Develop blood oxygen level dependent signal by metabolic/hemodynamic model using numerical methods

Abstract

Background and objectiveThe metabolic/hemodynamic (MH) model describes the blood flow mechanisms as well as the coupling between the hemodynamic responses and the metabolic activities in a blood vessel in the human brain. In the existing MH model, the blood flow out from a blood vessel is formulated as dependent only on the capillary volume. In fact, the blood flow out from a blood vessel depends not only on the capillary volume but also on the blood flow into the capillary bed. For this reason, the blood flow out formula of the existing model has been modified. In addition to implementing existing model modification to obtain better accuracy, we have used new methods to solve the model instead of conventional methods. MethodThe MH model describes physical phenomena of a blood vessel by eight processes equations (PEs). These PEs are often solved by using a local linearization (LL) scheme and the Taylor series method. In addition to the previously used Taylor series method, we have also used the Euler method and the Runge–Kutta (RK) method to solve the model instead of a LL scheme for estimating dynamical variables (DVs). By using these DVs, a Blood Oxygen Level Dependent (BOLD) signal is generated through a well-defined observation equation (OE). There are two OEs, called Obata and Friston. The Friston OE produces a BOLD signal from the cerebral blood volume and deoxy-hemoglobin content with their nonlinear properties; conversely, the Obata OE produces a BOLD signal without considering nonlinear properties. For this reason, we have used the Friston OE instead of the Obata OE to estimate the BOLD signal perfectly. ResultsAt 20% resting oxygen extraction fraction (ROEF), the BOLD signals of the modified and the existing model are identical, but when the ROEF increased up to 50% at its standard value, the modified model accuracy is increased by 16.12%–23.07% more than that of the existing model. The Euler and RK methods generate a BOLD signal 6.95% more accurately than that of Taylor series method from the modified model. ConclusionIn the model inversion process, this research will be helpful to estimate the model parameters and hidden states accurately.