Mathematical modeling of an NMR chemistry problem in ovarian cancer diagnostics

We use mathematical modeling via the fast Padé transform (FPT) with respect to a theoretically-designed problem based on time signals that are similar to NMR data as encoded from benign and malignant ovarian cyst fluid. The FPT reconstructed exactly all the input spectral parameters by using exceedingly small fractions of the full time signals both for those corresponding to the benign, as well as to the malignant case. The converged parametric results remained stable thereafter at longer signal lengths. The Padé absorption spectra yielded clear resolution of all the extracted physical metabolites. The capacity of the FPT to resolve and precisely quantify the physical resonances as encountered in benign versus malignant ovarian cystic fluid is demonstrated. The practical significance of such findings is enhanced by the avoidance of the time signals’ exponential tail which is embedded in the background, leading to problems in quantification. Without any fitting or numerical integration of peak areas, the FPT reliably yields the metabolite concentrations of major importance for distinguishing benign from malignant ovarian lesions. Thus, the FPT provides distinct advantages relative to the standard Fourier methodology, which is also stable, but has a number of drawbacks. These include limited resolution capacity, as well as non-parametric estimation, so that only a shape spectrum is generated and post-processing is necessary via, e.g., fitting or numerical integrations which are not unique. The FPT is also distinguished from other competitive parametric methods, which are generally unstable as a function of signal length N at a fixed bandwidth and, therefore, particularly unsuitable to clinical data. We conclude that these advantages of the FPT could be of definite benefit for ovarian cancer diagnostics via NMR and that this line of investigation should continue with encoded data from benign and malignant ovarian tissue, in vitro and in vivo. This avenue is of clinical urgency for early ovarian cancer detection, a goal which is still elusive and achievement of which would confer a major survival benefit.