Research

My areas of research are in the mathematical modeling of convection-enhanced delivery and hydrocephalus.

Convection-enhanced delivery is a therapeutic procedure developed over the past two decades to treat diseases and disorders of the central nervous system.  Chemotherapy is generally not very effective for treating cancers in the brain because of a cell layer in the arteries that feed the brain (an effect which is termed the blood–brain barrier).  This blood–brain barrier is the body’s self-defense mechanism that prevents unwanted chemicals from leaking from our blood supply into our brain and damaging it.  However, this generally beneficial mechanism unfortunately limits the delivery of beneficial drugs doctors would like to deliver to the brain to treat cancer and other illnesses, such as Parkinson’s disease.

To circumvent the blood–brain barrier, doctors developed a technique in which therapeutic drugs are delivered directly to the brain via catheters that have been surgically implanted through the skull (in contrast to indirect delivery through the vasculature).  The deposition of fluid and drugs into the brain has the added effect of convection to distribute the drugs more deeply throughout the brain (versus the more limited effect of diffusion that results from intravenous drug delivery).  However, this additional fluid pushes outward on the brain tissue from the location of the catheter, causing the tissue to displace and undergo stress.  This is a very similar phenomenon to hydrocephalus, except in convection-enhanced delivery the source of the fluid is external whereas in hydrocephalus the fluid is naturally produced.

In contrast, hydrocephalus is a disease in which cerebrospinal fluid produced in the center of the brain is unable to flow through the brain and be reabsorbed by tissue located between the brain and the skull.  This causes the fluid to pool in the middle of the brain and push outward, causing the tissue to be stressed and deform.  If the deformation is significant enough, damage may occur.

Selected Publications — Convection-Enhanced Delivery
(* denotes Lafayette College student)

• J. J. García, A. B. Molano, and J. H. Smith.  Description and validation of a finite element model of backflow during infusion into a brain tissue phantom.  Journal of Computational and Nonlinear Dynamics, 8:011017, 2013.
• J. H. Smith, K. A. Starkweather*, and J. J. García.  Implications of transvascular fluid exchange in nonlinear, biphasic analyses of flow-controlled infusion in brain.  Bulletin of Mathematical Biology, 74:881–907, 2012.
• J. H. Smith and J. J. García.  A nonlinear biphasic model of flow-controlled infusion in brain: Mass transport analyses.  Journal of Biomechanics, 44:524–531, 2011.
• J. H. Smith and J. J. García.  A nonlinear biphasic model of flow-controlled infusion in brain: Fluid transport and tissue deformation analyses.  Journal of Biomechanics, 42:2017–2025, 2009.
• J. J. García and J. H. Smith.  A biphasic hyperelastic model for the analysis of fluid flow and mass transport in brain tissue.  Annals of Biomedical Engineering, 37:375–386, 2009.
• J. H. Smith and J. A. C. Humphrey.  Interstitial transport and transvascular fluid exchange during infusion into brain and tumor tissue.  Microvascular Research, 73:58–73, 2007.

Selected Publications — Hydrocephalus
(* denotes Lafayette College student)

• J. A. Lefever*, J. J. García, and J. H. Smith.  A patient-specific, finite element model for noncommunicating hydrocephalus.  Journal of Biomechanics, 46:1447–1453, 2013.
• J. J. García and J. H. Smith.  A biphasic hyperelastic model for hydrocephalus.  Latin American Applied Research, 40:295–302, 2010.

Selected Conference Presentations
(* denotes Lafayette College student)

• J. H. Smith and J. J. García. Constitutive modeling of brain tissue using Ogden-type strain energy functions. 5th Biot Conference on Poromechanics, Vienna, Austria, July 10–12, 2013.
• A. Orozco, J. H. Smith, and J. J. García. Predictions of drug distribution during infusions into the brain using an axisymmetric finite element biphasic model that includes backflow. ASME 2013 Summer Bioengineering Conference, Sunriver, OR, June 26–29, 2013.
• A. Orozco, J. H. Smith, and J. J. García. Assessment of an exponential scaling relationship for backflow length in brain tissue. ASME 2013 Summer Bioengineering Conference, Sunriver, OR, June 26–29, 2013.
• W. R. Hendra*, J. A. Lefever*, J. J. García, and J. H. Smith. A flow-controlled finite element model for noncommunicating hydrocephalus. ASME 2013 Summer Bioengineering Conference, Sunriver, OR, June 26–29, 2013.
• A. Orozco, J. J. García, and J. H. Smith. Revised scaling relationship for backflow distance in brain tissue. Second International Meeting of the Society for CNS Interstitial Delivery of Therapeutics, Chicago, IL, October 5–6, 2012.
• J. J. García and J. H. Smith. Revised scaling relationship for backflow distance along an infusion catheter.  ASME 2012 Summer Bioengineering Conference, Fajardo, Puerto Rico, June 20–23, 2012.