A Monte Carlo simulation based on first-passage distributions for spatio-temporal detection on potentiometric sensor arrays

Abstract This paper presents a novel simulation approach for particle diffusion that uses Monte Carlo sampling of first-passage distributions to conduct spatio-temporal modelling for potentiometric sensing arrays. The Monte Carlo first-passage (MCFP) simulation algorithm prioritises speed to overcome limitations with currently available techniques. This paper applies the MCFP technique to simulate the detection of protons by arrays of ion-sensitive field-effect transistors (ISFETs) as a case study. The MCFP algorithms were validated against a benchmark random walk algorithm, with temporal MCFP output matching that of the random walk with an average $$r^2$$ r 2 value of 0.901. The simulations were further validated against experiments using a microchip-based ISFET array to observe a localised pH change created by an acid-containing glass capillary held at various heights from the sensing surface. MCFP simulations displayed an ability to accurately estimate the mean array output over time with an average $$r^2$$ r 2 value of $$0.749\pm 0.170$$ 0.749 ± 0.170 and a maximum of 0.986, whilst increasing simulation speed by over at least an order of magnitude compared to that of the random walk. MCFP simulations recreated several key trends of spatial signal patterns, with the proportional increase in the variance of the Gaussian consistent to within two standard deviations between experiments and simulations in all eight cases. MCFP simulations underestimated the variance in seven out of eight cases, likely due to fluid motion within the experimental setup, but were consistent to two standard deviations with experimental values for all four vertical array cross-sections. Graphical abstract This research article presents a novel Monte Carlo-based simulation approach for the detection of electrochemical species by potentiometric sensor arrays that combines first-passage time sampling with diffusion to capture spatio-temporal signals. This approach is validated using a CMOS-based ISFET array to detect pH changes from acid-filled glass capillaries