SAAM II: A general mathematical modeling rapid prototyping environment

Abstract

Simulation Analysis and Modeling II (SAAM II) is a graphical modeling software used in life sciences for compartmental model analysis, particularly, but not exclusively, appreciated in pharmacokinetics (PK) and pharmacodynamics (PD), metabolism, and tracer modeling. Its intuitive "circles and arrows" visuals allow users to easily build, solve, and fit compartmental models without the need for coding. It is suitable for rapid prototyping of models for complex kinetic analysis or PK/PD problems, and in educating students and non-modelers. Although it is straightforward in design, SAAM II incorporates sophisticated algorithms programmed in C to address ordinary differential equations, deal with complex systems via forcing functions, conduct multivariable regression featuring the Bayesian maximum a posteriori, perform identifiability and sensitivity analyses, and offer reporting functionalities, all within a single package. After 26 years from the last SAAM II tutorial paper, we demonstrate here SAAM II's updated applicability to current life sciences challenges. We review its features and present four contemporary case studies, including examples in target-mediated PK/PD, CAR-T-cell therapy, viral dynamics, and transmission models in epidemiology. Through such examples, we demonstrate that SAAM II provides a suitable interface for rapid model selection and prototyping. By enabling the fast creation of detailed mathematical models, SAAM II addresses a unique requirement within the mathematical modeling community.

FIGURE 1

A summary explanation and layout of SAAM II's graphical user interface.

FIGURE 2

Model scheme and results in designing covalent drugs in SAAM II. Users can utilize this design, considering the specific drug and target properties, to simulate the required dosage for achieving 90% target depletion. In this example, a dose of 3 mg is needed for a 70‐kg individual. (a) Yang's model – image reproduced with permission from reference. (b) Yang's model was converted into SAAM II through a simple drag‐and‐drop process of compartmental elements and their connections. Target‐mediated drug elimination and drug‐mediated inactivation are nonlinear fluxes. (c) Plasma concentration simulation of the covalent drug candidate. (d) Depletion of target concentration affected by the drug candidate with information on in vitro binding affinity. (e) Percentage reduction of the target from its baseline, aiming to achieve the desired 90% target depletion. According to the drug and target specs, this virtual candidate has the potential to be effective in vivo (and possibly safe in such a low amount).

FIGURE 3

Model scheme and results in reproducing CAR‐T kinetic features in SAAM II. (a) Stein's model describing the kinetics of a CAR‐T product – reproduced with permission from reference. (b) The Stein model reproduced in SAAM II with all the conditions specified in the reference as T _max = 1.3 weeks, C _max = 24e3 copies/μg, α = 0.11/weeks, β = 0.022/weeks, Fb = 0.0079, and foldx = 3.9. (c) The SAAM II model is then run to predict CAR‐T‐cell concentrations as copies/mcg (solid line) against observed concentrations in a patient (dots). The user can separately consider two distinct phases: cell expansion till T _max, and then cell contraction/persistence.

FIGURE 4

Model scheme and results in reproducing a PK/PD for an antiretroviral with an underlying HIV dynamic system in SAAM II. (a) The model described by Dixit and Perelson in equations was visualized and built in SAAM II. The model comprises a set of compartments 1–5 for the PD‐viral dynamic system and a 1‐compartment model for ritonavir PK. Additionally, there is a SAAM II delay block representing the time delay from when a cell is infected to when it becomes infective. (b) Example of viral load (HIV‐1 copies/mL blood) when the model is run for the infected patient that was not treated (black dashed line); or run for the infected patient treated by 600 mg ritonavir PO BID (solid blue line). The “sawtooth” pattern of the time course for the treated patient represents the fluctuating antiretroviral drug concentrations in the plasma, reflecting the peaks and troughs associated with the simulated daily regimen.

FIGURE 5

Model scheme and results for an SIR epidemiological approach implemented in SAAM II. A Susceptible Water Infected Removed (SWIR) epidemiological deterministic model for cholera outbreak was taken from Eisenberg et al. and replicated in SAAM II for computation of R₀ as a transmission index. (a) Original Eisenberg's SWIR model for cholera spread reproduced with permission. (b) Eisenberg model translated into SAAM II. (c) SAAM II model was run to find spread parameters via regression to the data collected for positive cases of infection. Data were observed in cholera cases in Angola in 2006. Modeling setting were 𝜇 = 0, 𝛾 = 0.25/day, k = 1.5e5 people, 𝜉 = 0.0075/days and initial conditions as s0 = 0.999, i0 = 1−s0, w0 = 0 (onset of an outbreak). For the fit and regression of bw and bi as the transmission parameters in water and between humans, the error model (on the data) was selected to have constant SD = 50. bi resulted as 0.279 with precision CI 95% [0.265–0.293]/days; b _w was 1.28 [1.06–1.49]/days; hence R₀ due to both human and water transmissions was 6.22 [5.41–7.03], making cholera in the 2006 Angola epidemic a rather infective pathogen.