Fig 1.
Schematic representation of the SMoRe GloS framework for sensitivity analysis of ABMs.
For simplicity, two ABM parameters, A1 and A2, and one surrogate model (SM) parameter, S1, are depicted. The first row shows Steps 1-4 of SMoRe GloS, where S1 is constrained as a function of A1 and A2. The black dots represent sampled ABM parameters, the gray bars indicate uncertainty in S1 and the blue planes represent the reconstructed parameter surfaces for S1. The salmon region denotes the interior of the ABM parameter space, defined by the convex hull of the sampled points. The second row illustrates Step 5, where any global sensitivity method can be applied. The white dots represent points in ABM parameter space sampled for computing global sensitivity, and the dashed black lines show the corresponding ranges of S1. The third row illustrates the implementation of the MOAT method in this framework. Points p0 and p1 are examples of white dots from the second row that represent points in ABM parameter space used to compute an elementary effect in A1. These points correspond to regions R0 and R1 in SM parameter space. The time series curves are the trajectories sampled from these regions. The purple and yellow distributions denote the output metric of interest calculated from each trajectory. The elementary effect is approximated by the difference between the means of these distributions.
Table 1.
List of ABM and surrogate model (SM) parameters.
Fig 2.
SMoRe GloS recapitulates global sensitivity of cell culture ABM.
A) ABM storyboard showing cells by location and cell-cycle phase. B) Time series of the G1/S and G2/M cell-cycle phases. C) ABM parameters included in the sensitivity analysis. The yellow box highlights local spatial parameters that are not explicitly captured by the surrogate model (SM). D) RSS distribution of SM fits to all ABM parameter vectors. Orange line indicates the log-normal distribution that best fits this distribution. E) Identifiability donuts of SM parameters where color indicates the identifiability index, and area the proportion of ABM parameter vectors for which the given SM parameter had that index. F) MOAT sensitivity analysis results using the ABM (Direct, black bars) and SMoRe GloS (Indirect, blue bars), ranked by decreasing sensitivity using the direct method. Spatial parameters not explicitly captured by the SM are highlighted in yellow.
Fig 3.
Surrogate model (SM) selection for the 3D vascular tumor growth ABM.
A) ABM storyboard showing vascular tumor growth. B) ABM parameters included in the sensitivity analysis. The yellow box highlights local spatial parameters that are not explicitly captured by the surrogate models (SMs). C) Fits of the SMs to ABM output at a representative ABM parameter vector. D) Histograms of log(RSS) values for each SM across all sampled ABM parameter vectors. E) Comparison of Akaike Information Criterion (AIC)-based relative log-likelihoods between the three SMs. Individual ABM parameter vectors are represented as darker colored dots. The x-axis shows the relative log-likelihood of the exponential model, and the y-axis shows the relative log-likelihood of the logistic model, both compared to the von Bertalanffy model. Positive (resp. negative) values indicate that von Bertalanffy is more (resp. less) likely than the alternative SM. The background is color-coded by the SM selected by AIC: yellow indicates preference for von Bertalanffy, red for logistic, and blue for exponential. The ABM parameter vector corresponding to panel C) is highlighted with a black circle. Dashed lines indicate where the log scales change sign. F-H) Identifiability donuts of SM parameters where color indicates the identifiability index, and area the proportion of ABM parameter vectors for which the given SM parameter had that index.
Fig 4.
SMoRe GloS recapitulates global sensitivity of multiple output ABM metrics using the logistic surrogate model (SM).
Each panel shows the resulting sensitivity values for different output metrics. The colors of the bars correspond to the SM, as shown in the legend in panel (C). A) Using final tumor size as the output metric. B) Using the area under the curve as the output metric. D) Using time to half the maximum tumor volume as the output metric. Note the break in the y-axis scale in A and B.
Fig 5.
Comparison of ABM simulations and CPU time for computing global sensitivities using MOAT and eFAST in 3D vascular tumor growth ABM.
A) Chart showing SMoRe GloS speedup (expressed as times faster) compared to direct implementation of global sensitivity analysis methods. The speedups exclude the setup time for the surrogate model. B) Number of ABM simulations and CPU time required to implement MOAT, eFAST, or both, either directly (blue bars) or with SMoRe GloS (yellow bars), including the setup time for the surrogate model. CPU time is based on assuming 1 ABM simulation takes 10 minutes.