Fluid Mechanics: Transport and Diffusion Analyses as Applied in Biomaterials Studies

Mukundakrishnan, Karthik; Ayyaswamy, P. S.

doi:10.1016/b978-0-08-055294-1.00095-7

Cited by 3 publications

(4 citation statements)

References 104 publications

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“…Typically, fluid flow requires solution to the Navier-Stokes equations while mass transfer involves the convection-diffusion equation. The review by Mukundakrishnan [23] adequately describes modeling of solute transport in living tissue. We make appropriate approximations relevant to transport in the vitreous humor.…”

Section: Mathematical Modelingmentioning

confidence: 99%

Mathematical Model of Macromolecular Drug Transport in a Partially Liquefied Vitreous Humor

Khoobyar

Penkova

Humayun³

et al. 2022

Journal of Heat Transfer

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The purpose of this study is to investigate the effect of partial liquefaction (due to ageing) of the vitreous humor on the transport of ocular drugs. In our model, the gel part of the vitreous is treated as a Darcy-type porous medium. A spherical region within the porous part of vitreous is in a liquid state which, for computational purposes, is also treated as a porous medium but with a much higher permeability. Using the finite element method, a time-dependent, three-dimensional model has been developed to computationally simulate (using the Petrov-Galerkin method) the transport of intravitreally injected macromolecules where both convection and diffusion are present. From a fluid physics and transport phenomena perspective, the results show many interesting features. For pressure-driven flow across the vitreous, the flow streamlines converge into the liquefied region as the flow seeks the fastest path of travel. Furthermore, as expected, with increased level of liquefaction, the overall flow rate increases for a given pressure drop. We have quantified this effect for various geometrical considerations. The flow convergence into the liquefied region has important implication for convective transport. One effect is the clear diversion of the drug as it reaches the liquefied region. In some instances, the entry point of the drug in the retinal region gets slightly shifted due to liquefaction. While the model has many approximations and assumptions, the focus is illustrating the effect of liquefaction as one of the building blocks towards a fully comprehensive model.

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Section: Mathematical Modelingmentioning

confidence: 99%

Mathematical Model of Macromolecular Drug Transport in a Partially Liquefied Vitreous Humor

Khoobyar

Penkova

Humayun³

et al. 2022

Journal of Heat Transfer

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“…For the experiment, the vitreous is considered to be a porous medium consisting of a meshwork of hyaluronic acid and collagen fibers. The mathematical description of transport processes in bioporous media is available in various books and classical papers Ai & Vafai, 2006;Mukundakrishnan & Ayyaswamy, 2011;Shafahi & Vafai, 2011;Khanafer & Vafai, 2006;Khanafer & Vafai, 2005). Mass-diffusion aspects have been detailed in our investigations on the diffusion coefficient measurement (Penkova et.…”

Section: Mathematical Modelmentioning

confidence: 99%

Measurement of the Hydraulic Conductivity of the Vitreous Humor

et al. 2020

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The hydraulic conductivity of the vitreous humor has been measured for the bovine eye. The experiment was carried out by placing it within upright cylindrical chamber, open at both ends, and letting its liquid content drain out of the bottom opening by gravity, through a 20μm nylon mesh filter. Additional negative pressure was provided at the exit by a hanging drainage tube. The diminishing vitreous volume was measured in terms of the height in the chamber and recorded as a function of time. The reduction in the vitreous liquid content also caused the hydraulic conductivity to reduce and this parameter was quantified on the basis of previously-developed theories of fibrous porous media that have been very well established. A theoretical model with a fully analytical expression for the vitreous volume undergoing drainage was developed and used as a least-squares best fit to deliver the initial hydraulic conductivity value of K 0 /μ=(7.8 ± 3.1) × 10 −12 m 2 (Pa-s). The measurements were made with the hyaloid membrane intact and therefore represents an effective conductivity for the entire system, including possible variations within the vitreous.

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“…To model the drug distribution in the vitreous, the three-dimensional mass diffusion equation, − ∇ 2 = 0 (15) was solved numerically. Since it was already established by Penkova et al [2] that for the timeframe of the experiments, the effect of the vitreous shape and adjacent tissue is negligible, the domain of interest for the numerical solution was defined as a sphere with a radius of 10 mm as illustrated in Figure 7(a).…”

Section: Finite-element Analysismentioning

confidence: 99%

“…It should be noted that in a living eye, both diffusive and convective transport are present in the vitreous, and these processes take place together [13]. The two processes are driven by different physical mechanisms, diffusion by a concentration gradient, and convection by water flow [14,15,16,17], but it has been common to treat the combined effect with an 'effective' diffusion coefficient. However, keeping the physics in sight, we shall treat the two processes as separate, and the present review focuses on pure diffusion.…”

Section: Introductionmentioning

confidence: 99%

Diffusive Transport in the Vitreous Humor: Experimental and Analytical Studies

Penkova

Moats

Humayun

et al. 2019

Journal of Heat Transfer

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In relation to intravitreal drug delivery, predictive mathematical models for drug transport are being developed, and to effectively implement these for retinal delivery, the information on biophysical properties of various ocular tissues is fundamentally important. It is therefore necessary to accurately measure the diffusion coefficient of drugs and drug surrogates in the vitreous humor. In this review, we present the studies conducted by various researchers on such measurements over the last several decades. These include imaging techniques (fluorescence and magnetic resonance imaging (MRI)) that make use of introducing a contrast agent or a labeled drug into the vitreous and tracking its diffusive movement at various time points. A predictive model for the same initial conditions when matched with the experimental measurements provides the diffusion coefficient, leading to results for various molecules ranging in size from approximately 0.1 to 160 kDa. For real drugs, the effectiveness of this system depends on the successful labeling of the drugs with suitable contrast agents such as fluorescein and gadolinium or manganese so that fluorescence or MR imagining could be conducted. Besides this technique, some work has been carried out using the diffusion apparatus for measuring permeation of a drug across an excised vitreous body from a donor chamber to the receptor by sampling assays from the chambers at various time intervals. This has the advantage of not requiring labeling but is otherwise more disruptive to the vitreous. Some success with nanoparticles has been achieved using dynamic light scattering (DLS), and presently, radioactive labeling is being explored.

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Fluid Mechanics: Transport and Diffusion Analyses as Applied in Biomaterials Studies

Cited by 3 publications

References 104 publications

Mathematical Model of Macromolecular Drug Transport in a Partially Liquefied Vitreous Humor

Mathematical Model of Macromolecular Drug Transport in a Partially Liquefied Vitreous Humor

Measurement of the Hydraulic Conductivity of the Vitreous Humor

Diffusive Transport in the Vitreous Humor: Experimental and Analytical Studies

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