Modelling the bold response, a numerical approach

Abstract

A comprehensive model of the BOLD response is presented, in which differential equations for cerebral O2 and hemoglobin (Hgb) transport are solved numerically. Several features of cerebral O2 transport can be investigated, and the consistency of current conceptions of BOLD responses tested. This study applies the model to the effects of arterial hematocrit, PaCO2 and PaO2, in responses elicited by functional activation (fBOLD) and physiological pertubation (pBOLD). The model uses 4 major compartments: arterial, capillary and venous as well as an extravascular compartment. Within the intravascular compartment the distribution of O2 between Hgb-bound and physically dissolved phases is updated for every time step, t, as a function of local pH, PCO2 and DPG. Total content of deoxy-Hgb is calculated as the sum of arterial, capillary and venous concentrations weighted by their respective volume fractions. The corresponding R2*-contribution is calculated as proposed by Ogawa et al. (1993). Relationships between PaO2, PaCO2 and CBF, as well as between CBF and CBV were taken from previous studies. The model predicted BOLD effects of the expected magnitude (1–3% at 1.5 T), and confirmed an inverse relation between fBOLD and baseline CBF. A slight decrease in fBOLD response was seen with high baseline hematocrit and constant CBF, but an increase was seen when concomitant flow decreases were included (in agreement with empirical results). During hypercapnia the predicted pBOLD response was high when CBF changes alone were included (figure 1: green curve), but attenuated by the accompanying CBV change (blue curve). The response was elevated when all effects were included (red curve), mainly due to the effect of arterial hyperoxia (hyperventilation), less to pH changes. Several physiological effects thus were predicted in accordance with established results. The model suggests that known effects of hematocrit may be due to accompanying flow changes. During hypercapnia, arterial hyperoxia is an important factor which should be taken into account when used in calibration experiments for CMRO2 determination. Numerical simulation seems helpful in interpreting BOLD effects caused by complex physiological responses.