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Digital Twins / Bayesian Digital Twin for Sparse-Data Optimization
Digital Twins · Bayesian ML · Optimization

A digital twin that prioritizes experiments when every run costs weeks.

Calibrates a 3-ODE tumor–macrophage model from 6 data points per case via MCMC, then screens immunotherapy schedules under CVaR0.10 risk — matching standard-of-care efficacy at ~31% lower drug exposure across 100 virtual patients.

  • PyMC / DEMetropolisZ
  • SciPy solve_ivp
  • CVaR optimization
  • Ollama + Gemma
  • ArviZ
Dose reduction
~31%
Virtual cases
100 · 0 failures
Posterior coverage
95% (SOC TIE)
Data per case
6 observations

In Preparation

End-to-end pipeline: physical microfluidic chip generates sparse observations that feed a digital twin engine combining a tumor-macrophage ODE, MCMC calibration, and CVaR optimization to output a front-loaded weekly dose schedule that matches no-treatment versus SOC versus optimized trajectories

Why it matters

Tumor-on-chip platforms reproduce the tumor microenvironment in microfluidic geometry, but they are slow and expensive to run and yield endpoint-biased, sparse data — a handful of time-points per chip. Empirical R848 schedule discovery is a combinatorial dead-end: even a modest 5-dose × 4-week grid is ~625 candidates.

The decision needed is not which schedule is best on average, but which schedule is safe for the patients who respond worst. A computational layer has to calibrate from sparse observations, propagate uncertainty into the objective, and rank schedules by their worst-case outcome — not their mean.

How it works

  • Mechanistic backbone. 3-ODE tumor–macrophage model with 7 fixed and 4 uncertain parameters (ρ, φ, ξ, k21) under truncated-normal priors from cited biology.
  • Virtual cohort. 100 virtual cases sampled from priors; SciPy solve_ivp RK45 forward simulation, 0/100 solver failures across phases.
  • MCMC calibration. DEMetropolisZ sampler, 4 chains × 8,000 draws per case (16,000 samples total). Max R̂ ≤ 1.01, mean ESS ~1,000 — clean diagnostics.
  • Risk-aware optimization. Maximize CVaR0.10[TIE(θ, u)] over weekly dose uk ∈ [0, 10] µg/mL, total budget ≤ 60 µg/mL.
  • LLM-augmented portal. Local Ollama + Gemma stack for cohort dashboard, new-case pipeline, structured case reports, and grounded Q&A. Fully on-device.
A clear microfluidic glass slide chip held between two fingers, with labeled inlet ports on the left and outlet ports on the right and green tumor spheroid visible in the central chamber
Platform The tumor-on-chip is the data source: U87 GBM spheroids with macrophages under perfused R848 dosing, observed at a small number of time-points per chip.
Macrophage repolarization flux F(t) = u(t) · η · M₂(t)

What we found

41.4 vs 60 µg/mL Total dose Same TIE distribution as SOC at 31% lower exposure; 71/100 cases within ±0.5 d.
+37% Repolarization efficiency Cells repolarized per µg·mL drug (+46% in the most aggressive quartile).
91 / 95% Posterior predictive coverage No-treatment / SOC TIE — strong despite weak marginal φ, k21 identifiability.
8.7 → 5.3 µg/mL Front-loaded schedule Optimal weekly dose decays through the cycle as M₂ population shrinks.
Two side-by-side box plots comparing Mean TIE and Risk-Aware TIE worst 10 percent across no-treatment, SOC 10 per week, and Optimized regimens across 100 virtual patients; SOC and Optimized show overlapping distributions while no-treatment sits clearly lower
Parity Mean and risk-aware (CVaR10) tumor-immune-equilibrium days — the Optimized regimen matches SOC distributionally while using a third less drug.
Heatmap of weekly R848 dose across 100 patients sorted by no-treatment TIE aggressiveness, with darker columns in weeks 1 and 2 and lighter columns in weeks 5 and 6 indicating front-loaded dosing
Front-loading Weekly dose heatmap across 100 cases — weeks 1–2 carry the heaviest dose where the M₂ pool is largest, weeks 5–6 ease off.
Four small panels showing prior versus posterior density curves for tumor proliferation rate rho, M1 kill rate phi, M2 over M1 recruitment bias xi, and M2 to M1 switch rate k21; rho concentrates noticeably tighter than the prior while phi and k21 nearly overlap their priors
Identifiability Posteriors over the four free parameters — ρ concentrates sharply, φ and k21 stay close to the prior. The hierarchy is the honest answer about what 6 data points can resolve.
Portal in action Dashboard, new-case pipeline, calibration drill-down, and grounded Q&A — all on-device, no cloud calls.
LLM chatbot panel inside the portal answering a query about its own role, listing the 3 ODE model, calibration parameters, and therapeutic outcomes it can reason about, with a disclaimer that the document represents a simulated clinical modeling exercise
Grounded Q&A Local Gemma model answers structured questions over the cohort — every answer traceable to a simulation case.

So what. Risk-aware decision support for any domain where each experiment is a serious commitment of time, money, or samples — catalyst tuning, electrochemical screening, alloy thermal cycles. The deliverable is not a point prediction but a defensible ranking under posterior uncertainty.

Paper & resources

Manuscript In preparation · 2026
Predictive DT framework Kapteyn, Pretorius & Willcox — Nat. Comp. Sci. (2021)
Tumor–macrophage ODE basis Mahlbacher et al. — J. ImmunoTherapy Cancer (2018)
Author Prashant Dhakal
BibTeX · in preparation 
@unpublished{dhakal2026bdt,
  title   = {A Bayesian Digital Twin for Risk-Aware Schedule Prioritization under Sparse Tumor-on-Chip Observations},
  author  = {Dhakal, Prashant and Wang, Shiren},
  year    = {2026}, note = {Manuscript in preparation; PhD dissertation Topic~2}
}