Physically Constrained Inverse-Gaussian Deconvolution of Diffusion-Broadened Drift-Tube Ion Mobility Spectra

Peak overlap limits chemical assignment in drift-tube ion mobility spectrometry (DT-IMS). Diffusion broadening is commonly modeled with symmetric Gaussian kernels, although a fixed detector records ion first-passage times. We developed an inverse-Gaussian-Nernst-Townsend-Einstein (IG-NTE) deconvolution framework in which the point-spread function (PSF) follows an inverse-Gaussian distribution and its temporal width is constrained by instrument settings through the NTE relation. The resulting drift-time-dependent measurement operator was inverted by nonnegative Richardson-Lucy iteration without peak-width calibration or specification of component number. In simulations, relative to a Gaussian kernel, IG-NTE deconvolution reduced the average full-residual root-mean-square value by 11.4%, the right-tail residual by 18.1%, and the mean absolute peak-area deviation from 5.10% to 1.19%. Applied to a 63Ni DT-IMS instrument, the method separated ethyl 2-methylpentanoate and 1,8-cineole responses 0.040 ms apart while retaining 2,6-di-tert-butylpyridine (DTBP) as a single-component control. It also recovered paired alkyl-pyrazine mobility features consistent with protonation site- and hydration-dependent collision cross sections. In the negative mode, dichloromethane-derived chloride responses assigned to 35Cl− and 37Cl− exhibited a 3.08:1 area ratio and were supported by GC-TOF-MS. These results show that detector-domain transport modeling can improve the effective reconstructed resolution of diffusion-broadened DT-IMS spectra without hardware modification, provided that controls and forward residual analysis are used to assess reconstruction artifacts.