To design a computationally efficient model for ultrasonic neuromodulation (UNMOD) of morphologically realistic multi-compartmental neurons based on intramembrane cavitation. Approach: A Spatially Extended Neuronal Intramembrane Cavitation model that accurately predicts observed fast Charge Oscillations (SECONIC) is designed. A regular spiking cortical Hodgkin-Huxley type nanoscale neuron model of the bilayer sonophore and surrounding proteins is used. The accuracy and computational efficiency of SECONIC is compared with the Neuronal Intramembrane Cavitation Excitation (NICE) and multiScale Optimized model of Neuronal Intramembrane Cavitation (SONIC). Main results: Membrane charge redistribution between different compartments should be taken into account via fourier series analysis in an accurate multicompartmental UNMOD-model. Approximating charge and voltage traces with the harmonic term and first two overtones results in reasonable goodness-of-fit, except for high ultrasonic pressure (adjusted R-squared ≥ 0.61). Taking into account the first eight overtones results in a very good fourier series fit (adjusted Rsquared ≥ 0.96) up to 600 kPa. Next, the dependency of effective voltage and rate parameters on charge oscillations is investigated. The two-tone SECONIC-model is one to two orders of magnitude faster than the NICE-model and demonstrates accurate results for ultrasonic pressure up to 100 kPa. Significance: Up to now, the underlying mechanism of UNMOD is not well understood. Here, the extension of the bilayer sonophore model to spatially extended neurons via the design of a multi-compartmental UNMOD-model, will result in more detailed predictions that can be used to validate or falsify this tentative mechanism. Furthermore, a multi-compartmental model for UNMOD is required for neural engineering studies that couple finite difference time domain simulations with neuronal models. Here, we propose the SECONICmodel, extending the SONIC-model by taking into account charge redistribution between compartments.

To investigate the importance of membrane charge oscillations and redistribution in multicompartmental ultrasonic neuromodulation (UNMOD) intramembrane cavitation models. Methods: The Neuronal Intramembrane Cavitation Excitation (NICE) model and multi-Scale Optimized model of Neuronal Intramembrane Cavitation (SONIC) of UNMOD are compared for a nanoscale multicompartmental and point neuron approximation of the bilayer sonophore and surrounding proteins. The temporal dynamics of charge oscillations and their effect on the resulting voltage oscillations are investigated by fourier series analysis. Results: Comparison of excitation thresholds and neuronal response between nanoscale multi-compartmental and point models, implemented in the SONIC and NICE framework, demonstrates that the explicit modeling of fast spatial charge redistribution is critical for an accurate multi-compartmental UNMOD-model. Furthermore, the importance of modeling partial protein coverage is quantified by the excitability thresholds. Subsequently, we establish by fourier analysis that these charge oscillations are slowly changing in time. Conclusion: Fast charge redistribution significantly alters neuronal excitability in a multi-compartmental nanoscale UNMOD-model. Also the mutual exclusivity between protein and sonophore coverage should be taken into account, when simulating the dependency of neuronal excitability on coverage fractions. Charge oscillations are periodic and their fourier components change on a slow timescale. Furthermore, the resulting voltage oscillations decrease in energy with overtone number, implying that an extension of the existing multiscale model (SONIC) to multi-compartmental neurons is possible by taking into account a limited number of fourier components. Significance: First steps are taken towards a morphologically realistic and computationally efficient UNMOD-model, improving our understanding of the underlying ultrasonic neuromodulation mechanisms.

Optogenetics has a lot of potential to become an effective neuromodulative therapy for clinical applications. Selecting the correct opsin is crucial to have an optimal optogenetic tool. With computational modeling, the neuronal response to the current dynamics of an opsin can be extensively and systematically tested. Unlike electrical stimulation where the effect is directly defined by the applied field, the stimulation in optogenetics is indirect, depending on the selected opsin's non-linear kinetics. With the continuous expansion of opsin possibilities, computational studies are difficult due to the need for an accurate model of the selected opsin first. To this end, we propose a double two-state opsin model as alternative to the conventional three and four state Markov models used for opsin modeling. Furthermore, we provide a fitting procedure, which allows for autonomous model fitting starting from a vast parameter space. With this procedure, we successfully fitted two distinctive opsins (ChR2(H134R) and MerMAID). Both models are able to represent the experimental data with great accuracy and were obtained within an acceptable time frame. This is due to the absence of differential equations in the fitting procedure, with an enormous reduction in computational cost as result. The performance of the proposed model with a fit to ChR2(H134R) was tested, by comparing the neural response in a regular spiking neuron to the response obtained with the non-instantaneous, four state Markov model (4SB), derived by Williams et al. (2013). Finally, a computational speed gain was observed with the proposed model in a regular spiking and sparse Pyramidal-Interneuron-Network-Gamma (sPING) network simulation with respect to the 4SB-model, due to the former having two differential equations less. Consequently, the proposed model allows for computationally efficient optogenetic neurostimulation and with the proposed fitting procedure will be valuable for further research in the field of optogenetics.

Objective: In temporal interference (TI) deep brain stimulation (DBS), the neurons of mice react to two interfering sinusoids with a slightly different frequency. This is called a temporal interference (TI) signal. It was previously seen that for the same input intensity, the neurons do not react to a purely sinusoidal signal. This study aims to get a better understanding into the mechanism for this, which is largely unknown. Methods: This study makes use of single compartment models to computationally simulate the response of neurons to the sinusoidal and TI-waveform. This study also compares different neuron models to get insight in which models are able to model the experimental behavior. Results: It was found that integrate-and-fire models do not reflect the experimental behavior while the Hodgkin-Huxley and Frankenhaeuer-Huxley model do reflect this behavior. It was seen that changing the characteristics of the ion gates in the Frankenhaeuser-Huxley model alters the response to both sinusoidal and TI signal. It can even make sure that the firing threshold of the sinusoidal input becomes lower than that of the TI input. Conclusion: The results show that the ion-gates have a big influence on the behavior and their characteristics can define the way the neuron reacts to sinusoidal and TI inputs. Significance: This paper makes advances both in terms of biophysical insight of the neuron as well as the insight in computational modelling of TI-stimulation.