Kambiz VafaiKambiz VafaiMay 17, 2007May 17, 2007

The Role of Porous Media in AddressingThe Role of Porous Media in AddressingSome Challenging Issues in BiomedicalSome Challenging Issues in Biomedical

EngineeringEngineering

Mechanical Engineering Department, University of California, Riverside, 92521

Background and SocietalBackground and SocietalImpactImpact

• Porous Media models can provide a realistic representation of tissuesand organs such as arterial wall

• Porous media theory provides a unique perspective to biotransportphenomena, with a potential to address some of the most challengingproblems.

• Porous media approach will provide medical scientists withsubstantial insight into several biological phenomena which can beused to develop new prophylactic, diagnostic, and therapeuticprocedures for improving human health

State-of-the-ArtState-of-the-Art•• Significant advances have been accomplished in applying porousSignificant advances have been accomplished in applying porous

media theory in modeling biomedical applications such as:media theory in modeling biomedical applications such as:

1.1. Transport in biological tissuesTransport in biological tissues

2.2. Tissue EngineeringTissue Engineering

3.3. Transport in Brain TissuesTransport in Brain Tissues

4.4. Medical imaging (MRI)Medical imaging (MRI)

5.5. Drug deliveryDrug delivery

6. Hyperthermic Sessions (for destroying malignant cells)

Transport in Brain TissueTransport in Brain Tissue Tissue Generation UtilizingScaffolds

Nanoparticles for DrugDelivery

Transport in anTransport in anarteryartery

Transport across BloodTransport across BloodBrain BarrierBrain Barrier

Technical PrinciplesTechnical Principles••Great majority of tissues and organs can be treated as porous media.Great majority of tissues and organs can be treated as porous media.

••Porous media theory can be applicable to all scales: macro, micro, Porous media theory can be applicable to all scales: macro, micro, nanonano,,organ, tissue, and cell.organ, tissue, and cell.

••Theory and Modeling of porous media has evolved substantially, Theory and Modeling of porous media has evolved substantially, e.g.e.g. the thegeneralized equation of transport through porous media.generalized equation of transport through porous media.

••Newly emerging technologies employ the porous media theory, Newly emerging technologies employ the porous media theory, i.e.i.e.nanoporous nanoporous silicon sensors for biological applications.silicon sensors for biological applications.

••Reflection Coefficients in Porous MediaReflection Coefficients in Porous Media

••Some real-world flow phenomena involve the selectiveSome real-world flow phenomena involve the selectivediffusion/convection of species in porous media and/or through porousdiffusion/convection of species in porous media and/or through porousmembranes. Examples of such phenomena include species transportmembranes. Examples of such phenomena include species transportthrough arterial walls or in tumor modulesthrough arterial walls or in tumor modules

BarriersBarriers

••Accurate evaluation of basic properties such asAccurate evaluation of basic properties such aspermeability, porosity, effective diffusivity, etc.permeability, porosity, effective diffusivity, etc.

••Poor connection between scales (multi-scale modeling)Poor connection between scales (multi-scale modeling)

••Inadequate collaboration between Medical and EngineeringInadequate collaboration between Medical and EngineeringScientistsScientists

••Multiphysics Multiphysics modelingmodeling

••Computational CostComputational Cost

1. Transport in Biological Tissues1. Transport in Biological Tissues••Several analytical and numerical works have explored the mechanism ofSeveral analytical and numerical works have explored the mechanism oftransport of macromolecules within the arterial walltransport of macromolecules within the arterial wall

••Multilayer model is the most complex model which takes into account theMultilayer model is the most complex model which takes into account theheterogeneous properties of the layers constituting the wallheterogeneous properties of the layers constituting the wall at the microscopicat the microscopicor macroscopic levelsor macroscopic levels

••Due to its complexity, a larger number of parameters are required toDue to its complexity, a larger number of parameters are required tocharacterize the physical properties of each layercharacterize the physical properties of each layer

••A new fundamental four-layer model is required for the description of the massA new fundamental four-layer model is required for the description of the masstransport in the arterial wall coupled with the mass transport in the arterialtransport in the arterial wall coupled with the mass transport in the arteriallumen.lumen.

••The endothelium, The endothelium, intimaintima, internal elastic lamina (IEL) and media layers can be, internal elastic lamina (IEL) and media layers can betreated as macroscopically porous media and mathematically modeled usingtreated as macroscopically porous media and mathematically modeled usingproper types of the volume averaged porous media equationsproper types of the volume averaged porous media equations

••The filtration and osmotic reflection coefficients should beThe filtration and osmotic reflection coefficients should beemployed to account for selective rejection of species by theemployed to account for selective rejection of species by themembranes and to incorporate osmotic pressuremembranes and to incorporate osmotic pressure

••Since the porous media are selectively permeable to certainSince the porous media are selectively permeable to certainspecies such as LDL, filtration reflection coefficient has to bespecies such as LDL, filtration reflection coefficient has to beintroduced to account for this effect.introduced to account for this effect.

••In some cases osmotic effect in the transport modelingIn some cases osmotic effect in the transport modelingshould be considered when the maximum osmotic pressureshould be considered when the maximum osmotic pressuregradient in these layers is comparable to the hydraulicgradient in these layers is comparable to the hydraulicpressure gradient.pressure gradient.

2. Tissue Engineering2. Tissue Engineering••Tissue engineering is an interdisciplinary field that involves cell biology,Tissue engineering is an interdisciplinary field that involves cell biology,materials science, reactor engineering, and clinical research with the goal ofmaterials science, reactor engineering, and clinical research with the goal ofcreating new tissues and organscreating new tissues and organs

••The number of organs available for transplantation is farThe number of organs available for transplantation is farexceeded by the number of patients needing such proceduresexceeded by the number of patients needing such procedures••In 2000 alone, approximately 72,000 people in the United States were on theIn 2000 alone, approximately 72,000 people in the United States were on thewaiting list for an organ transplant due to end-stage organ failure, but only 23,000waiting list for an organ transplant due to end-stage organ failure, but only 23,000transplants were performed. This shortfall provides additional impetus fortransplants were performed. This shortfall provides additional impetus forprogress in tissue engineeringprogress in tissue engineering••In order to achieve significant tissue structures, there must be appropriateIn order to achieve significant tissue structures, there must be appropriatetransport of nutrients to and waste from the cells as they begin to form a tissue ortransport of nutrients to and waste from the cells as they begin to form a tissue ororganorgan••One strategy is to utilize a biodegradable porous polymer so that it supports theOne strategy is to utilize a biodegradable porous polymer so that it supports thecells until their growth is completedcells until their growth is completed

••This polymer must be porous so that nutrients can easily reach the cellsThis polymer must be porous so that nutrients can easily reach the cellsand have enough space for the growth of the cells and have cell-friendlyand have enough space for the growth of the cells and have cell-friendlydegradable by-productsdegradable by-products••The efficient design and manufacture of a complex scaffold withThe efficient design and manufacture of a complex scaffold withoptimum porosity and interconnectivity is substantial for tissueoptimum porosity and interconnectivity is substantial for tissueengineering applications.engineering applications.The essential principle of tissue engineering isThe essential principle of tissue engineering isto combine a scaffold with cells for tissue replacement or repair.to combine a scaffold with cells for tissue replacement or repair.

Scaffold

3. Transport in Brain Tissues3. Transport in Brain Tissues•In the neuroscience context, the extracellular space (ECS-Interstitial space between cells, occupied by fluid as well asamorphous and fibrous substances) constitutes themicroenvironment of brain cells

•It is a conduit for cellular metabolities and a route for drugdelivery

••Therefore, the Therefore, the extracellular extracellular spacespacerepresents a significant communicationrepresents a significant communicationchannel between neurons, and betweenchannel between neurons, and betweenneurons and neurons and glial glial cells (provide supportcells (provide supportand protection for neurons)and protection for neurons) ECSECS

••Porosity and the Porosity and the tortuosity tortuosity affect theaffect theactivity-related accumulation ofactivity-related accumulation ofsubstances in the extracellular spacesubstances in the extracellular space(ECS), their movements towards the(ECS), their movements towards theadjacent neurons and glial cellsadjacent neurons and glial cells

•Changes in these parameters can therefore profoundlyinfluence signal transmission, susceptibility of the nervoustissue to anoxia (A total lack of oxygen) and seizures and couldbe an important factor in manifestation of the central neuronssystem (CNS) diseases

RecommendationsRecommendations••Multiphysics Multiphysics modeling: modeling: i.e.i.e. Fluid-wall interaction in arteries and its effect on Fluid-wall interaction in arteries and its effect onsolute transportsolute transport

••There is a need for a fluid-structure interactionThere is a need for a fluid-structure interaction ( (FSI) approach in studying theFSI) approach in studying thetransport of macromolecules in the arterial walls under transport of macromolecules in the arterial walls under pulsatile pulsatile flow conditionflow conditionand utilizing a porous media approach to analyze the arterial walls. and utilizing a porous media approach to analyze the arterial walls. This isThis isbecausebecause the forces associated with the flow may deform the arterial walls andthe forces associated with the flow may deform the arterial walls andconsequently alter the properties of the wall which in turn affect the flow structureconsequently alter the properties of the wall which in turn affect the flow structurein the lumen as well as the transport process of macromolecules from the lumenin the lumen as well as the transport process of macromolecules from the lumento the arterial wallsto the arterial walls

••Since the wall of the artery is deformable, a complex coupling exists between the lumenSince the wall of the artery is deformable, a complex coupling exists between the lumenand the arterial wall. Thus, the variations in the porosity and permeability of the deformableand the arterial wall. Thus, the variations in the porosity and permeability of the deformablearterial wall should be considered in such analysis arterial wall should be considered in such analysis (e.g. Tissue Engineering)(e.g. Tissue Engineering)

••Variations in the physical properties of the arterial walls such as Young modulus andVariations in the physical properties of the arterial walls such as Young modulus andPoissonPoisson’’s ratio should be considered in any future studies since the materials of the wallss ratio should be considered in any future studies since the materials of the wallsare nonlinear, non-homogeneous, and anisotropicare nonlinear, non-homogeneous, and anisotropic

••Reflection coefficients should be properly evaluated and utilized in theReflection coefficients should be properly evaluated and utilized in thegoverning transport equations when modeling arterial walls to account forgoverning transport equations when modeling arterial walls to account forselective rejection of species and the osmotic pressure.selective rejection of species and the osmotic pressure.

••Many biomedical applications such as drug delivery, tissue engineering,Many biomedical applications such as drug delivery, tissue engineering,hyperthermia, and many others can be modeled using porous media theoryhyperthermia, and many others can be modeled using porous media theory

••Focus on the fundamentals rather than getting lost in detailsFocus on the fundamentals rather than getting lost in details••Stronger link between theory, numerical modeling, and experimentation.Stronger link between theory, numerical modeling, and experimentation.

••Broader application of porous media theory to biotransport phenomena:Broader application of porous media theory to biotransport phenomena:transport within Kidney, tumors, lung, etc.transport within Kidney, tumors, lung, etc.••Improved evaluation of properties: permeability, effective diffusivity, etc.Improved evaluation of properties: permeability, effective diffusivity, etc.

••Multiscale Multiscale modeling: cell to tissue to organmodeling: cell to tissue to organ

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