Abstract: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 rel… Show more
“…Tau pathology induced by the injection of tau seeds into the mouse brain supports the idea that the harmful species can be transmitted from the inoculation sites to synaptically connected brain regions [85, 86]. Actually, the spreading of toxic tau species is chiefly attributed to the axonal transportation [87], and thus, due to the porous structure of axonal bundles [88–90], it is expected that, at the mesoscale, tau pathology is propagated by a nonlinear diffusion process. Further, cell culture and animal model studies have indicated that misfolded tau species can be transmitted trans-synaptically among neurons, both anterogradely and retrogradely [91, 92], and recently, researchers have also investigated directionally biased spreading of tauopathies using an in-silico model mimicking the two-neuron system [93] and a diffusion equation with the linear Laplacian operator on the mouse connectome [94].…”
Section: Modeling Tauopathy Progression In the Mouse Brainmentioning
In a variety of practical applications, there is a need to investigate diffusion or reaction-diffusion processes on complex structures, including brain networks, that can be modeled as weighted undirected and directed graphs. As an instance, the celebrated Fisher-Kolmogorov-Petrovsky-Piskunov (Fisher-KPP) reaction-diffusion equation are becoming increasingly popular for use in graph frameworks by substituting the standard graph Laplacian operator for the continuous one to study the progression of neurodegenerative diseases such as tauopathies including Alzheimer's disease (AD). However, due to the porous structure of neuronal fibers, the spreading of toxic species can be governed by an anomalous diffusion process rather than a normal one, and if this is the case, the standard graph Laplacian cannot adequately describe the dynamics of the spreading process. To capture such more complicated dynamics, we propose a diffusion equation with a nonlinear Laplacian operator and a generalization of the Fisher-KPP reaction-diffusion equation on undirected and directed networks using extensions of fractional polynomial (FP) functions. A complete analysis is also provided for the extended FP diffusion equation, including existence, uniqueness, and convergence of solutions, as well as stability of equilibria. Moreover, for the extended FP Fisher-KPP reaction-diffusion equation, we derive a family of positively invariant sets allowing us to establish existence, uniqueness, and boundedness of solutions. Finally, we conclude by investigating nonlinear diffusion on a directed one-dimensional lattice and then modeling tauopathy progression in the mouse brain to gain a deeper understanding of the potential applications of the proposed extended FP equations.
“…Tau pathology induced by the injection of tau seeds into the mouse brain supports the idea that the harmful species can be transmitted from the inoculation sites to synaptically connected brain regions [85, 86]. Actually, the spreading of toxic tau species is chiefly attributed to the axonal transportation [87], and thus, due to the porous structure of axonal bundles [88–90], it is expected that, at the mesoscale, tau pathology is propagated by a nonlinear diffusion process. Further, cell culture and animal model studies have indicated that misfolded tau species can be transmitted trans-synaptically among neurons, both anterogradely and retrogradely [91, 92], and recently, researchers have also investigated directionally biased spreading of tauopathies using an in-silico model mimicking the two-neuron system [93] and a diffusion equation with the linear Laplacian operator on the mouse connectome [94].…”
Section: Modeling Tauopathy Progression In the Mouse Brainmentioning
In a variety of practical applications, there is a need to investigate diffusion or reaction-diffusion processes on complex structures, including brain networks, that can be modeled as weighted undirected and directed graphs. As an instance, the celebrated Fisher-Kolmogorov-Petrovsky-Piskunov (Fisher-KPP) reaction-diffusion equation are becoming increasingly popular for use in graph frameworks by substituting the standard graph Laplacian operator for the continuous one to study the progression of neurodegenerative diseases such as tauopathies including Alzheimer's disease (AD). However, due to the porous structure of neuronal fibers, the spreading of toxic species can be governed by an anomalous diffusion process rather than a normal one, and if this is the case, the standard graph Laplacian cannot adequately describe the dynamics of the spreading process. To capture such more complicated dynamics, we propose a diffusion equation with a nonlinear Laplacian operator and a generalization of the Fisher-KPP reaction-diffusion equation on undirected and directed networks using extensions of fractional polynomial (FP) functions. A complete analysis is also provided for the extended FP diffusion equation, including existence, uniqueness, and convergence of solutions, as well as stability of equilibria. Moreover, for the extended FP Fisher-KPP reaction-diffusion equation, we derive a family of positively invariant sets allowing us to establish existence, uniqueness, and boundedness of solutions. Finally, we conclude by investigating nonlinear diffusion on a directed one-dimensional lattice and then modeling tauopathy progression in the mouse brain to gain a deeper understanding of the potential applications of the proposed extended FP equations.
“…For improvement, specific models can be developed to describe a certain drug delivery process based on the findings from biochemical studies. Microscale research ( 98 ) and the application of advanced medical imaging techniques ( 99 ) can support the determination of drug and tissue properties. Fig.…”
Purpose
Tissue hydraulic permeability of brain tumours can vary considerably depending on the tissue microstructure, compositions in interstitium and tumour cells. Its effects on drug transport and accumulation remain poorly understood.
Methods
Mathematical modelling is applied to predict the drug delivery outcomes in tumours with different tissue permeability upon convection-enhanced delivery. The modelling is based on a 3-D realistic tumour model that is extracted from patient magnetic resonance images.
Results
Modelling results show that infusing drugs into a permeable tumour can facilitate a more favourable hydraulic environment for drug transport. The infused drugs will exhibit a relatively uniform distribution and cover a larger tumour volume for effective cell killing. Cross-comparisons show the delivery outcomes are more sensitive to the changes in tissue hydraulic permeability and blood pressure than the fluid flow from the brain ventricle. Quantitative analyses demonstrate that increasing the fluid gain from both the blood and brain ventricle can further improve the interstitial fluid flow, and thereby enhance the delivery outcomes. Furthermore, similar responses to the changes in tissue hydraulic permeability can be found for different types of drugs.
Conclusions
Tissue hydraulic permeability as an intrinsic property can influence drug accumulation and distribution. Results from this study can deepen the understanding of the interplays between drug and tissues that are involved in the drug delivery processes in chemotherapy.
“…36,[51][52][53][54][55] Furthermore, CED studies and clinical investigations of the cerebral oedema propagation show a clear influence of the directionality and organisation of axonal fibres on fluid flow and diffusion within the tissue. 17,56,57,58,59 Let us turn our attention more closely to the results obtained in terms of myelin content. Axonal features are bounded by the outer ring of myelin sheaths, so all the data expressed in this research are representative of the "outer diameter" of the axon.…”
There is an increased need and focus to understand how local brain microstructure affects the transport of drug molecules directly administered to the brain tissue, for example in convection-enhanced delivery procedures. This study reports the first systematic attempt to characterize the cytoarchitecture of commissural, long association and projection fibers, namely: the corpus callosum, the fornix and the corona radiata. Ovine samples from three different subjects were stained with osmium tetroxide (to enhance contrast from cell organelles and the fibers), embedded in resin and then imaged using scanning electron microscope combined with focused ion beam milling to generate 3D volume reconstructions of the tissue at subcellular spatial resolution. Particular focus has been given to the characteristic cytological feature of the white matter: the axons and their alignment in the tissue. Via 2D images a homogeneous myelination has been estimated via detection of ~40% content of lipids in all the different fiber tracts. Additionally, for each tract, a 3D reconstruction of relatively large volumes (15μm x 15μm x 15μm – including a significant number of axons) has been performed. Namely, outer axonal ellipticity, outer axonal cross-sectional area and their relative perimeter have been measured. The study of well-resolved microstructural features provides useful insight into the fibrous organization of the tissue, whose micromechanical behaviour is that of a composite material presenting elliptical tortuous tubular fibers embedded in the extra-cellular matrix. Drug flow can be captured through microstructurally-based models, leading to a workflow to enable physically-accurate simulations of drug delivery to the targeted tissue.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
