Computational model of interstitial transport in the spinal cord using diffusion tensor imaging

Effect of infusion direction on convection-enhanced drug delivery to anisotropic tissue

Convection-enhanced delivery (CED) can effectively overcome the blood-brain barrier by infusing drugs directly into diseased sites in the brain using a catheter, but its clinical performance still needs to be improved. This is strongly related to the highly anisotropic characteristics of brain white matter, which results in difficulties in controlling drug transport and distribution in space. In this study, the potential to improve the delivery of six drugs by adjusting the placement of the infusion catheter is examined using a mathematical model and accurate numerical simulations that account simultaneously for the interstitial fluid (ISF) flow and drug transport processes in CED. The results demonstrate the ability of this direct infusion to enhance ISF flow and therefore facilitate drug transport. However, this enhancement is highly anisotropic, subject to the orientation of local axon bundles and is limited within a small region close to the infusion site. Drugs respond in different ways to infusion direction: the results of our simulations show that while some drugs are almost insensitive to infusion direction, this strongly affects other compounds in terms of isotropy of drug distribution from the catheter. These findings can serve as a reference for planning treatments using CED.

Image-based predictive modelling frameworks for personalised drug delivery in cancer therapy

Personalised drug delivery enables a tailored treatment plan for each patient compared to conventional drug delivery, where a generic strategy is commonly employed. It can not only achieve precise treatment to improve effectiveness but also reduce the risk of adverse effects to improve patients' quality of life. Drug delivery involves multiple interconnected physiological and physicochemical processes, which span a wide range of time and length scales. How to consider the impact of individual differences on these processes becomes critical. Multiphysics models are an open system that allows well-controlled studies on the individual and combined effects of influencing factors on drug delivery outcomes while accommodating the patient-specific in vivo environment, which is not economically feasible through experimental means. Extensive modelling frameworks have been developed to reveal the underlying mechanisms of drug delivery and optimise effective delivery plans. This review provides an overview of currently available models, their integration with advanced medical imaging modalities, and code packages for personalised drug delivery. The potential to incorporate new technologies (i.e., machine learning) in this field is also addressed for development.

Cross-hemicord spinal fiber reorganization associates with cortical sensory and motor network expansion in the rat model of hemicontusion cervical spinal cord injury

Magnetic resonance imaging plays an important role in characterizing microstructural changes and reorganization after traumatic injuries to the nervous system. In this study, we tested the feasibility of ex-vivo spinal cord diffusion tensor imaging (DTI) in combination with in vivo brain functional MRI to characterize spinal reorganization and its supraspinal association after a hemicontusion cervical spinal cord injury (SCI). DTI parameters (fractional anisotropy [FA], mean diffusion [MD]) and fiber orientation changes related to reorganization in the contused cervical spinal cord were compared to sham specimens. Altered fiber density and fiber directions occurred across the ipsilateral and contralateral hemicords but with only ipsilateral FA and MD changes. The hemicontusion SCI resulted in ipsilateral fiber breaks, voids and vivid fiber reorientations along the injury epicenter. Fiber directional changes below the injury level were primarily inter-hemispheric, indicating prominent below-level cross-hemispheric reorganization. In vivo resting state functional connectivity of the brain from the respective rats before obtaining the spinal cord samples indicated spatial expansion and increased connectivity strength across both the sensory and motor networks after SCI. The consistency of the neuroplastic changes along the neuraxis (both brain and spinal cord) at the single-subject level, indicates that distinctive reorganizational relationships exist between the spinal cord and the brain post-SCI.

Multi-Scale and Multi-Physics Models of the Transport of Therapeutic/Diagnostic Cancer Agents

The effectiveness of tumor treatment heavily relies on the successful delivery of anticancer drugs [...].

Diffusion in multicomponent aqueous alcoholic mixtures

The Fick diffusion coefficient matrix of the highly associating quaternary mixture water + methanol + ethanol + 2-propanol as well as its ternary and binary subsystems is analyzed with molecular dynamics simulation techniques. Three of the ternary subsystems are studied in this sense for the first time. The predictive capability of the employed force fields, which were sampled with the Green–Kubo formalism and Kirkwood–Buff integration, is confirmed by comparison with experimental literature data on vapor-liquid equilibrium, shear viscosity and Fick diffusion coefficient, wherever possible. A thorough analysis of the finite size effects on the simulative calculation of diffusion coefficients of multicomponent systems is carried out. Moreover, the dependence of the Fick diffusion coefficient matrix on the velocity reference frame and component order is analyzed. Their influence is found to be less significant for the main matrix elements, reaching a maximum variation of 19%. The large differences found for the cross elements upon variation of the reference frame hinder a straightforward interpretation of the Fick diffusion coefficient matrix with respect to the presence of diffusive coupling effects.

Utilizing Dynamic Contrast-Enhanced Magnetic Resonance Imaging (DCE-MRI) to Analyze Interstitial Fluid Flow and Transport in Glioblastoma and the Surrounding Parenchyma in Human Patients

Background: Glioblastoma (GBM) is the deadliest and most common brain tumor in adults, with poor survival and response to aggressive therapy. Limited access of drugs to tumor cells is one reason for such grim clinical outcomes. A driving force for therapeutic delivery is interstitial fluid flow (IFF), both within the tumor and in the surrounding brain parenchyma. However, convective and diffusive transport mechanisms are understudied. In this study, we examined the application of a novel image analysis method to measure fluid flow and diffusion in GBM patients. Methods: Here, we applied an imaging methodology that had been previously tested and validated in vitro, in silico, and in preclinical models of disease to archival patient data from the Ivy Glioblastoma Atlas Project (GAP) dataset. The analysis required the use of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI), which is readily available in the database. The analysis results, which consisted of IFF flow velocity and diffusion coefficients, were then compared to patient outcomes such as survival. Results: We characterized IFF and diffusion patterns in patients. We found strong correlations between flow rates measured within tumors and in the surrounding parenchymal space, where we hypothesized that velocities would be higher. Analyzing overall magnitudes indicated a significant correlation with both age and survival in this patient cohort. Additionally, we found that neither tumor size nor resection significantly altered the velocity magnitude. Lastly, we mapped the flow pathways in patient tumors and found a variability in the degree of directionality that we hypothesize may lead to information concerning treatment, invasive spread, and progression in future studies. Conclusions: An analysis of standard DCE-MRI in patients with GBM offers more information regarding IFF and transport within and around the tumor, shows that IFF is still detected post-resection, and indicates that velocity magnitudes correlate with patient prognosis.

Integrating Diffusion Tensor Imaging and Neurite Orientation Dispersion and Density Imaging to Improve the Predictive Capabilities of CED Models

This paper aims to develop a comprehensive and subject-specific model to predict the drug reach in Convection-Enhanced Delivery (CED) interventions. To this end, we make use of an advance diffusion imaging technique, namely the Neurite Orientation Dispersion and Density Imaging (NODDI), to incorporate a more precise description of the brain microstructure into predictive computational models. The NODDI dataset is used to obtain a voxel-based quantification of the extracellular space volume fraction that we relate to the white matter (WM) permeability. Since the WM can be considered as a transversally isotropic porous medium, two equations, respectively for permeability parallel and perpendicular to the axons, are derived from a numerical analysis on a simplified geometrical model that reproduces flow through fibre bundles. This is followed by the simulation of the injection of a drug in a WM area of the brain and direct comparison of the outcomes of our results with a state-of-the-art model, which uses conventional diffusion tensor imaging. We demonstrate the relevance of the work by showing the impact of our newly derived permeability tensor on the predicted drug distribution, which differs significantly from the alternative model in terms of distribution shape, concentration profile and infusion linear penetration length.

Regression of Recurrent Spinal Cord High-Grade Glioma After Convection-Enhanced Delivery of Nimustine Hydrochloride: Case Reports and Literature Review

BACKGROUND

Spinal cord high-grade glioma has poor prognosis. Especially, no treatment protocols have been established for recurrent cases.

OBJECTIVE

To apply a novel treatment method, convection-enhanced delivery (CED), for recurrent high-grade glioma. CED can deliver chemotherapeutic agents directly into the intramedullary lesion and possibly lead to remarkable regression of enlarging tumors that are, otherwise, difficult to control.

METHODS

Two patients developed high-grade glioma in the thoracic spinal cord. Partial resection and chemotherapy and radiotherapy induced remission of the disease. However, following the initial treatment, recurrence was noted in the spinal cord at 6 and 12 mo, respectively. No effective treatment was available for these recurrent lesions. Therefore, the authors decided to use CED to infuse nimustine hydrochloride (ACNU) directly into the spinal cord. During the procedure, the infusion cannula was inserted into the spinal cord lesion under intraoperative computed tomography scan.

RESULTS

After ACNU CED, successive magnetic resonance imaging confirmed remarkable shrinkages of the tumors in both cases. However, the patient's preinfusion symptoms, including bilateral lower extremity weakness, did not change after the treatment. Importantly, overall survivals of the 2 patients were as long as 67 and 33 mo.

CONCLUSION

The authors report the first 2 cases of recurrent spinal cord high-grade glioma. ACNU CED dramatically regressed enhanced mass lesions and provided local tumor controls in the spinal cord.

Effect of tissue permeability and drug diffusion anisotropy on convection-enhanced delivery

Although convection-enhanced delivery (CED) can successfully facilitate a bypass of the blood brain barrier, its treatment efficacy remains highly limited in clinic. This can be partially attributed to the brain anisotropic characteristics that lead to the difficulties in controlling the drug spatial distribution. Here, the responses of six different drugs to the tissue anisotropy are examined through a parametric study performed using a multiphysics model, which considers interstitial fluid flow, tissue deformation and interlinked drug transport processes in CED. The delivery outcomes are evaluated in terms of the penetration depth and delivery volume for effective therapy. Simulation results demonstrate that the effective penetration depth in a given direction can be improved with the increase of the corresponding component of anisotropic characteristics. The anisotropic tissue permeability could only reshape the drug distribution in space but has limited contribution to the total effective delivery volume. On the other hand, drugs respond in different ways to the anisotropic diffusivity. The large delivery volumes of fluorouracil, carmustine, cisplatin and doxorubicin could be achieved in relatively isotropic tissue, while paclitaxel and methotrexate are able to cover enlarged regions into anisotropic tissues. Results obtained from this study serve as a guide for the design of CED treatments.

MRI of Whole Rat Brain Perivascular Network Reveals Role for Ventricles in Brain Waste Clearance

Investigating the mechanisms by which metabolic wastes are cleared from nervous tissue is important for understanding natural function and the pathophysiology of several neurological disorders including Alzheimer's disease. Recent evidence suggests clearance may be the function of annular spaces around cerebral blood vessels, called perivascular spaces (PVS), through which cerebrospinal fluid (CSF) is transported from the subarachnoid space into brain parenchyma to exchange with interstitial fluid (also known as the glymphatic system). In this work, an MRI-based methodology was developed to reconstruct the PVS network in whole rat brain to better elucidate both PVS uptake and clearance pathways. MR visible tracer (Gd-albumin) was infused in vivo into the CSF-filled lateral ventricle followed by ex vivo high-resolution MR imaging at 17.6 T with an image voxel volume two orders of magnitude smaller than previously reported. Imaged tracer distribution patterns were reconstructed to obtain a more complete brain PVS network. Several PVS connections were repeatedly highlighted across different animals, and new PVS connections between ventricles and different parts of the brain parenchyma were revealed suggesting a possible role for the ventricles as a source or sink for solutes in the brain. In the future, this methodology may be applied to understand changes in the PVS network with disease.

A computational fluid dynamics approach to determine white matter permeability

Glioblastomas represent a challenging problem with an extremely poor survival rate. Since these tumour cells have a highly invasive character, an effective surgical resection as well as chemotherapy and radiotherapy is very difficult. Convection-enhanced delivery (CED), a technique that consists in the injection of a therapeutic agent directly into the parenchyma, has shown encouraging results. Its efficacy depends on the ability to predict, in the pre-operative phase, the distribution of the drug inside the tumour. This paper proposes a method to compute a fundamental parameter for CED modelling outcomes, the hydraulic permeability, in three brain structures. Therefore, a bidimensional brain-like structure was built out of the main geometrical features of the white matter: axon diameter distribution extrapolated from electron microscopy images, extracellular space (ECS) volume fraction and ECS width. The axons were randomly allocated inside a defined border, and the ECS volume fraction as well as the ECS width maintained in a physiological range. To achieve this result, an outward packing method coupled with a disc shrinking technique was implemented. The fluid flow through the axons was computed by solving Navier-Stokes equations within the computational fluid dynamics solver ANSYS. From the fluid and pressure fields, an homogenisation technique allowed establishing the optimal representative volume element (RVE) size. The hydraulic permeability computed on the RVE was found in good agreement with experimental data from the literature.

The need for mathematical modelling of spatial drug distribution within the brain

The blood brain barrier (BBB) is the main barrier that separates the blood from the brain. Because of the BBB, the drug concentration-time profile in the brain may be substantially different from that in the blood. Within the brain, the drug is subject to distributional and elimination processes: diffusion, bulk flow of the brain extracellular fluid (ECF), extra-intracellular exchange, bulk flow of the cerebrospinal fluid (CSF), binding and metabolism. Drug effects are driven by the concentration of a drug at the site of its target and by drug-target interactions. Therefore, a quantitative understanding is needed of the distribution of a drug within the brain in order to predict its effect. Mathematical models can help in the understanding of drug distribution within the brain. The aim of this review is to provide a comprehensive overview of system-specific and drug-specific properties that affect the local distribution of drugs in the brain and of currently existing mathematical models that describe local drug distribution within the brain. Furthermore, we provide an overview on which processes have been addressed in these models and which have not. Altogether, we conclude that there is a need for a more comprehensive and integrated model that fills the current gaps in predicting the local drug distribution within the brain.

Improving the Predictions of Computational Models of Convection-Enhanced Drug Delivery by Accounting for Diffusion Non-gaussianity

Convection-enhanced delivery (CED) is an innovative method of drug delivery to the human brain, that bypasses the blood-brain barrier by injecting the drug directly into the brain. CED aims to target pathological tissue for central nervous system conditions such as Parkinson's and Huntington's disease, epilepsy, brain tumors, and ischemic stroke. Computational fluid dynamics models have been constructed to predict the drug distribution in CED, allowing clinicians advance planning of the procedure. These models require patient-specific information about the microstructure of the brain tissue, which can be collected non-invasively using magnetic resonance imaging (MRI) pre-infusion. Existing models employ the diffusion tensor, which represents Gaussian diffusion in brain tissue, to provide predictions for the drug concentration. However, those predictions are not always in agreement with experimental observations. In this work we present a novel computational fluid dynamics model for CED that does not use the diffusion tensor, but rather the diffusion probability that is experimentally measured through diffusion MRI, at an individual-participant level. Our model takes into account effects of the brain microstructure on the motion of drug molecules not taken into account in previous approaches, namely the restriction and hindrance that those molecules experience when moving in the brain tissue, and can improve the drug concentration predictions. The duration of the associated MRI protocol is 19 min, and therefore feasible for clinical populations. We first prove theoretically that the two models predict different drug distributions. Then, using in vivo high-resolution diffusion MRI data from a healthy participant, we derive and compare predictions using both models, in order to identify the impact of including the effects of restriction and hindrance. Including those effects results in different drug distributions, and the observed differences exhibit statistically significant correlations with measures of diffusion non-Gaussianity in brain tissue. The differences are more pronounced for infusion in white-matter areas of the brain. Using experimental results from the literature along with our simulation results, we show that the inclusion of the effects of diffusion non-Gaussianity in models of CED is necessary, if reliable predictions that can be used in the clinic are to be generated by CED models.

Fluid outflow in the rat spinal cord: the role of perivascular and paravascular pathways

BACKGROUND

Cerebrospinal fluid (CSF) is thought to flow into the brain via perivascular spaces around arteries, where it mixes with interstitial fluid. The precise details concerning fluid outflow remain controversial. Although fluid dynamics have been studied in the brain, little is known about spinal cord fluid inflow and outflow. Understanding the normal fluid physiology of the spinal cord may give insight into the pathogenesis of spinal cord oedema and CSF disorders such as syringomyelia. We therefore aimed to determine the fluid outflow pathways in the rat spinal cord.

METHODS

A fluorescent tracer, Alexa-Fluor^®-647 Ovalbumin, was injected into the extracellular space of either the cervicothoracic lateral white matter or the grey matter in twenty-two Sprague-Dawley rats over 250 s. The rats were sacrificed at 20 or 60 min post injection. Spinal cord segments were sectioned and labelled with vascular antibodies for immunohistochemistry.

RESULTS

Fluorescent tracer was distributed over two to three spinal levels adjacent to the injection site. In grey matter injections, tracer spread radially into the white matter. In white matter injections, tracer was confined to and redistributed along the longitudinal axonal fibres. Tracer was conducted towards the pial and ependymal surfaces along vascular structures. There was accumulation of tracer around the adventitia of the intramedullary arteries, veins and capillaries, as well as the extramedullary vessels. A distinct layer of tracer was deposited in the internal basement membrane of the tunica media of arteries. In half the grey matter injections, tracer was detected in the central canal.

CONCLUSIONS

These results suggest that in the spinal cord interstitial fluid movement is modulated by tissue diffusivity of grey and white matter. The central canal, and the compartments around or within blood vessels appear to be dominant pathways for fluid drainage in these experiments. There may be regional variations in fluid outflow capacity due to vascular and other anatomical differences between the grey and white matter.

Subject-specific multi-poroelastic model for exploring the risk factors associated with the early stages of Alzheimer's disease

There is emerging evidence suggesting that Alzheimer's disease is a vascular disorder, caused by impaired cerebral perfusion, which may be promoted by cardiovascular risk factors that are strongly influenced by lifestyle. In order to develop an understanding of the exact nature of such a hypothesis, a biomechanical understanding of the influence of lifestyle factors is pursued. An extended poroelastic model of perfused parenchymal tissue coupled with separate workflows concerning subject-specific meshes, permeability tensor maps and cerebral blood flow variability is used. The subject-specific datasets used in the modelling of this paper were collected as part of prospective data collection. Two cases were simulated involving male, non-smokers (control and mild cognitive impairment (MCI) case) during two states of activity (high and low). Results showed a marginally reduced clearance of cerebrospinal fluid (CSF)/interstitial fluid (ISF), elevated parenchymal tissue displacement and CSF/ISF accumulation and drainage in the MCI case. The peak perfusion remained at 8 mm s⁻¹ between the two cases.

Insights from mathematical modeling for convection-enhanced intraputamenal delivery of GDNF

Glial cell line-derived neurotrophic factor (GDNF) is a potential therapy for Parkinson’s disease (PD) promoting survival and functional recovery of dopaminergic neurons when delivered to the degenerated striatum. To study the aspects of intraputamenal delivery of GDNF, a mathematical model of recombinant methionyl human GDNF (r-metHuGDNF) convection in the human putamen has been developed. The convection-enhanced delivery infusions of r-metHuGDNF were simulated at rates up to 5 μL/min. The high-rate infusions (≥1 μL/min) permit rapid and uniform distribution of drug with up to 75% of the distribution volume having a concentration within 5% of the infusate concentration. No relevant differences in distribution at infusion rates of 3 and 5 μL/min were found. The patterns of GDNF distribution were analyzed in relation to the anatomy of the posterior dorsal putamen, and a cylindrical shape was found to be preferable considering risks of target overflow. A magnetic resonance (MR) tracer Gd-DTPA (Magnevist®) was evaluated as a surrogate in clinical studies, and the most accurate prediction of GDNF distribution was calculated immediately after infusion. The clearance of GDNF from the striatum is confirmed to be slow, with a half-life of ca. 19 h.

Convection-enhanced delivery of a hydrophilic nitrosourea ameliorates deficits and suppresses tumor growth in experimental spinal cord glioma models

BACKGROUND

Convection-enhanced delivery (CED) is a technique allowing local infusion of therapeutic agents into the central nervous system, circumventing the blood-brain or spinal cord barrier.

OBJECTIVE

To evaluate the utility of nimustine hydrochloride (ACNU) CED in controlling tumor progression in an experimental spinal cord glioma model.

METHODS

Toxicity studies were performed in 42 rats following the administration of 4 μl of ACNU CED into the mid-thoracic spinal cord at concentrations ranging from 0.1 to 10 mg/ml. Behavioral analyses and histological evaluations were performed to assess ACNU toxicity in the spinal cord. A survival study was performed in 32 rats following the implantation of 9 L cells into the T8 spinal cord. Seven days after the implantation, rats were assigned to four groups: ACNU CED (0.25 mg/ml; n = 8); ACNU intravenous (i.v.) (0.4 mg; n = 8); saline CED (n = 8); saline i.v. (n = 8). Hind limb movements were evaluated daily in all rats for 21 days. Tumor sizes were measured histologically.

RESULTS

The maximum tolerated ACNU concentration was 0.25 mg/ml. Preservation of hind limb motor function and tumor growth suppression was observed in the ACNU CED (0.25 mg/ml) and ACNU i.v. groups. Antitumor effects were more prominent in the ACNU CED group especially in behavioral analyses (P < 0.05; log-rank test).

CONCLUSIONS

ACNU CED had efficacy in controlling tumor growth and preserving neurological function in an experimental spinal cord tumor model. ACNU CED can be a viable treatment option for spinal cord high-grade glioma.

Voxelized Model of Brain Infusion That Accounts for Small Feature Fissures: Comparison With Magnetic Resonance Tracer Studies

Convection enhanced delivery (CED) is a promising novel technology to treat neural diseases, as it can transport macromolecular therapeutic agents greater distances through tissue by direct infusion. To minimize off-target delivery, our group has developed 3D computational transport models to predict infusion flow fields and tracer distributions based on magnetic resonance (MR) diffusion tensor imaging data sets. To improve the accuracy of our voxelized models, generalized anisotropy (GA), a scalar measure of a higher order diffusion tensor obtained from high angular resolution diffusion imaging (HARDI) was used to improve tissue segmentation within complex tissue regions of the hippocampus by capturing small feature fissures. Simulations were conducted to reveal the effect of these fissures and cerebrospinal fluid (CSF) boundaries on CED tracer diversion and mistargeting. Sensitivity analysis was also conducted to determine the effect of dorsal and ventral hippocampal infusion sites and tissue transport properties on drug delivery. Predicted CED tissue concentrations from this model are then compared with experimentally measured MR concentration profiles. This allowed for more quantitative comparison between model predictions and MR measurement. Simulations were able to capture infusate diversion into fissures and other CSF spaces which is a major source of CED mistargeting. Such knowledge is important for proper surgical planning.

Properties of convective delivery in spinal cord gray matter: laboratory investigation and computational simulations

OBJECT Convection-enhanced delivery (CED) is a method for distributing small and large molecules locally into the interstitial space of the spinal cord. Delivering these molecules to the spinal cord is otherwise difficult due to the blood-spinal cord barrier. Previous research has proven the efficacy of CED for delivering molecules over long distances along the white matter tracts in the spinal cord. Conversely, the characteristics of CED for delivering molecules to the gray matter of the spinal cord remain unknown. The purpose of this study was to reveal regional distribution of macromolecules in the gray and white matter of the spinal cord with special attention to the differences between the gray and white matter. METHODS Sixteen rats (F344) underwent Evans blue dye CED to either the white matter (dorsal column, 8 rats) or the gray matter (ventral horn, 8 rats) of the spinal cord. The rates and total volumes of infusion were 0.2 μl/min and 2.0 μl, respectively. The infused volume of distribution was visualized and quantified histologically. Computational models of the rat spinal cord were also obtained to perform CED simulations in the white and gray matter. RESULTS The ratio of the volume of distribution to the volume of infusion in the gray matter of the spinal cord was 3.60 ± 0.69, which was comparable to that of the white matter (3.05 ± 0.88). When molecules were injected into the white matter, drugs remained in the white matter tract and rarely infused into the adjacent gray matter. Conversely, when drugs were injected into the gray matter, they infiltrated laterally into the white matter tract and traveled longitudinally and preferably along the white matter. In the infusion center, the areas were larger in the gray matter CED than in the white matter (Mann-Whitney U-test, p < 0.01). In computational simulations, the aforementioned characteristics of CED to the gray and white matter were reaffirmed. CONCLUSIONS In the spinal cord, the gray and white matter have distinct characteristics of drug distribution by CED. These differences between the gray and white matter should be taken into account when considering drug delivery to the spinal cord. Computational simulation is a useful tool for predicting drug distributions in the normal spinal cord.

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.

Multi-component modelling of human brain tissue: a contribution to the constitutive and computational description of deformation, flow and diffusion processes with application to the invasive drug-delivery problem

Human brain tissue is complex and multi-component in nature. It consists of an anisotropic hyperelastic solid material composed of tissue cells and blood vessel walls. Brain tissue is permeated by two viscous pore liquids, the interstitial fluid and the blood. Both liquids are mobile within the tissue and exhibit a significant anisotropic perfusion behaviour. To model this complex aggregate, the well-founded Theory of Porous Media, a continuum-mechanical approach for the description of multi-component aggregates, is used. To include microscopic information, the model is enhanced by tissue characteristics obtained from medical imaging techniques. Moreover, the model is applied to invasive drug-delivery strategies, i.e. the direct extra-vascular infusion of therapeutic agents. For this purpose, the overall interstitial fluid is treated as a real two-component mixture of a liquid solvent and a dissolved therapeutic solute. Finally, the continuum-mechanical model results in a set of strongly coupled partial differential equations which are spatially discretised using mixed finite elements and solved in a monolithic manner with an implicit Euler time-integration scheme. Numerical examples demonstrate the applicability of the presented model.

Influence of neuropathology on convection-enhanced delivery in the rat hippocampus

Local drug delivery techniques, such as convention-enhanced delivery (CED), are promising novel strategies for delivering therapeutic agents otherwise limited by systemic toxicity and blood-brain-barrier restrictions. CED uses positive pressure to deliver infusate homogeneously into interstitial space, but its distribution is dependent upon appropriate tissue targeting and underlying neuroarchitecture. To investigate effects of local tissue pathology and associated edema on infusate distribution, CED was applied to the hippocampi of rats that underwent electrically-induced, self-sustaining status epilepticus (SE), a prolonged seizure. Infusion occurred 24 hours post-SE, using a macromolecular tracer, the magnetic resonance (MR) contrast agent gadolinium chelated with diethylene triamine penta-acetic acid and covalently attached to albumin (Gd-albumin). High-resolution T1- and T2-relaxation-weighted MR images were acquired at 11.1 Tesla in vivo prior to infusion to generate baseline contrast enhancement images and visualize morphological changes, respectively. T1-weighted imaging was repeated post-infusion to visualize final contrast-agent distribution profiles. Histological analysis was performed following imaging to characterize injury. Infusions of Gd-albumin into injured hippocampi resulted in larger distribution volumes that correlated with increased injury severity, as measured by hyperintense regions seen in T2-weighted images and corresponding histological assessments of neuronal degeneration, myelin degradation, astrocytosis, and microglial activation. Edematous regions included the CA3 hippocampal subfield, ventral subiculum, piriform and entorhinal cortex, amygdalar nuclei, middle and laterodorsal/lateroposterior thalamic nuclei. This study demonstrates MR-visualized injury processes are reflective of cellular alterations that influence local distribution volume, and provides a quantitative basis for the planning of local therapeutic delivery strategies in pathological brain regions.

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.

Sensitivity analysis of an image-based solid tumor computational model with heterogeneous vasculature and porosity

An MR image-based computational model of a murine KHT sarcoma is presented that allows the calculation of plasma fluid and solute transport within tissue. Such image-based models of solid tumors may be used to optimize patient-specific therapies. This model incorporates heterogeneous vasculature and tissue porosity to account for nonuniform perfusion of an MR-visible tracer, gadolinium-diethylenetriamine pentaacetic acid (Gd-DTPA). Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) was conducted following intravenous infusion of Gd-DTPA to provide 1 h of tracer-concentration distribution data within tissue. Early time points (19 min) were used to construct 3D K(trans) and porosity maps using a two-compartment model; tracer transport was predicted at later time points using a 3D porous media model. Model development involved selecting an arterial input function (AIF) and conducting a sensitivity analysis of model parameters (tissue, vascular, and initial estimation of solute concentration in plasma) to investigate the effects on transport for a specific tumor. The developed model was then used to predict transport in two additional tumors. The sensitivity analysis suggests that plasma fluid transport is more sensitive to parameter changes than solute transport due to the dominance of transvascular exchange. Gd-DTPA distribution was similar to experimental patterns, but differences in Gd-DTPA magnitude at later time points may result from inaccurate selection of AIF. Thus, accurate AIF estimation is important for later time point prediction of low molecular weight tracer or drug transport in smaller tumors.

Predicting DNA-mediated drug delivery in interior carcinoma using electromagnetically excited nanoparticles

Tumor-site-specific delivery of anti-cancer drugs remains one of the most prevailing problems in cancer treatment. While conventional means of chemo-delivery invariably leave different degrees of side-effects on healthy tissues, in recent times, intelligent chemical designs have been exploited to reduce the cross-consequences. In particular, the strategies involving superparamaganetic nanoparticles with surface assembled oligonucleotides as therapeutic carrier have raised affirmative promises. Process is designed in such a way that the therapeutic molecules are released preferentially at target site as the complementary oligonucleotide chains dissociate over the heat generated by the nanoparticles under the excitation of low frequency electromagnetic energy. In spite of the preliminary demonstrations, analytical comprehension of the entire process especially on the purview of non-trivial interactions between stochastic phase-transition phenomena of oligonucleotide chains and hierarchical organization of in vivo transport processes remains unknown. Here, we propose an integrated computational predictive model to interpret the efficacy of drug delivery in the aforementioned process. The basic physics of heat generation by superparamagnetic nanoparticles in presence of external electromagnetic field has been coupled with transient biological heat transfer model and the statistical mechanics based oligonucleotide denaturation dynamics. Conjunctionally, we have introduced a set of hierarchically appropriate transport processes to mimic the in vivo drug delivery system. The subsequent interstitial diffusion and convection of the various species involved in the process over time was simulated assuming a porous media model of the carcinoma. As a result, the model predictions exhibit excellent congruence with available experimental results. To delineate a broader spectrum of a priori speculations, we have investigated the effects of different tunable parameters such as magnetizing field strength, nanoparticle size, diffusion coefficients, porous media parameters and different oligonucleotide sequences on temperature rise and site-specific drug release. The proposed model, thus, provides a generic framework for the betterment of nanoparticle mediated drug delivery, which is expected to impart significant impact on cancer therapy.

SIMULATING CONVECTION-ENHANCED DELIVERY IN THE PUTAMEN USING PROBABILISTIC TRACTOGRAPHY

The treatment of brain diseases is complicated by the presence of the blood-brain barrier. This barrier limits the crossing of therapeutic molecules from the blood vessels into the brain. Today, direct intracerebral infusion applying convection-enhanced delivery (CED) is proposed to circumvent this problem and enhance the area of distribution of infusate beyond the parameters of diffusion. Several factors affect the efficacy, predictability and replicability of CED, such as the catheter model, infusion rate and site of infusion. We set out to investigate if probabilistic tractography can be used to model the infusion flow and predict the intracerebral movement of molecules. In this study we describe a modeling and analysis framework based upon probabilistic tractography. This framework was used to compare probabilistic tractography modeling and actual CED infusion measurements in the putamen of non-human primates, as this gray matter structure is proposed as a target for CED treatment of Parkinson's disease.

Time-reversal Techniques in Ultrasound-assisted Convection-enhanced Drug Delivery to the Brain: Technology Development and In Vivo Evaluation

We describe a drug delivery method that combines Time-Reversal Acoustics (TRA) with Convection-Enhanced Delivery (CED) to improve the delivery of therapeutics to the interstitium of the brain. The Ultrasound-assisted CED approach (UCED) circumvents the blood-brain barrier by infusing compounds through a cannula that is inserted into the brain while simultaneously delivering ultrasound to improve the penetration of pharmaceuticals. CED without ultrasound-assistance has been used to treat a variety of neural disorders, including glioblastoma multiforme, a malignancy that presents a very poor prognosis for patients. We describe a novel system that is used to infuse fluids into the brain parenchyma while simultaneously exposing the tissue to safe levels of 1-MHz, low intensity, ultrasound energy. The system includes a combined infusion needle-hydrophone, a 10-channel ultralow-output impedance amplifier, a broad-band ultrasound resonator, and MatLab®-based TRA control and user-interface. TRA allows easy coupling of ultrasound therapy through the skull without complex phase-correction and array design. The smart targeting UCED system has been tested in vivo and results show it provides 1.5-mm spatial resolution for UCED and improves tracer distribution in the brain over CED alone.

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

A biphasic nonlinear mathematical model is proposed for the mass transport that occurs during constant flow-rate infusions into brain tissue. The model takes into account geometric and material nonlinearities and a hydraulic conductivity dependent upon strain. The biphasic and convective-diffusive transport 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 the inclusion of these nonlinearities produced modest changes in the interstitial concentration but important variations in drug penetration and bulk concentration. Increased penetration of the drug but smaller bulk concentrations were obtained at smaller strains caused by combination of parameters such as increased Young's modulus and initial hydraulic conductivity. This indicates that simulations of constant flow-rate infusions under the assumption of infinitesimal deformations or rigidity of the tissue may yield lower bulk concentrations near the infusion cavity and over-predictions of the penetration of the infused agent. The analyses also showed that decrease in the infusion flow rate of a fixed amount of drug results in increased penetration of the infused agent. From the clinical point-of-view, this may promote a safer infusion that delivers the therapeutic range over the desired volume while avoiding damage to the tissue by minimizing deformation and strain.

Diffusion-convection effects on drug distribution at the cell membrane level in a patch-clamp setup

We present a model-based method for estimating the effective concentration of the active drug applied by a pressure pulse to an individual cell in a patch-clamp setup, which could be of practical use in the analysis of ligand-induced whole-cell currents recorded in patch-clamp experiments. Our modelling results outline several important factors which may be involved in the high variability of the electric response of the cells, and indicate that with a pressure pulse duration of 1s and diameter of the perfusion tip of 600 μm, elevated amounts of drug can accumulate locally between the pipette tip and the cell. Hence, the effective agonist concentration at the cell membrane level can be consistently higher than the initial concentration inside the perfusion tubes. We performed finite-difference and finite-element simulations to investigate the diffusion/convection effects on the agonist distribution on the cell membrane. Our model can explain the delay between the commencement of acetylcholine application and the onset of the whole-cell current that we recorded on human rhabdomyosarcoma TE671 cells, and reproduce quantitatively the decrease of signal latency with the concentration of agonist in the pipette. Results also show that not only the geometry of the bath chamber and pipette tip, but also the transport parameters of the diffusive and convective phenomena in the bath solution are determinant for the amplitude and kinetics of the recorded currents and have to be accounted for when analyzing patch-clamp data.

Retro-convection enhanced drug delivery: a computational study

Retro-convection enhanced delivery (R-CED) is an emerging drug delivery method to overcome the blood brain barrier (BBB). We have developed a mathematical model to understand the fluid flow and mass transfer in the interstitium of brain tissue in R-CED therapy. The model was used to predict pressure distributions, fluid flow patterns, and drug concentration profiles. Some numerical results were obtained by computer simulations. Three kinds of microdialysis membranes used in R-CED protocols were analyzed in detail. While fluid flow was independent of the choice of membranes, mass transfer processes and drug distributions were found to be highly dependent on the choice of membranes. Sensitivity analysis on a variety of parameters and over a wide range of parameter values was carried out. Although R-CED turned out to be efficacious in generating fluid flows within the brain tissue, it did not favor a large effective treatment volume and needed to be re-examined and re-evaluated experimentally.

A voxelized model of direct infusion into the corpus callosum and hippocampus of the rat brain: model development and parameter analysis

Recent experimental studies have shown convective-enhanced delivery (CED) to be useful for transporting macromolecular therapeutic agents over large tissue volumes in the central nervous system (CNS). There are limited tools currently available for predicting tissue distributions in the brain. We have developed a voxelized modeling methodology in which CNS tissues are modeled as porous media, and transport properties and anatomical boundaries are determined semi-automatically on a voxel-by-voxel basis using diffusion tensor imaging (DTI). By using this methodology, 3D extracellular transport models of the rat brain were developed. Macromolecular tracer distributions following CED in two different infusion sites (corpus callosum and hippocampus) were predicted. Sensitivity of models to changes in infusion parameters, transport properties, and modeling parameters was determined. Predicted tracer distributions were most sensitive to changes in segmentation threshold, DTI resolution, tissue porosity, and infusion site. This DTI-based voxelized modeling methodology provides a potentially rapid means of estimating CED transport.

Characterization of an Anisotropic Hydrogel Tissue Substrate for Infusion Testing

Artificial tissue models that capture specific transport properties are useful for investigating physical phenomena important to drug delivery. In this study, an in vitro tissue model was developed and characterized with the goal of mimicking aligned tissue. An anisotropic porous medium was developed by the construction of a 1% agarose hydrogel implanted with different volume fractions (~ 5, 10, and 20%) of 10-μm-diameter glass fibers. The developed substrate was able to capture anisotropic transport after the direct infusion of a macromolecular tracer, Evans blue albumin (EBA). To further characterize the test substrate, the diffusion tensor of water was measured by diffusion tensor imaging, and the ratios of the diffusivities in the directions parallel and perpendicular to the glass fibers were 1.16, 1.20, and 1.26 for 5, 10, and 20% fiber volume fractions, respectively. The hydraulic conductivity was estimated by the measurement of pressure gradients across samples under controlled microflow conditions in the direction parallel to implanted fibers. The hydraulic conductivities at various hydrogel concentrations without fibers and in a 1% hydrogel with various fiber volume fractions were measured; for example, K(||) = 1.20 × 10(-12) m(4) N(-1) s(-1) (where K(||) is the conductivity component in the direction parallel to the glass fibers) for 20% fiber volume fractions. Also, EBA distributions were fit to porous medium transport models to estimate hydraulic conductivity in the direction perpendicular to glass fibers. The estimated ratio of directional hydraulic conductivity, K(||)/K(⊥) (where K(⊥) is the conductivity component in the direction perpendicular to the glass fibers), ranged from approximately 3 to 5, from 6 to 10, and from 40 to 90 for 5, 10, and 20% fiber volume fractions, respectively. These agarose hydrogel models provided convenient media for quantifying infusion protocols at low flow rates.

Voxelized model of interstitial transport in the rat spinal cord following direct infusion into white matter

Direct tissue infusion, e.g., convection-enhanced delivery (CED), is a promising local delivery technique for treating diseases of the central nervous system. Predictive models of spatial drug distribution during and following direct tissue infusion are necessary for treatment optimization and planning of surgery. In this study, a 3D interstitial transport modeling approach in which tissue properties and anatomical boundaries are assigned on a voxel-by-voxel basis using tissue alignment data from diffusion tensor imaging (DTI) is presented. The modeling approach is semi-automatic and utilizes porous media transport theory to estimate interstitial transport in isotropic and anisotropic tissue regions. Rat spinal cord studies compared predicted distributions of albumin tracer (for varying DTI resolution) following infusion into the dorsal horn with tracer distributions measured by Wood et al. in a previous study. Tissue distribution volumes compared favorably for small infusion volumes (<4 microl). The presented DTI-based methodology provides a rapid means of estimating interstitial flows and tracer distributions following CED into the spinal cord. Quantification of these transport fields provides an important step toward development of drug-specific transport models of infusion.

Rigorous mathematical modeling techniques for optimal delivery of macromolecules to the brain

Several treatment modalities for neurodegenerative diseases or tumors of the central nervous system involve invasive delivery of large molecular weight drugs to the brain. Despite the ample record of experimental studies, accurate drug targeting for the human brain remains a challenge. This paper proposes a systematic design method of administering drugs to specific locations in the human brain based on first principles transport in porous media. The proposed mathematical framework predicts achievable treatment volumes in target regions as a function of brain anatomy and infusion catheter position. A systematic procedure to determine the optimal infusion and catheter design parameters that maximize the penetration depth and volumes of distribution will be discussed. The computer simulations are validated with agarose gel phantom experiments and rat data. The rigorous computational approach will allow physicians and scientists to better plan the administration of therapeutic drugs to the central nervous system.

Diffusion in brain extracellular space

Diffusion in the extracellular space (ECS) of the brain is constrained by the volume fraction and the tortuosity and a modified diffusion equation represents the transport behavior of many molecules in the brain. Deviations from the equation reveal loss of molecules across the blood-brain barrier, through cellular uptake, binding, or other mechanisms. Early diffusion measurements used radiolabeled sucrose and other tracers. Presently, the real-time iontophoresis (RTI) method is employed for small ions and the integrative optical imaging (IOI) method for fluorescent macromolecules, including dextrans or proteins. Theoretical models and simulations of the ECS have explored the influence of ECS geometry, effects of dead-space microdomains, extracellular matrix, and interaction of macromolecules with ECS channels. Extensive experimental studies with the RTI method employing the cation tetramethylammonium (TMA) in normal brain tissue show that the volume fraction of the ECS typically is approximately 20% and the tortuosity is approximately 1.6 (i.e., free diffusion coefficient of TMA is reduced by 2.6), although there are regional variations. These parameters change during development and aging. Diffusion properties have been characterized in several interventions, including brain stimulation, osmotic challenge, and knockout of extracellular matrix components. Measurements have also been made during ischemia, in models of Alzheimer's and Parkinson's diseases, and in human gliomas. Overall, these studies improve our conception of ECS structure and the roles of glia and extracellular matrix in modulating the ECS microenvironment. Knowledge of ECS diffusion properties is valuable in contexts ranging from understanding extrasynaptic volume transmission to the development of paradigms for drug delivery to the brain.

Computational methods for predicting drug transport in anisotropic and heterogeneous brain tissue

Effective drug delivery for many neurodegenerative diseases or tumors of the central nervous system is challenging. Targeted invasive delivery of large macromolecules such as trophic factors to desired locations inside the brain is difficult due to anisotropy and heterogeneity of the brain tissue. Despite much experimental research, prediction of bio-transport phenomena inside the brain remains unreliable. This article proposes a rigorous computational approach for accurately predicting the fate of infused therapeutic agents inside the brain. Geometric and physiological properties of anisotropic and heterogeneous brain tissue affecting drug transport are accounted for by in-vivo diffusion tensor magnetic resonance imaging data. The three-dimensional brain anatomy is reconstructed accurately from subject-specific medical images. Tissue anisotropy and heterogeneity are quantified with the help of diffusion tensor imaging (DTI). Rigorous first principles physical transport phenomena are applied to predict the fate of a high molecular weight trophic factor infused into the midbrain. Computer prediction of drug distribution in humans accounting for heterogeneous and anisotropic brain tissue properties have not been adequately researched in open literature before.

Voxelized model of interstitial transport in nervous tissue following direct infusion into white matter

Direct infusion of therapeutic agents into the brain and spinal cord is a promising local delivery method that circumvents the blood-brain barrier and blood-spinal cord barriers. Predictive models of interstitial (extracellular) distribution during direct infusion would be useful in treatment optimization and planning. To account for large infusion volumes, such models should incorporate tissue boundaries and anisotropic tissue properties. We have developed a rapid, semi-automatic computational modeling approach that utilizes diffusion tensor imaging data to predict interstitial tissue distributions of injected tracers. The developed methodology was validated for direct infusion into the dorsal white matter column of the rat spinal cord.

Prediction of convection-enhanced drug delivery to the human brain

The treatment for many neurodegenerative diseases of the central nervous system (CNS) involves the delivery of large molecular weight drugs to the brain. The blood brain barrier, however, prevents many therapeutic molecules from entering the CNS. Despite much effort in studying drug dispersion with animal models, accurate drug targeting in humans remains a challenge. This article proposes an engineering approach for the systematic design of targeted drug delivery into the human brain. The proposed method predicts achievable volumes of distribution for therapeutic agents based on first principles transport and chemical kinetics models as well as accurate reconstruction of the brain geometry from patient-specific diffusion tensor magnetic resonance imaging. The predictive capabilities of the methodology will be demonstrated for invasive intraparenchymal drug administration. A systematic procedure to determine the optimal infusion and catheter design parameters to maximize penetration depth and volumes of distribution in the target area will be discussed. The computational results are validated with agarose gel phantom experiments. The methodology integrates interdisciplinary expertise from medical imaging and engineering. This approach will allow physicians and scientists to design and optimize drug administration in a systematic fashion.

Biphasic finite element model of solute transport for direct infusion into nervous tissue

Infusion-based techniques are promising drug delivery methods for treating diseases of the nervous system. Direct infusion into tissue parenchyma circumvents the blood-brain barrier, localizes delivery, and facilitates transport of macromolecular agents. Computational models that predict interstitial flow and solute transport may aid in protocol design and optimization. We have developed a biphasic finite element (FE) model that accounts for local, flow-induced tissue swelling around an infusion cavity. It solves for interstitial fluid flow, tissue deformation, and solute transport in surrounding isotropic gray matter. FE solutions for pressure-controlled infusion were validated by comparing with analytical solutions. The influence of deformation-dependent hydraulic permeability was considered. A transient, nonlinear relationship between infusion pressure and infusion rate was determined. The sensitivity of convection-dominated solute transport (i.e., albumin) over a range of nervous tissue properties was also simulated. Solute transport was found to be sensitive to pressure-induced swelling effects mainly in regions adjacent to the infusion cavity (r/a 0 <or= 5 where a 0 is the outer cannula radius) for short times infusion simulated (3 min). Overall, the biphasic approach predicted enhanced macromolecular transport for small volume infusions (e.g., 2 microL over 1 h). Solute transport was enhanced by decreasing Young's modulus and increasing hydraulic permeability of the tissue.