Calibrated fMRI ^1,2 allows to estimate relative changes in the Cerebral Metabolic Rate of Oxygen (rCMRO₂) from combined BOLD and ASL measurements during a functional task. The method relies on a macroscopic biophysical model of the BOLD response – the Davis model ¹ - that was originally derived from simplified physiological assumptions. However, with the advance of microscopic techniques to measure the cortical microvasculature in vivo, a lot of these physiological assumptions have been shown to be inaccurate. First, it was shown that most of the vascular volume increase originates from the arterial compartment rather than the venous pool as previously thought ³. Second, it was demonstrated that almost 50% of the extraction of oxygen occurs before the capillary bed and therefore the oxygen saturation in the capillaries is much lower than previously thought ⁴. To take into account this new data, it has been suggested that some of the parameters of the original Davis model that were computed meticulously based on the erroneous physiological assumptions must rather be treated as free parameters that can be optimized to reflect multiple physiological and biophysical effects ⁵. Motivated by this approach, we optimized the free parameters of the Davis model by using our recent simulation technique ⁶ based on oxygen-sensitive Two-Photon microscopic measurements of the cortical microvasculature ⁷ together with first principle Monte Carlo simulations of proton diffusion across the two-photon volumes.

A schematic overview of the entire procedure is shown in Fig. 1. Oxygen-sensitive Two-Photon measurements were performed as described previously ⁷. PO2 measurements were integrated in six Vascular Anatomical Network (VAN) models ⁵ (Fig. 2) that simulated the physiological response to different arterial dilations (10, 20, 30 %) and random levels of changes in CMRO₂ (0-30 %). The temporal evolution of oxygen saturation was converted to a shift in magnetic susceptibility that was used to compute a magnetic perturbation (ΔB) volume at each time-point following the simulated functional response. The resulting fMRI signals were computed by simulating the diffusion of 10⁷ protons in the ΔB volume at each time point. An extra simulation was performed with no CMRO₂ changes but 20 % arterial dilation to simulate the hypercapnic calibration run. The Davis model can be written as $$δS=M(1-rCBF^{\alpha-\beta}·rCMRO_2^{\beta})$$ where rCBF represents relative change in cerebral blood flow, M is the calibration constant and α and β are free parameters. The Davis model was applied to each of the synthetic BOLD responses generated to estimate rCMRO2 and these values were compared individually to the true microscopic rCMRO₂'s originally inputted to the VAN models. A least-square optimization procedure was implemented to find the value for α and β that minimizes the errors between the simulated and the recovered rCMRO₂'s.

As shown in Fig. 3A, our simulations at 3T show that the Davis model with its original parameters α=0.38 and β=1.5 underestimates changes in CMRO₂ by 33% (i.e. that a recovered increase in CMRO₂ of 20% means a 14% real increase in CMRO₂). From the optimization procedure, we found that the values of α and β that minimize the error between the simulated and the recovered rCMRO₂’s were α=-0.05 and β=0.98 (Fig. 3B). It is important to recognize, though, that the optimized parameter values no longer correspond to the physiological effects they were originally introduced to model and should be treated simply as fitting parameters ⁵. The versatility of our modeling technique allowed to repeat this entire procedure for different B0-field strengths, ranging from 1.5 to 14T. The optimal α’s and β’s for each B₀ are shown in Tab. 1. The value of 0.66 for the slope of the linear fit showed in Fig. 3A demonstrates that the original Davis model underestimate changes in CMRO₂ by about 33%. To compensate for this bias, new values for the free parameters were derived using an optimization procedure. With the optimized parameters, the slope of the linear fit is close to unity indicating that most of the systematic bias inherent to the simplified biophysical model has been removed by adjusting the free parameters. Therefore, using these optimized values will result in more accurate measurements of CMRO₂ in future studies. Our work provides a microscopic validation of the calibrated fMRI approach routinely used in human studies. It demonstrates the power of the method to estimate relative changes in CMRO2 with good accuracy. This should encourage researchers to utilize this method despite its demanding experimental setup. Moreover, our modeling technique allowed to optimize the calibrated fMRI procedure by removing all systemic biases.