An efficient multistage algorithm for full calibration of the hemodynamic model from BOLD signal responses.

We propose a computational strategy that falls into the category of prediction/correction iterative-type approaches, for calibrating the hemodynamic model. The proposed method is used to estimate consecutively the values of the two sets of model parameters. Numerical results corresponding to both synthetic and real functional magnetic resonance imaging measurements for a single stimulus as well as for multiple stimuli are reported to highlight the capability of this computational methodology to fully calibrate the considered hemodynamic model.

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.

Efficient solution methodology for calibrating the hemodynamic model using functional Magnetic Resonance Imaging (fMRI) measurements.

Our aim is to propose a numerical strategy for retrieving accurately and efficiently the biophysiological parameters as well as the external stimulus characteristics corresponding to the hemodynamic mathematical model that describes changes in blood flow and blood oxygenation during brain activation. The proposed method employs the TNM-CKF method developed in [1], but in a prediction/correction framework. We present numerical results using both real and synthetic functional Magnetic Resonance Imaging (fMRI) measurements to highlight the performance characteristics of this computational methodology.

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.

On the characterization of single-event related brain activity from functional Magnetic Resonance Imaging (fMRI) measurements.

We propose an efficient numerical technique for calibrating the mathematical model that describes the single-event related brain response when fMRI measurements are given. This method employs a regularized Newton technique in conjunction with a Kalman filtering procedure. We have applied this method to estimate the biophysiological parameters of the Balloon model that describes the hemodynamic brain responses.

Theoretical study of the fibrous capsule tissue growth around a disk-shaped implant.

We analyze the mathematical properties of the fibrous capsule tissue concentration around a disk-shaped implant. We establish stability estimates as well as monotonicity results that illustrate the sensitivity of this growth to the biocompatibility index parameters of the implant. In addition, we prove that the growth of the tissue increases exponentially in time toward an asymptotic regime.

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

We propose a new mathematical model that describes the growth of fibrous tissue around rigid, disk-shaped implants. A solution methodology based on an efficient regularized iterative method is presented to calibrate the model from some measurements of the capsule tissue concentration. Numerical results obtained with synthetic data are presented to demonstrate the ability of the proposed solution methodology to determine the model parameters corresponding to a given implant.