To improve the robustness of cerebral oxygen extraction fraction estimation by dual calibrated fMRI, and to produce in-vivo estimates of tissue oxygen tension without additional data acquisition.

We have recently proposed a forward modelling method for the estimation of OEF using the dual calibrated fMRI methodology⁴. This method allows for the simultaneous estimation of resting OEF, resting blood flow (CBF), BOLD-weighted blood volume (CBV) and the flow-related cerebral vascular reactivity (CVR). In this work we re-parameterise the minimisation problem in terms of PtO₂, CBF, CBV and CVR. In this parameterisation OEF is an internal parameter that is derived as a function of PtO₂, CBV and CBF. This follows from the flow-diffusion modelling undertaken by ³, where the biophysically supported OEF is modelled as a function of the mean transit time (MTT), PtO₂, and an equal forward and reverse diffusion rate constant k. The MTT can be estimated from CBV/CBF and the rate constant is fixed to achieve a typical OEF (0.3) for normal resting physiological values (MTT = 1.4 s, PtO₂ = 25 mmHg), as per ³. The steady state value of OEF for a wide range of MTT and PtO₂ values can be calculated using numerical integration techniques to provide a lookup table for OEF (see figure 1). Thus, estimates OEF via the dual calibrated BOLD method can be constrained to obey the flow-diffusion model. In the work presented by ³ a model was presented that allows capillary transit time heterogeneity (CTTH) to be included in estimates of OEF. However, for consistency with standard BOLD models, CTTH effects have not been included in our current implementation.

The performance of the proposed technique was assessed against the standard dual calibrated fMRI technique in a cohort of 10 healthy volunteers. Image data were acquired on a 3 T whole body MRI system. Functional data were acquired using a pulsed arterial spin labelling (ASL) using a QUIPSS II acquisition scheme. This sequence used a dual-echo gradient echo (GRE) readout (TE1 = 2.7 ms TE2 = 29 ms, TR = 2.2 s, flip angle 90°, FOV 22 cm, matrix 64 × 64, 12 slices of 7 mm thickness with an inter-slice gap of 1 mm, TI1 = 700 ms, TI2 = 1500 ms). Respiratory challenges consisted of 3 periods of hypercapnia (5% CO₂) and 2 periods of hyperoxia (50% O₂) interleaved with room air, for a total acquisition time of 18 minutes. Data were analysed using our proposed forward modelling method, ⁴ using a regularised non-linear least squares minimisation to solve for the parameter estimates.

Estimates of OEF are more closely correlated to the mean transit time (MTT) when they are constrained by the biophysical flow-diffusion relationship (see figure 1). Using the non-constrained fitting method a positive relationship is found between MTT and OEF with an R² of 0.51. This correlation is expected as a longer MTT allows for greater extraction of oxygen. When the OEF estimates are constrained by the biophysical flow-diffusion relationship the R² increases to 0.88. This increase in R² represents better agreement with the biophysical model of oxygen extraction and so is expected in the proposed method. The coefficient of variance (COV) of OEF estimates is reduced from 35% to 27% when using the constrained fitting method. This reduction in COV results in a significant reduction in implausible estimates of resting OEF, as can be seen from the example parameter maps in figure 2, and the associated histograms in figure 3. Estimates of PtO₂ have a group mean value of 24.5 mmHg, which are found to have a negative correlation with resting CBF (R² = 0.23).The proposed method of OEF estimation by calibrated fMRI demonstrates reduced variance in parameter estimates and better agreement with expected biophysiological processes when compared to standard analysis methods. We suggest that the incorporation of flow-diffusion modelling into quantitative calibrated fMRI measurements could significantly improve the robustness and accuracy of in-vivo estimates, while simultaneously providing additional information on tissue oxygen tension that may prove useful in the assessment of disease and brain function.