The search for negative amplitude components in quasi-continuos distributions of relaxation times: the example of 1H magnetization Exchange in articular cartilage and hydrated collagen

When inverting nuclear magnetic resonance relaxation data in order to obtain quasi-continuous distributions of relaxation times for fluids in porous media, it is common practice to impose a non-negative (NN) constraint on the distributions. While this approach can be useful in reducing the effects of data distortion and/or preventing wild oscillations in the distributions, it may give misleading results in the presence of real negative amplitude components. Here, some examples of valid negative components for articular cartilage and hydrated collagen are given. The validity of a negative peak may be accepted (dismissed) by a high (low) cost of NN in error of fit. Computed distributions for simulated data using observed signal-to-noise ratios also verify the need for some negative components. The results may be of interest for the application of magnetization exchange contrast in the imaging of articular cartilage to determine changes associated with pathologies and ageing. Other important porous media exist where exchange phenomena and negative relaxation components cannot be disregarded.