A nonlinear biphasic model of flow-controlled infusions in brain: mass transport analyses

A comprehensive review on modeling aspects of infusion-based drug delivery in the brain

Brain disorders represent an ever-increasing health challenge worldwide. While conventional drug therapies are less effective due to the presence of the blood-brain barrier, infusion-based methods of drug delivery to the brain represent a promising option. Since these methods are mechanically controlled and involve multiple physical phases ranging from the neural and molecular scales to the brain scale, highly efficient and precise delivery procedures can significantly benefit from a comprehensive understanding of drug-brain and device-brain interactions. Behind these interactions are principles of biophysics and biomechanics that can be described and captured using mathematical models. Although biomechanics and biophysics have received considerable attention, a comprehensive mechanistic model for modeling infusion-based drug delivery in the brain has yet to be developed. Therefore, this article reviews the state-of-the-art mechanistic studies that can support the development of next-generation models for infusion-based brain drug delivery from the perspective of fluid mechanics, solid mechanics, and mathematical modeling. The supporting techniques and database are also summarized to provide further insights. Finally, the challenges are highlighted and perspectives on future research directions are provided. STATEMENT OF SIGNIFICANCE: Despite the immense potential of infusion-based drug delivery methods for bypassing the blood-brain barrier and efficiently delivering drugs to the brain, achieving optimal drug distribution remains a significant challenge. This is primarily due to our limited understanding of the complex interactions between drugs and the brain that are governed by principles of biophysics and biomechanics, and can be described using mathematical models. This article provides a comprehensive review of state-of-the-art mechanistic studies that can help to unravel the mechanism of drug transport in the brain across the scales, which underpins the development of next-generation models for infusion-based brain drug delivery. More broadly, this review will serve as a starting point for developing more effective treatments for brain diseases and mechanistic models that can be used to study other soft tissue and biomaterials.

Convection-enhanced delivery with controlled catheter movement: A parametric finite element analysis

Convection-enhanced delivery (CED) is an investigational method for delivering therapeutics directly to the brain for the treatment of glioblastoma. However, it has not become a common clinical therapy due to an inability of CED treatments to deliver therapeutics in a large enough tissue volume to fully saturate the target region. We have recently shown that the combination of controlled catheter movement and constant pressure infusions can be used to significantly increase volume dispersed (Vd ) in an agarose gel brain tissue phantom. In the present study, we develop a computational model to predict Vd achieved by various retraction rates with both constant pressure and constant flow rate infusions. An increase in Vd is achieved with any movement rate, but increase in Vd between successive movement rates drops off at rates above 0.3-0.35 mm/min. Finally, we found that infusions with retraction result in a more even distribution in concentration level compared to the stationary catheter, suggesting a potential increased ability for moving catheters to have a therapeutic impact regardless of the required therapeutic concentration level.

Insights into Infusion-Based Targeted Drug Delivery in the Brain: Perspectives, Challenges and Opportunities

Targeted drug delivery in the brain is instrumental in the treatment of lethal brain diseases, such as glioblastoma multiforme, the most aggressive primary central nervous system tumour in adults. Infusion-based drug delivery techniques, which directly administer to the tissue for local treatment, as in convection-enhanced delivery (CED), provide an important opportunity; however, poor understanding of the pressure-driven drug transport mechanisms in the brain has hindered its ultimate success in clinical applications. In this review, we focus on the biomechanical and biochemical aspects of infusion-based targeted drug delivery in the brain and look into the underlying molecular level mechanisms. We discuss recent advances and challenges in the complementary field of medical robotics and its use in targeted drug delivery in the brain. A critical overview of current research in these areas and their clinical implications is provided. This review delivers new ideas and perspectives for further studies of targeted drug delivery in the brain.

A Hybrid Reactive Multiphasic Mixture With a Compressible Fluid Solvent

Mixture theory is a general framework that has been used to model mixtures of solid, fluid, and solute constituents, leading to significant advances in modeling the mechanics of biological tissues and cells. Though versatile and applicable to a wide range of problems in biomechanics and biophysics, standard multiphasic mixture frameworks incorporate neither dynamics of viscous fluids nor fluid compressibility, both of which facilitate the finite element implementation of computational fluid dynamics solvers. This study formulates governing equations for reactive multiphasic mixtures where the interstitial fluid has a solvent which is viscous and compressible. This hybrid reactive multiphasic framework uses state variables that include the deformation gradient of the porous solid matrix, the volumetric strain and rate of deformation of the solvent, the solute concentrations, and the relative velocities between the various constituents. Unlike standard formulations which employ a Lagrange multiplier to model fluid pressure, this framework requires the formulation of a function of state for the pressure, which depends on solvent volumetric strain and solute concentrations. Under isothermal conditions the formulation shows that the solvent volumetric strain remains continuous across interfaces between hybrid multiphasic domains. Apart from the Lagrange multiplier-state function distinction for the fluid pressure, and the ability to accommodate viscous fluid dynamics, this hybrid multiphasic framework remains fully consistent with standard multiphasic formulations previously employed in biomechanics. With these additional features, the hybrid multiphasic mixture theory makes it possible to address a wider range of problems that are important in biomechanics and mechanobiology.

Three-dimensional nonlinear finite element model to estimate backflow during flow-controlled infusions into the brain

Convection-enhanced delivery is a technique to bypass the blood–brain barrier and deliver therapeutic drugs into the brain tissue. However, animal investigations and preliminary clinical trials have reported reduced efficacy to transport the infused drug in specific zones, attributed mainly to backflow, in which an annular gap is formed outside the catheter and the fluid preferentially flows toward the surface of the brain rather than through the tissue in front of the cannula tip. In this study, a three-dimensional human brain finite element model of backflow was developed to study the influence of anatomical structures during flow-controlled infusions. Predictions of backflow length were compared under the influence of ventricular pressure and the distance between the cannula and the ventricles. Simulations with zero relative ventricle pressure displayed similar backflow length predictions for larger cannula-ventricle distances. In addition, infusions near the ventricles revealed smaller backflow length and the liquid was observed to escape to the longitudinal fissure and ventricular cavities. Simulations with larger cannula-ventricle distances and nonzero relative ventricular pressure showed an increase of fluid flow through the tissue and away from the ventricles. These results reveal the importance of considering both the subject-specific anatomical details and the nonlinear effects in models focused on analyzing current and potential treatment options associated with convection-enhanced delivery optimization for future clinical trials.

Convection-Enhanced Delivery: Connection to and Impact of Interstitial Fluid Flow

Convection-enhanced delivery (CED) is a method used to increase transport of therapeutics in and around brain tumors. CED works through locally applying a pressure differential to drive fluid flow throughout the tumor, such that convective forces dominate over diffusive transport. This allows therapies to bypass the blood brain barrier that would otherwise be too large or solely rely on passive diffusion. However, this also drives fluid flow out through the tumor bulk into surrounding brain parenchyma, which results in increased interstitial fluid (IF) flow, or fluid flow within extracellular spaces in the tissue. IF flow has been associated with altered transport of molecules, extracellular matrix rearrangement, and triggering of cellular motility through a number of mechanisms. Thus, the results of a simple method to increase drug delivery may have unintended consequences on tissue morphology. Clinically, prediction of dispersal of agents via CED is important to catheter design, placement, and implementation to optimize contact of tumor cells with therapeutic agent. Prediction software can aid in this problem, yet we wonder if there is a better way to predict therapeutic distribution based simply on IF flow pathways as determined from pre-intervention imaging. Overall, CED based therapy has seen limited success and we posit that integration and appreciation of altered IF flow may enhance outcomes. Thus, in this manuscript we both review the current state of the art in CED and IF flow mechanistic understanding and relate these two elements to each other in a clinical context.

Parametric Study of the Design Variables of an Arborizing Catheter on Dispersal Volume Using a Biphasic Computational Model

Convection-enhanced delivery (CED) is an investigational therapy developed to circumvent the limitations of drug delivery to the brain. Catheters are used in CED to locally infuse therapeutic agents into brain tissue. CED has demonstrated clinical utility for treatment of malignant brain tumors; however, CED has been limited by lack of CED-specific catheters. Therefore, we developed a multiport, arborizing catheter to maximize drug distribution for CED. Using a multiphasic finite element (FE) framework, we parametrically determined the influence of design variables of the catheter on the dispersal volume of the infusion. We predicted dispersal volume of a solute infused in a permeable hyperelastic solid matrix, as a function of separation distance (ranging from 0.5 to 2.0 cm) of imbedded infusion cavities that represented individual ports in a multiport catheter. To validate the model, we compared FE solutions of pressure-controlled infusions to experimental data of indigo carmine dye infused in agarose tissue phantoms. The Tc50, defined as the infusion time required for the normalized solute concentration between two sources to equal 50% of the prescribed concentration, was determined for simulations with infusion pressures ranging from 1 to 4 kPa. In our validated model, we demonstrate that multiple ports increase dispersal volume with increasing port distance but are associated with a significant increase in infusion time. Tc50 increases approximately tenfold when doubling the port distance. Increasing the infusion flow rate (from 0.7 μL/min to 8.48 μL/min) can mitigate the increased infusion time. In conclusion, a compromise of port distance and flow rate could improve infusion duration and dispersal volume.

Convection-enhanced delivery to the central nervous system

Convection-enhanced delivery (CED) is a bulk flow–driven process. Its properties permit direct, homogeneous, targeted perfusion of CNS regions with putative therapeutics while bypassing the blood-brain barrier. Development of surrogate imaging tracers that are co-infused during drug delivery now permit accurate, noninvasive real-time tracking of convective infusate flow in nervous system tissues. The potential advantages of CED in the CNS over other currently available drug delivery techniques, including systemic delivery, intrathecal and/or intraventricular distribution, and polymer implantation, have led to its application in research studies and clinical trials. The authors review the biophysical principles of convective flow and the technology, properties, and clinical applications of convective delivery in the CNS.

In vivo evaluation of needle force and friction stress during insertion at varying insertion speed into the brain

BACKGROUND

Convection enhanced delivery (CED) infuses drugs directly into brain tissue. Needle insertion is required and results in tissue damage which can promote flowback along the needle track and improper targeting. The goal of this study was to evaluate friction stress (calculated from needle insertion force) as a measure of tissue contact and damage during needle insertion for varying insertion speeds.

NEW METHOD

Forces and surface dimpling during needle insertion were measured in rat brain in vivo. Needle retraction forces were used to calculate friction stresses. These measures were compared to track damage from a previous study. Differences between brain tissues and soft hydrogels were evaluated for varying insertion speeds: 0.2, 2, and 10mm/s.

RESULTS

In brain tissue, average insertion force and surface dimpling increased with increasing insertion speed. Average friction stress along the needle-tissue interface decreased with insertion speed (from 0.58 ± 0.27 to 0.16 ± 0.08 kPa). Friction stress varied between brain regions: cortex (0.227 ± 0.27 kPa), external capsule (0.222 ± 0.19 kPa), and CPu (0.383 ± 0.30 kPa). Hydrogels exhibited opposite trends for dimpling and friction stress with insertion speed.

COMPARISON WITH EXISTING METHODS

Previously, increasing needle damage with insertion speed has been measured with histological methods. Friction stress appears to decrease with increasing tissue damage and decreasing tissue contact, providing the potential for in vivo and real time evaluation along the needle track.

CONCLUSION

Force derived friction stress decreased with increasing insertion speed and was smaller within white matter regions. Hydrogels exhibited opposite trends to brain tissue.

A patient-specific, finite element model for noncommunicating hydrocephalus capable of large deformation

A biphasic model for noncommunicating hydrocephalus in patient-specific geometry is proposed. The model can take into account the nonlinear behavior of brain tissue under large deformation, the nonlinear variation of hydraulic conductivity with deformation, and contact with a rigid, impermeable skull using a recently developed algorithm. The model was capable of achieving over a 700 percent ventricular enlargement, which is much greater than in previous studies, primarily due to the use of an anatomically realistic skull recreated from magnetic resonance imaging rather than an artificial skull created by offsetting the outer surface of the cerebrum. The choice of softening or stiffening behavior of brain tissue, both having been demonstrated in previous experimental studies, was found to have a significant effect on the volume and shape of the deformed ventricle, and the consideration of the variation of the hydraulic conductivity with deformation had a modest effect on the deformed ventricle. The model predicts that noncommunicating hydrocephalus occurs for ventricular fluid pressure on the order of 1300 Pa.

Voxelized computational model for convection-enhanced delivery in the rat ventral hippocampus: comparison with in vivo MR experimental studies

Convection-enhanced delivery (CED) is a promising local delivery technique for overcoming the blood-brain barrier (BBB) and treating diseases of the central nervous system (CNS). For CED, therapeutics are infused directly into brain tissue and the drug agent is spread through the extracellular space, considered to be highly tortuous porous media. In this study, 3D computational models developed using magnetic resonance (MR) diffusion tensor imaging data sets were used to predict CED transport in the rat ventral hippocampus using a voxelized modeling previously developed by our group. Predicted albumin tracer distributions were compared with MR-measured distributions from in vivo CED in the ventral hippocampus up to 10 μL of Gd-DTPA albumin tracer infusion. Predicted and measured tissue distribution volumes and distribution patterns after 5 and 10 μL infusions were found to be comparable. Tracers were found to occupy the underlying landmark structures with preferential transport found in regions with less fluid resistance such as the molecular layer of the dentate gyrus. Also, tracer spread was bounded by high fluid resistance layers such as the granular cell layer and pyramidal cell layer of dentate gyrus. Leakage of tracers into adjacent CSF spaces was observed towards the end of infusions.

Implications of transvascular fluid exchange in nonlinear, biphasic analyses of flow-controlled infusion in brain

A nonlinear, coupled biphasic-mass transport model that includes transvascular fluid exchange is proposed for flow-controlled infusions in brain tissue. The model accounts for geometric and material nonlinearities, a hydraulic conductivity dependent on deformation, and transvascular fluid exchange according to Starling's law. The governing equations were implemented in a custom-written code assuming spherical symmetry and using an updated Lagrangian finite-element algorithm. Results of the model indicate that, using normal physiological values of vascular permeability, transvascular fluid exchange has negligible effects on tissue deformation, fluid pressure, and transport of the infused agent. As vascular permeability may be increased artificially through methods such as administering nitric oxide, a parametric study was conducted to determine how increased vascular permeability affects flow-controlled infusion. Increased vascular permeability reduced both tissue deformation and fluid pressure, possibly reducing damage to tissue adjacent to the infusion catheter. Furthermore, the loss of fluid to the vasculature resulted in a significantly increased interstitial fluid concentration but a modestly increased tissue concentration. From a clinical point of view, this increase in concentration could be beneficial if limited to levels below which toxicity would not occur. However, the modestly increased tissue concentration may make the increase in interstitial fluid concentration difficult to assess in vivo using co-infused radiolabeled agents.