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KAUST-IAMCS Workshop on Modeling and Simulation of Wave Propagation and Applications

Rabia Djellouli, California State University at Northridge
Can Electrical Current-Based Therapy Disrupt Fibrous Capsule Tissue Growth Around Biomaterial Implants?

Abstract

Biomaterial implants have been widely used for a variety of applications such as dental implants, glaucoma drainage implants, orthopedic prosthesis, cardiovascular prosthesis for vessels or heart valves, glucose sensors as either warning or feedback control sensors for artificial pancreas devices, drug delivery devices, breast implants, etc.

Implantation of biomaterials creates the so-called "foreign-body" response which includes the formation of a fibrous capsule to shield the body from the foreign object by creating a fibrous wall of tissue of varying thickness between the two. This fibrous capsule surrounds or encapsulates the implant. The formation of fibrous tissue around an implant is normal, and is an integral part of the "wound-healing" process of the body's response to the implant material. The problems begin to surface when the fibrous capsule tightens and "squeezes" the implant to the point that it hampers the performance of the implant and ultimately leads to failure. Therefore, an invasive surgery to remove the fibrous formation and/or the implant is inevitable in most cases.

Vast research efforts have focused on addressing the issue of fibrous capsule formation by mainly improving the so-called "biocompatibility" of the implants. The objective here is to avoid, or at least, minimize capsule formation around implanted materials. This is generally attempted by disguising the implants with coatings that mimic body conditions. The success of this approach, if any, remains very limited and therefore, capsule formation still remains problematic. Consequently, the quest for a reliable and less traumatic procedure to prevent, or at least, diminish the effects of fibrous capsule formation represents a major challenge for the biomedical community.

Electrical current-based techniques have emerged recently for addressing several challenging issues such as adult stem cells (their proliferation and differentiation with microwave and electrical stimulation as well as for purging their preparations of contaminating myeloma cells), electrodesiccation and curettage (using electrical current to dehydrate) for skin cancer treatment, and more recently, radio frequency ablation for inoperable liver cancer (radio frequency ablation) which has been approved just recently by the FDA. Electrical devices like implanted neurostimulators have been in use for decades. These devices deliver current pulses between 0.1-0.5 V with frequencies of 10-300 Hz. While generating electrical currents to tissue, there seems to be some encapsulation but little, if any, inflammation caused by these stimulators. Therefore, the idea of applying low electrical current at the local implant site to alter the initial capsule formation and to disrupt any aggregation of material near the implant is a very attractive alternative (non-invasive) procedure for addressing efficiently the problem of capsule formation.

Our ultimate objective is to conduct a mathematical analysis and a numerical investigation as well as in vivo experiments to assess the performance of using electrical current for disrupting fibrous capsule formation. To this end, we proceed into two steps. We first propose a new one-dimensional mathematical model that describes the growth of fibrous tissue around a given rigid, disk-shaped implant and then we calibrate its parameters from a limited set of concentration profile measurements. This model is, to the best of our knowledge, a new model that describes the fibrous tissue concentration as a function of time and the radial distance from the implant. The development of this model is a preliminary step before considering more complex implants in terms of shape and material properties. It should be noted that many of the ideas and issues presented here are relevant to the case of general-shaped implants. In studying this particular case, we will shed some light on this phenomenon which is still not fully understood from both a biological point of view and a modeling aspect. We consider within this work a model based on a diffusion equation. The parameters of this model characterize the properties of both the implant and the body into which it is implanted. We then present a solution methodology based on a regularized Newton method to compute, from some fibrous capsule tissue measurements, the parameters corresponding to a given implant. Note the Newton method is used to address the nonlinear aspect of the inverse problem, whereas the Tikhonov regularization technique is incorporated to the Newton algorithm to deal with its ill-posed nature. Numerical results based on both synthetic and in vivo data are presented to illustrate the performance of the solution methodology as well as the validity of the mathematical model. The second step of this work addresses the electrical therapy aspect. This problem can be formulated mathematically as a design problem where the objective is to identify parameters of a partial differential operator to achieve a desired effect. It is proposed to design, implement, and validate a regularized Newton-type method for solving this class of inverse problems. In vivo experiments will be conducted to accurately verify and validate the numerical results.

The potential outcome of this collaborative research project includes, among others, information that would be helpful in developing a better understanding on how to apply electrical stimulation to optimize specific outcomes, versus the current mode of trial and error to final suitable treatment regimes. In addition, it has a great potential for benefiting for example the in vivo sensor community particularly those fabricating glucose sensors and drug delivery devices. Furthermore, the mathematical difficulties, computational issues, and solution approaches addressed in this proposal are relevant to many important problems in other application areas such as network communication, geophysical exploration, structural dynamics, and aeroelasticity.

Acknowledgments

This project is supported by MiniMed/Medtronic and the office of Graduate Studies at CSUN under grant #E1270. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of MiniMed/Medtronic or of the office of Graduate Studies at CSUN.