeper understanding on the relationships between particle size/surface charge of NPs and their D in WM has been obtained. The results from this study and the developed modelling framework provide important tools for the development of nano-drugs and nano-carriers to cure brain diseases.

Theoretical evaluation of enhanced gold nanoparticle delivery to PC3 tumors due to increased hydraulic conductivity or recovered lymphatic function after mild whole body hyperthermia

The objective of this study is to investigate the effect of hyperthermia-induced improvement of hydraulic conductivity and lymphatic function on both tumoral IFP reduction and nanoparticle delivery to PC3 tumors. We developed a theoretical model for nanoparticle transport in a tumor incorporating Starling's law, Darcy's law, transient convection, and diffusion of chemical species in porous media, and nanoparticle accumulation in tumors. Results have shown that both mechanisms were effective to decrease the IFP at the tumor center from 1600 Pa in the control without heating to 800 Pa in tumors with whole body heating. IFP reductions not only elevate the nanoparticle concentration in the tumor, but also result in a more uniform nanoparticle concentration in the tumor than that in the control without heating. Due to the IFP reductions at the tumor center and/or local blood perfusion increases, the final amount of accumulated nanoparticles in the tumor increased by more than 35-95% when compared to the control without heating. We conclude that increases in the hydraulic conductivity and recovery of lymphatic functions are possible mechanisms that lead to IFP reductions and enhancement in nanoparticle deposition in PC3 tumors observed in our in vivo experimental studies.

Factors affecting peak impact force during soccer headers and implications for the mitigation of head injuries

It has been documented that up to 22% of all soccer injuries are concussions. This is in part due to players purposely using their head to direct the ball during play. To provide a more complete understanding of head trauma in soccer athletes, this study characterized the effects of four soccer ball characteristics (size, inflation pressure, mass, velocity) on the resulting peak impact force as it relates to the potential for incurring neurophysiological changes. A total of six hundred trials were performed on size 4 and 5 soccer balls as well as a novel lightweight soccer ball. Impact force was measured with a force plate and ball velocity was determined using motion capture. These data were used, in conjunction with dimensional analysis to relate impact force to ball size, mass, velocity, and pressure. Reasonable reductions in allowable ball parameters resulted in a 19.7% decrease in peak impact force. Adjustments to ball parameters could reduce a high cumulative peak translational acceleration soccer athlete down into a previously defined safer low loading range. In addition, it was noted that water absorption by soccer balls can result in masses that substantially increase impact force and quickly surpass the NCAA weight limit for game play. Additional research is required to determine whether varying soccer ball characteristics will enable soccer players to avoid persistent neurophysiological deficits or what additional interventions may be necessary and the legal implications of these data are discussed.

Mitigating the Consequences of Subconcussive Head Injuries

Subconcussive head injury represents a pathophysiology that spans the expertise of both clinical neurology and biomechanical engineering. From both viewpoints, the terms injury and damage, presented without qualifiers, are synonymously taken to mean a tissue alteration that may be recoverable. For clinicians, concussion is evolving from a purely clinical diagnosis to one that requires objective measurement, to be achieved by biomedical engineers. Subconcussive injury is defined as subclinical pathophysiology in which underlying cellular- or tissue-level damage (here, to the brain) is not severe enough to present readily observable symptoms. Our concern is not whether an individual has a (clinically diagnosed) concussion, but rather, how much accumulative damage an individual can tolerate before they will experience long-term deficit(s) in neurological health. This concern leads us to look for the history of damage-inducing events, while evaluating multiple approaches for avoiding injury through reduction or prevention of the associated mechanically induced damage.

Mixture theory modeling for characterizing solute transport in breast tumor tissues

Background

Tumor numerical models have been used to quantify solute transport with a single capillary embedded in an infinite tumor expanse, but measurements from different mammalian tumors suggest that a tissue containing a single capillary with an infinite intercapillary distance assumption is not physiological. The present study aims to investigate the limits of the intercapillary distance within which nanoparticle transport resembles solute extravasation in a breast tumor model as a function of the solute size, the intercapillary separation, and the flow direction in microvessels.

Methods

Solute transport is modeled in a breast tumor for different vascular configurations using mixture theory. A comparison of a single capillary configuration (SBC) with two parallel cylindrical blood vessels (2 BC) and a lymph vessel parallel to a blood vessel (BC_LC) embedded in the tissue cylinder is performed for five solute molecular weights between 0.1 kDa and 70 kDa. The effects of counter flow (CN) versus co-current flow (CO) on the solute accumulation were also investigated and the scaling of solute accumulation-decay time and concentration was explored.

Results

We found that the presence of a second capillary reduces the extravascular concentration compared to a single capillary and this reduction is enhanced by the presence of a lymph vessel. Varying the intercapillary distance with respect to vessel diameter shows a deviation of 10-30% concentration for 2 BC and 45-60% concentration for BC_LC configuration compared to the reference SBC configuration. Finally, we introduce a non-dimensional time scale that captures the concentration as a function of the transport and geometric parameters. We find that the peak solute concentration in the tissue space occurs at a non-dimensional time, T peak ∗ = 0.027 ± 0.018, irrespective of the solute size, tissue architecture, and microvessel flow direction.

Conclusions

This work suggests that the knowledge of such a unique non-dimensional time would allow estimation of the time window at which solute concentration in tissue peaks. Hence this can aid in the design of future therapeutic efficacy studies as an example for triggering drug release or laser excitation in the case of photothermal therapies.

A computational study of cancer hyperthermia based on vascular magnetic nanoconstructs

The application of hyperthermia to cancer treatment is studied using a novel model arising from the fundamental principles of flow, mass and heat transport in biological tissues. The model is defined at the scale of the tumour microenvironment and an advanced computational scheme called the embedded multiscale method is adopted to solve the governing equations. More precisely, this approach involves modelling capillaries as one-dimensional channels carrying flow, and special mathematical operators are used to model their interaction with the surrounding tissue. The proposed computational scheme is used to analyse hyperthermic treatment of cancer based on systemically injected vascular magnetic nanoconstructs carrying super-paramagnetic iron oxide nanoparticles. An alternating magnetic field is used to excite the nanoconstructs and generate localized heat within the tissue. The proposed model is particularly adequate for this application, since it has a unique capability of incorporating microvasculature configurations based on physiological data combined with coupled capillary flow, interstitial filtration and heat transfer. A virtual tumour model is initialized and the spatio-temporal distribution of nanoconstructs in the vascular network is analysed. In particular, for a reference iron oxide concentration, temperature maps of several different hypothesized treatments are generated in the virtual tumour model. The observations of the current study might in future guide the design of more efficient treatments for cancer hyperthermia.

A MATHEMATICAL COUPLED MODEL OF OXYGEN TRANSPORT IN THE MICROCIRCULATION: THE EFFECT OF CONVECTION–DIFFUSION ON OXYGEN TRANSPORT

This paper is aimed at examining the effect of convection–diffusion on oxygen transport at the micro-level. A coupled model of the convection–diffusion and molecular diffusion of oxygen is developed, and the solid deformation resulting from capillary fluctuations and the seepage of tissue fluid are incorporated into this model. The results indicate that (1) the oxygen concentration calculated from this coupled model is higher than that given by molecular diffusion models, both within the capillaries and tissue (maximum difference of 16%); (2) convection–diffusion has the greatest effect in tissue surrounding the middle of the capillary, and enhances the amount of oxygen transported to cells far from the oxygen source; (3) larger permeability coefficients or smaller diffusion coefficients produce a more obvious convection–diffusion effect; (4) a counter-current flow occurs near the inlet and outlet ends of the capillary. This model also provides a foundation for the study of how oxygen affects tumor growth.

Characterization of cancellous and cortical bone strain in the in vivo mouse tibial loading model using microCT-based finite element analysis

The in vivo mouse tibial loading model has been increasingly used to understand the mechanisms governing the mechanobiological responses of cancellous and cortical bone tissues to physical stimuli. Accurate characterization of the strain environment throughout the tibia is fundamental in relating localized mechanobiological processes to specific strain stimuli in the skeleton. MicroCT-based finite element analysis, together with diaphyseal strain gauge measures, was conducted to quantify the strain field in the tibiae of 16-wk-old female C57Bl/6 mice during in vivo dynamic compressive loading. Despite a strong correlation between the experimentally-measured and computationally-modeled strains at the gauge site, no correlations existed between the strain at the gauge site and the peak strains in the proximal cancellous and midshaft cortical bone, indicating the limitations of using a single diaphyseal strain gauge to estimate strain in the entire tibia. The peak compressive and tensile principal strain magnitudes in the proximal cancellous bone were 10% and 34% lower than those in the midshaft cortical bone. Sensitivity analyses showed that modeling bone tissue as a heterogeneous material had a strong effect on cancellous strain characterization while cortical strain and whole-bone stiffness were primarily affected by the presence of the fibula and the proximal boundary conditions. These results show that microCT-based finite element analysis combined with strain gauge measures provides detailed resolution of the tissue-level strain in both the cancellous and cortical bones of the mouse tibia during in vivo compression loading, which is necessary for interpreting localized patterns of modeling/remodeling and, potentially, gene and protein expression in skeletal mechanobiology studies.