The calibrated BOLD method is sensitive to bias in the measurement of the calibration parameter M¹. The original and most popular method for measuring M involves using hypercapnia, making an assumption that hypercapnia does not affect cerebral oxygen metabolism (CMRO₂)². This assumption has since been challenged³ and recent studies have used a corrective term, based on literature values of a reduction in CMRO₂ with hypercapnia⁴. This is not ideal, as this value may vary across subjects, and will depend on the level of hypercapnia achieved. Here we propose a new approach, using a graded hypercapnia design and the assumption that CMRO₂ changes linearly with hypercapnia level⁵, such that we can measure M without assuming prior knowledge of the scale of CMRO₂ change. We apply this approach to data presented previously⁶.Fifteen subjects participated in 2 sessions in which scans were acquired at 3T using a PICORE QUIPSS II dual-echo ASL sequence (12 slices, 64x64 matrix, TE1=3.3ms, TE2=29ms, TR=2200ms, FOV=22cm, slice thickness/gap=7/1mm, TI1=600ms, TI2=1500ms, reps=490). End-tidal CO₂ levels were changed at 2-minute intervals between baseline, +4mmHg and +8mmHg values, in a randomized order. CBF time series were calculated from the first echo by separating tag and control time series, interpolating to the TR and subtracting. A similar procedure using averaging rather than subtraction yielded BOLD time series from the second echo. The resulting time series were averaged over visual and motor cortex grey matter voxels, before averaging across sessions for each subject. The assumed linear change in CMRO₂ with ΔP_ETCO₂ was incorporated into the calibrated BOLD equation: $$\frac{ΔBOLD_{HC}}{BOLD_0} = M \left[1-\left(\frac{CBF_{HC}}{CBF_0}\right)^{α-β}\cdot\left(1+κ\cdotΔP_{ET}CO_2\right)^β\right]$$ where κ is the fractional change in CMRO₂ per mmHg change in ΔP_ETCO₂. Optimised α/β values of 0.14/0.91 were used⁷. A two-parameter non-linear fitting routine was used to calculate M and κ, by solving two simultaneous equations (+4mmHg and +8mmHg hypercapnia levels). Subjects that reached the boundary conditions of the non-linear fitting routine were removed from further analysis (boundary conditions 1<M<20%; -5<κ<+5%/mmHg). For comparison with the iso-metabolic assumption, a one-parameter fit was also made, to calculate M from the same two equations, fixing κ = 0.The two parameter fit gave M = 9.2±1.4% (N = 13 of the 15 subjects) and M = 4.7±0.7% (N = 13), in the visual and motor cortices respectively. The dose-dependent hypercapnia CMRO₂ parameter κ = -1.9±0.5%/mmHg and κ = -2.0±0.8%/mmHg showed significant reductions in CMRO₂ with hypercapnia level (p = 0.005 and p = 0.03). The two-parameter fit resulted in significantly lower M values than the one-parameter fit for all subjects that did not reach the boundary conditions for both fits (Figure 1; p<0.05 for both visual (N = 9) and motor (N = 13) cortices).Through use of a graded hypercapnia gas challenge, we are able to remove the bias caused by a reduction in CMRO₂ during hypercapnia, whilst simultaneously calculating the dose-wise CMRO₂ change with hypercapnia. The scale of the CMRO₂ reduction is broadly similar to previous studies³. The measured M values are reduced when taking into account the effect of hypercapnia on CMRO₂, correcting a previous overestimation in CMRO₂ task-response values. The assumption of a linear dependence of CMRO₂ on hypercapnia level was based on an observed linear electrophysiological relationship with hypercapnia level⁵. Both effects have been attributed to similar neurochemical origins⁸, so it is likely that they will both scale in the same linear manner. Even if the relationship includes some non-linearity, bias introduced by a linear correction will be smaller than the bias from no correction. Previous correction approaches using literature values will also implicitly make the same linear assumption, whilst not accounting for variability due to experimental differences and inter-subject variability.