Probabilistic averaging: an instinctive method of averaging according to data confidence applied to Cardiac 31P MRS

Objective Cardiac P MRS is a potentially highly useful tool for probing cardiac energetics and informing clinical management of heart disease, but whose precision suffers from low signal to noise ratio and overlapping peaks. In addition, however, valuable information describing the variance of a spectrum’s fitting remains unused or ineffectively used when determining changes in cardiac PCr/ATP in response to treatment or disease. The widely used t-test (paired and unpaired) assumes that the variance remains unchanged between experiments. This is not a valid assumption to make in cardiac P MRS because the signal to noise quality can change due to factors such as shim, coil loading (tune and match), subject motion. Using cardiac P MRS data as an example application, this work demonstrates an intuitive approach for weighting data according to the variance associated with fitted peak amplitudes and specifying a probability for each outcome. The Cramér-Rao lower bound (CRLB) of variance is widely used as a measure of attainable precision by MRS fitting algorithms where standard deviations can not be obtained by repeated measurement.