Modeling capsule tissue growth around disk-shaped implants: a numerical and in vivo study

A novel approach to calibrate the hemodynamic model using functional Magnetic Resonance Imaging (fMRI) measurements

BACKGROUND

The calibration of the hemodynamic model that describes changes in blood flow and blood oxygenation during brain activation is a crucial step for successfully monitoring and possibly predicting brain activity. This in turn has the potential to provide diagnosis and treatment of brain diseases in early stages.

NEW METHOD

We propose an efficient numerical procedure for calibrating the hemodynamic model using some fMRI measurements. The proposed solution methodology is a regularized iterative method equipped with a Kalman filtering-type procedure. The Newton component of the proposed method addresses the nonlinear aspect of the problem. The regularization feature is used to ensure the stability of the algorithm. The Kalman filter procedure is incorporated here to address the noise in the data.

RESULTS

Numerical results obtained with synthetic data as well as with real fMRI measurements are presented to illustrate the accuracy, robustness to the noise, and the cost-effectiveness of the proposed method.

COMPARISON WITH EXISTING METHOD(S)

We present numerical results that clearly demonstrate that the proposed method outperforms the Cubature Kalman Filter (CKF), one of the most prominent existing numerical methods.

CONCLUSION

We have designed an iterative numerical technique, called the TNM-CKF algorithm, for calibrating the mathematical model that describes the single-event related brain response when fMRI measurements are given. The method appears to be highly accurate and effective in reconstructing the BOLD signal even when the measurements are tainted with high noise level (as high as 30%).

Numerical investigation of the electrical current effect on the fibrous tissue growth around biomaterials

The objective of this study is to assess numerically the effect of applying electrical current on the fibrous tissue growth around polyethylene disk-shaped implants while subcutaneously placed inside 60 day old male Han-Wistar rats. This problem can be formulated as a design problem where the goal is to determine the parameters of a partial differential operator to achieve a desired effect. These electrical current parameters are computed using a regularized iterative method. The obtained results reveal that employing an appropriate electrical current profile can reduce the fibrous tissue concentration around the considered implant by up to 80%. This preliminary study tends to demonstrate the effectiveness of this novel and non-invasive approach to shield the implant from intolerable levels of fibrous tissue growth, which consequently expands the lifespan and functionality of implanted devices, as well as avoids costly and traumatic surgical procedures.