Global Sensitivity Analysis of High-Dimensional Neuroscience Models: An Example of Neurovascular Coupling

Abstract

The complexity and size of state-of-the-art cell models have significantly increased in part due to the requirement that these models possess complex cellular functions which are thought-but not necessarily proven-to be important. Modern cell models often involve hundreds of parameters; the values of these parameters come, more often than not, from animal experiments whose relationship to the human physiology is weak with very little information on the errors in these measurements. The concomitant uncertainties in parameter values result in uncertainties in the model outputs or Quantities of Interest (QoIs). Global Sensitivity Analysis (GSA) aims at apportioning to individual parameters (or sets of parameters) their relative contribution to output uncertainty thereby introducing a measure of influence or importance of said parameters. New GSA approaches are required to deal with increased model size and complexity; a three stage methodology consisting of screening (dimension reduction), surrogate modeling, and computing Sobol' indices, is presented. The methodology is used to analyze a physiologically validated numerical model of neurovascular coupling which possess 160 uncertain parameters. The sensitivity analysis investigates three quantities of interest (QoIs), the average value of K + in the extracellular space, the average volumetric flow rate through the perfusing vessel, and the minimum value of the J.actin/myosin complex in the smooth muscle cell. GSA provides a measure of the influence of each parameter, for each of the three QoIs, giving insight into areas of possible physiological dysfunction and areas of further investigation.

Global Sensitivity Analysis: a new generation of mighty estimators based on rank statistics

“…As shown in [17], the above approximation performs well for the considered QoI. We assign to each variable X 1 , .…”

“…Now we illustrate the nature and performance of the Cramér-von-Mises indices and their corresponding Chaterjee estimators as a screening mechanism for high-dimensional problems. To do so, we consider the neurovascular coupling model from [17]. Mathematically, this corresponds to the following differentialalgebraic equation (DAE) system As above, regard Y as a function of the unknown parameters, i.e., Y = f (X 1 , .…”

“…In our implementation, the values of W * are obtained by solving the above DAE system (Equations ( 38) and (39)) by the MATLAB routine ode15s (it can be checked that (38) and ( 39) form an index one system). Further, in the current example, N = 67 and p = 160 and the distributions of most of the X i 's are uniform and allowed to vary ±10% from nominal values (see [17] for additional details). We compare the results from the Chaterjee estimators as described above to those resulting from the linear regression f (X 1 , .…”

Global sensitivity analysis informed model reduction and selection applied to a Valsalva maneuver model

“…Though we acknowledge that SIs may be impractical for very large differential equation systems with hundreds of state variables and parameters, such as pharmacokinetics models, we suggest a multi-level approach. One can use simpler to compute but possibly less informative GSA measures first to identify a set of unimportant parameters and then perform a more comprehensive analysis on the remaining parameters [13]. We propose our GSA-informed model reduction methodology as an alternative approach to the balanced truncation method in the model reduction formulation proposed by Snowden et al [39].…”

Quantitative roles of ion channel dynamics on ventricular action potential

“…Sensitivity analysis requires a broad, computationally demanding sample of the aimed parameter search space, especially when the cell model contains the higher-order nonlinear ODEs. These methods among others help us to understand how each parameter affects the change of membrane potential in excitable cell models [ 21 , 22 ].…”