Table 1.
Simulation protocols used in this study.
Those indicated as clinical trial correspond to the regimens used in [33], and those indicated as NHP study correspond to the regimens tested in NHPs herein. HRZEM combinations refer solely to the computational studies. Optimization refers to the regimens we further tested with our optimization protocol to determine dosing and sterilization time to predict the best performers.
Fig 1.
CFU trends within the in silico repository of simulated granuloma generated by GranSim after the start of infection.
Each curve represents a single granuloma simulation with a single parameter set using GranSim, and black dots are CFU counts from NHP granulomas [46,47]. Each individual data point comes from a granuloma of a unique NHP; however, multiple data points at the same time step may come from the same NHP if that NHP has developed multiple granulomas by the time they were necropsied. In total, the data points come from 42 monkeys and 646 granulomas, and each monkey has 2–40 granulomas (the median is 14.5, 25th and 75th percentiles are 9 and 20, respectively.). Based on their CFU trajectories, we categorize granulomas into low–CFU (blue curves, N = 100) and high–CFU (red curves, N = 100) granulomas. Low–CFU granulomas represent granulomas that have controlled bacterial burden; high–CFU granulomas are those where bacterial growth is uncontrollable by the immune system, respectively [8,49,50].
Fig 2.
Comparison of moxifloxacin–containing regimens to the standard regimen for the human study and GranSim.
(A) Results from the REMoxTB clinical trial [33]. Probability that a patient has a sputum culture–positive status decreases over the course of treatment, and this decline is more pronounced for moxifloxacin–containing regimens. Control (HRZE), HRZM and RMZE groups have 510, 514 and 524 patients, respectively. This figure is adapted from Fig 2B of [33] (Data points (x) extracted by WebPlotDigitizer). (B,C) GranSim predictions for (B) the fraction of unsterilized granulomas and (C) sterilization times upon treatment with HRZE, HRZM and RMZE (*p<0.001, one–tailed paired t–test). The central red lines in box plots represent the median, whereas the bottom and the top edges of boxes represent 25th and 75th percentiles, respectively. For the REMoxTB study and the simulations, in the control groups, patients/granulomas are treated with HRZE for 8 weeks, followed by an 18–week long HR treatment. In HRZM and RMZE groups, patients/granulomas are treated with HRZM and RMZE for 17 weeks, respectively (see Methods and Table 1). In (B) and (C), each group has 200 simulated granulomas.
Fig 3.
Comparing NHP and GranSim regimens.
Comparison of the standard regimen (HRZE) to two moxifloxacin–containing regimens, HMZE and RMZE, between in silico studies with GranSim (panels A–C) and in vivo NHP studies (panels D and E). (A) The sterilization times of granulomas averaged over 200 granulomas in GranSim. Note that we assign the maximum simulation time of 60 days as a sterilization time for unsterilized granulomas (*p<0.001, one–tailed paired t–test). The central red lines in box plots represent the median, whereas the bottom and the top edges of boxes represent 25th and 75th percentiles, respectively. (B, E) Percentage of granulomas that are unsterilized by treatment end for (B) NHP studies and (E) GranSim. Colored dots in (E) represent the percentage of unsterilized granulomas per NHP. (C) The fraction of granulomas which are unsterilized as a function of simulated treatment time using GranSim. (D) The average total CFU per NHP after treatment with the corresponding regimens for two months (n = 7 animals in the control group, n = 3 animals in HRZE group, n = 4 animals in HMZE, n = 2 animals in RMZE). Statistical analyses were not performed on the NHP data due to small numbers of animals per group.
Fig 4.
Comparison of metabolic activity (measured by SUVR) change post treatment in NHP and GranSim.
Comparison of metabolic activity changes (A) in NHP granulomas and (B) using GranSim. (A) Change in standardized uptake value ratio (SUVR) per NHP granuloma (colored dots) in 8 weeks (SUVR8weeks−SUVRpre–treatment) when NHP are treated with HRZE (n = 3 animals), HMZE (n = 4 animals) and RMZE (n = 2 animals) for 8 weeks (n = 7 animals in control case, i.e., without treatment). Color shades of the dots in each column indicate NHPs and the diamonds are the median of SUVR change/granuloma for each NHP. (B) Change in FDG avidity per granuloma simulated using GranSim (FDG avidity8weeks−FDG aviditypretreatment) averaged over 200 granulomas (*p<0.0005, one–tailed paired t–test). The central red lines in box plots represent the median, whereas the bottom and the top edges of boxes represent 25th and 75th percentiles, respectively.
Fig 5.
Comparison of 200 simulations for all HRZEM four–way regimens using GranSim.
Comparison of (A–C) sterilizing rates and (D–F) sterilization times of 4–way combinations of HRZEM for (A and D) 100 high–CFU, (B and E) 100 low–CFU and (C and F) a combination of 100 high–and 100 low–CFU granulomas. Significance test was performed only between HRZE and moxifloxacin–containing regimens (*p<0.0001, one–tailed paired t–test). The central lines in box plots represent the median, whereas the bottom and the top edges of boxes represent 25th and 75th percentiles, respectively.
Fig 6.
Simulated treatments with 4–way, 3–way, 2–way regimen comparison from HRZEM.
Comparison of (A–C) sterilizing rates and (D–F) sterilization times of all regimen combinations of HRZEM to HRZE (thick green curve in all panels) in (A and D) 100 high–CFU, (B and E) 100 low–CFU and (C and F) a combination of 100 high–and 100 low–CFU granulomas. Significance test was performed only between HRZE and all other regimens (*p<0.01, one–tailed paired t–test). The central lines in box plots represent the median, whereas the bottom and the top edges of boxes represent 25th and 75th percentiles, respectively. Colored curves indicate the regimens that clear granulomas faster than HRZE, i.e., they have a significantly lower sterilization times. Gray curves represent regimens with slower sterilization.
Fig 7.
Pareto front optimization study simulating all 4–way combinations of HRZEM to find regimens that minimize both average sterilization time and total dose.
Pareto front optimization identifying optimal dose and sterilization times for: (A) HRZM, (B) HRME, (C) HMZE, (D) RMZE and (E) HRZE. In each panel (A–E), red dots represent the (non–dominating) regimens that belong to the Pareto set (see Tables B–F in S1 Appendix for the doses of each antibiotic in the regimens that belong to Pareto sets) whereas black dots are the regimens that are not optimal based on the objectives. Green dots show the regimen based on the current standard doses recommended by CDC [4]. (F) Pareto sets for all regimens (same as red dots in panels A–E) compared to the standard regimen HRZE with CDC–recommended doses (X in Panel F). Dots in the dashed gray rectangle indicate the regimens that have lower total drug dose and lower average sterilization times (see Table 2 for the doses of each antibiotic in these regimens). Triangles indicate optimized regimens with 3–way combinations, as the optimal doses of one antibiotic (E or Z) in these regimens are predicted as 0.
Table 2.
Simulated Doses of Antibiotics that optimize treatment objectives (compare with Fig 7).
The doses for each antibiotic in the regimens that have lower average sterilization time and lower dosage than the standard regimen (black row) as shown in Fig 7F (i.e., all regimens in dashed gray rectangle). The underlined rows indicate optimal 3–way combinations, where the optimal dose of E or Z is predicted as 0.
Fig 8.
An overview of the hybrid agent–based model that simulates granuloma formation and function, GranSim, and how pharmacokinetics (PK) and pharmacodynamics (PD) of antibiotics are incorporated in GranSim.
A) Our simulations begin with GranSim generating a large library of granulomas to be used for regimen testing. B) Antibiotic concentrations in plasma are simulated by a compartmental, ordinary differential equation model (ka, CL and Q are rate constants between compartments) with one (Z, E and M) or two transit compartments (H and R) representing oral absorption (one transit compartment shown in the figure). (C) Antibiotics in the plasma permeate through vascular sources into the lung tissue, i.e., onto the spatial grid of GranSim, where antibiotics can: diffuse, bind to caseum, be taken up by macrophages and penetrate into a granuloma. (D) We determine a killing rate for each Mtb phenotype (k1, k2 and k3) based on the local antibiotic concentration in their environment (grid compartment) (C1, C2 and C3) using a Hill equation calibrated to each Mtb type (nonreplicating, intracellular and extracellular). Emax_N, Emax_I and Emax_E are maximum–killing rate constants, respectively, C50N, C50I and C50E are the concentration at half maximal killing, respectively and hN, hI and hE are Hill curve constants for nonreplicating, intracellular and extracellular Mtb, respectively.