Estimating a modified Grubb's exponent in healthy human brains with near infrared spectroscopy and transcranial Doppler.

The relationship between cerebral blood volume (CBV) and flow (CBF) has been widely studied. One of the most significant early studies was by Grubb et al (1974 Stroke 5 630-9), who conducted hypercapnia studies in primates with positron emission tomography (PET) and empirically found CBV = 0.8 CBF(0.38). The exponent used here has since been known as the Grubb's exponent. In this paper, we define a similar exponent known as the modified Grubb's exponent, G', which is based on CBV and cerebral blood flow velocity (CBFV) estimated by near infrared spectroscopy (NIRS) and transcranial Doppler respectively, i.e. G' = log(CBV/CBV(0))/log(CBFV/CBFV(0)), where CBV(0) and CBFV(0) are baseline values. The aim of this study was to estimate the nominal value of the modified Grubb's exponent in healthy human brains. We conducted hypercapnia and hypocapnia studies on 14 healthy adult subjects. The correlation coefficient between log(CBV/CBV(0)) and log(CBFV/CBFV(0)) is 0.71 (p < 0.0001). We found a modified Grubb's exponent of 0.13 (the 95% confidence bounds are 0.10 and 0.17) which is expectedly lower than the conventional Grubb's exponents estimated by other techniques. The modified Grubb's exponent is a simple measure to quantify the hemodynamics between local CBV and global CBFV in the brain and as such may provide insight on brain physiology. Both NIRS and transcranial Doppler techniques are non-invasive and portable, facilitating future studies in other population groups such as brain-injured patients.