  In this study, we develop a methodology for model reduction and selection
informed by global sensitivity analysis (GSA) methods. We apply these
techniques to a control model that takes systolic blood pressure and thoracic
tissue pressure data as inputs and predicts heart rate in response to the
Valsalva maneuver (VM). The study compares four GSA methods based on Sobol'
indices (SIs) quantifying the parameter influence on the difference between the
model output and the heart rate data. The GSA methods include standard scalar
SIs determining the average parameter influence over the time interval studied
and three time-varying methods analyzing how parameter influence changes over
time. The time-varying methods include a new technique, termed limited-memory
SIs, predicting parameter influence using a moving window approach. Using the
limited-memory SIs, we perform model reduction and selection to analyze the
necessity of modeling both the aortic and carotid baroreceptor regions in
response to the VM. We compare the original model to three systematically
reduced models including (i) the aortic and carotid regions, (ii) the aortic
region only, and (iii) the carotid region only. Model selection is done
quantitatively using the Akaike and Bayesian Information Criteria and
qualitatively by comparing the neurological predictions. Results show that it
is necessary to incorporate both the aortic and carotid regions to model the
VM.
