# Sensitivity Analysis of a Numerical Model for Percutaneous Auxicular Vagus Nerve Stimulation
## 1 Introduction  
The vagus nerve is an important constituent of the autonomic nervous system and plays a major role in the regulation of metabolic homeostasis. The sympathetic and parasympathetic (vagal) branches of the autonomic nervous system control and regulate the function of glands, organs, and involuntary muscles throughout the body [1]. Specific stimulation of the afferent vagus nerve can trigger both inhibitory and excitatory modulation of the autonomic nervous system. Vagus nerve stimulation may thus reduce pain [2], increase blood perfusion [3, 4], and downregulate inflammation [5, 6], all highly beneficial, for instance, in the treatment of chronic pain or peripheral arterial disease.  
Today, cervical vagus nerve stimulation by implanted stimulators is used as a non-pharmacogical treatment for drug-resistant epilepsy, congestive heart failure, and major depression [7, 8]. Less-invasive ways of stimulation were developed to minimize the stimulation risks by using electrodes in targeted regions of the auricle and access afferent A\(\beta\) fibers of the auricular branch of the vagus nerve(ABVN) [9; 10; 11]. A shortcoming of current applications of ABVN stimulation is the mostly empirical selection of both the stimulation regions in the ear and the stimulation patterns with mostly unknown variations of therapeutic/physiologic effects, which may lead to overstimulation with unfavorable recruitment of pain-related A& fibers or under-stimulation. Omnipresent inter-patient variability is neglected, while safety margins when stimulating different fibers are missing. To elevate the understanding of stimulation mechanisms, a realistic numerical model for percutaneous auricular vagus nerve stimulation (pVNS) at the human auricle including nerves and vessels was recently developed by our group [12]. The study provides a better understanding of the electric potential and current distribution in tissues surrounding the stimulation electrodes. For the first time, the quantitative sensitivity of the stimulation thresholds and the percentage of activated axons to the electrodes' depth and position were reported.  
However, due to the dense innervation of the auricle with various nerves, high sensitivity and specificity of stimulation is of huge importance [11]. By stimulation of different nerves, opposite physiological reactions and an even adverse therapeutic outcome may be elicited. Thus, a sensitivity analysis (SA) of the numerical model is an invaluable tool to better quantify the dependence of the numerical model developed in Reference [12] to different parameters. SA is used to link the uncertainty in the model output to different sources of uncertainty in the model parameters [13; 14; 15; 16]. It is also used to identify the most contributing input parameter and to ascertain the interaction effects within the model. Thus, we can achieve better model verification and understanding, factor prioritization, and model simplification.  
The objective of this study is to perform a SA of a numerical model for pVNS. We start by specifying the input parameters range of values. Then we investigate the effects of the axon fiber diameter, number of axons, model temperature, ear conductivity, as well as electrodes' penetration depth and position on the stimulation thresholds for single and bundled axons. The final goal is to identify and prioritize the most influential parameters, to identify non-influential parameters in order to fix them to nominal values, and to map the output behavior as a function of the parameters by limiting the input range values to a specific domain if necessary.