Bayesian Cardiovascular Digital Twin
5-state Kalman filter/smoother with UKF nonlinear dynamics
Exploratory N=1 Physiological State-Space Model
Bayesian Cardiovascular Digital Twin
This page compresses 176 wearable days into five latent physiological states, combining a Kalman smoother with UKF nonlinear dynamics to track recovery, instability, and treatment response. Use it for relative trajectory tracking and model diagnostics, not for diagnosis or causal proof.
5 latent states5 wearable inputsAcute event 2026-02-09Ruxolitinib 2026-03-16HEV Dx 2026-03-18Post-HSCT Patient
Strongest modeled shift
In range+14.17 SD
Autonomic Tone · Improved · p<0.001 · exploratory
Best short-term fit
In rangeR-sq 0.625
HRV (RMSSD) · RMSE 7.11 ms
Residual checks
Watch2/5
Ljung-Box p > 0.05 across modeled sensors
Post-drug window
In range109 days
HEV diagnosed 2026-03-18 confounds the early window
Full-window trajectory
Nightly HRV (RMSSD) and heart rate, with Ruxolitinib start and HEV diagnosis marked and the baseline / Jakavi-only / Jakavi+beta-blocker phases shaded.
Days Modeled
Info176
2026-01-08 to 2026-07-02
Post-Drug Days
109
Since 2026-03-16
Innovation Alerts
3
43 total across the modeled window
Avg Sensor Coverage
92.8%
Lowest: SpO2 (78%)
Residual Checks
Partial2/5
Ljung-Box p>0.05 across modeled sensors
READ THIS FIRST
Read This First
If someone opens only one part of this page, it should be this block. It summarizes the signal, the diagnostics that support the model, and the reasons the interpretation remains exploratory.
What the model suggests
- Strongest modeled post-drug shift: Autonomic Tone +14.17 SD (p<0.001, exploratory).
- Best one-step predictive stream: HRV (RMSSD) with R-sq 0.625 and RMSE 7.11 ms.
- Recent instability is limited: 3 innovation alerts in the last 7 days (43 total across the modeled window).
What supports the model
- Residual diagnostics pass for 2/5 modeled sensors.
- Average sensor coverage is 92.8%; lowest coverage is SpO2 at 78%.
- HRV (RMSSD) contributes the largest information share at 46.9%.
Why caution is still needed
- This is a single-patient (N=1) exploratory model, not a validated clinical instrument.
- The post-drug window is 109 days; findings remain descriptive, not confirmatory.
- HEV diagnosed 2026-03-18 may confound early post-drug shifts after ruxolitinib started on 2026-03-16.
STATE TRAJECTORIES
Latent State Trajectories
The Kalman smoother estimates 5 latent physiological states from noisy, intermittent sensor data. Solid lines show the smoothed posterior mean; shaded bands show 95% credible intervals. Dotted lines overlay the UKF estimates for comparison. Vertical markers indicate the Feb 9 acute event, Mar 16 ruxolitinib start, and Mar 18 HEV diagnosis.
DRUG RESPONSE
Ruxolitinib Drug Response (started 2026-03-16)
Latent-state shifts are standardized, so the pre/post comparison shows magnitude rather than raw clinical units. Use this block to gauge which modeled subsystems moved most after treatment began. HEV diagnosed on 2026-03-18 may confound late-March movement.
Largest shiftAutonomic Tone+14.17 SD · Improved · p<0.001
Fastest fitted responseAutonomic Tone23.4 days to reach modeled equilibrium
Positive shifts indicate a higher modeled state load after treatment start; time constants estimate how quickly the post-drug response stabilized. P-values here are unadjusted and should be treated as descriptive, not confirmatory.
| State | Pre-drug Mean | Post-drug Mean | Shift (SD) | How to read direction | Direction | p-value | Time Constant |
|---|---|---|---|---|---|---|---|
| Autonomic Tone | -0.98 | 0.53 | +14.174 | Higher = stronger vagal/recovery signal | Improved (pre/post drug) | p<0.001 | 23.4 days |
| Cardiac Reserve | -0.93 | 0.36 | +1.967 | Higher = better modeled cardiovascular resilience | Improved (pre/post drug) | p<0.001 | 30.0 days |
| Circadian Phase | 1.04 | -0.14 | -3.079 | Direction is descriptive; interpret with timing context | Stable (pre/post drug) | p<0.001 | 30.0 days |
| Inflammation Level | -0.60 | 0.19 | +1.543 | Higher = worse modeled inflammatory load | Worsened (pre/post drug) | p<0.001 | 30.0 days |
| Sleep Quality | -0.30 | 0.09 | +1.156 | Higher = better modeled sleep/recovery signal | Improved (pre/post drug) | p<0.001 | 30.0 days |
OBS VS MODEL
Observations vs Model Estimates
Raw sensor observations (dots) overlaid with the model's filtered estimates (lines). Good model fit is indicated by the line tracking the dots closely. Vertical markers indicate the Feb 9 acute event, Mar 16 ruxolitinib start, and Mar 18 HEV diagnosis.
PREDICTION
Prediction Performance
One-step-ahead residuals show how quickly the model tracks changes in physiology. Higher R-sq and lower RMSE indicate the latent-state model is anticipating the next observation well. Vertical markers are shown on the time-series subplots for the acute event, treatment start, and HEV diagnosis.
Per-sensor forecast quality
HRV (RMSSD)
R-sq 0.625
RMSE 7.11 ms
Heart Rate
R-sq 0.457
RMSE 7.82 bpm
Sleep Efficiency
R-sq 0.060
RMSE 5.02 %
Temperature Deviation
R-sq -0.007
RMSE 0.33 C
SpO2
R-sq -0.146
RMSE 0.80 %
Innovation alerts (43 total, 3 in last 7 days)
2026-06-25: SpO2 deviation = 3.0 sigma
2026-07-01: Heart Rate deviation = 2.5 sigma
2026-07-02: HRV (RMSSD) deviation = 2.3 sigma
KF VS UKF
KF vs UKF Comparison
The Unscented Kalman Filter uses nonlinear circadian dynamics and exponential autonomic decay with sigma-point propagation (no Jacobian needed). Large differences from the linear KF suggest significant nonlinear dynamics.
SENSOR FUSION
Multi-Modal Sensor Fusion Quality
This block shows which wearable streams are carrying the latent-state estimates and whether the residuals still contain structure the model failed to absorb.
Sensor contribution to state estimation
HRV (RMSSD)
46.9%
share of the fused state-estimation signal
Heart Rate
24.8%
share of the fused state-estimation signal
Sleep Efficiency
10.6%
share of the fused state-estimation signal
Temperature Deviation
9.4%
share of the fused state-estimation signal
SpO2
8.3%
share of the fused state-estimation signal
Residual diagnostics
White noise residuals (Ljung-Box p > 0.05) indicate the model captures temporal structure well. Significant autocorrelation suggests model misspecification for that sensor.
Disclaimer: This is a computational model for research and self-monitoring purposes only. It is NOT a medical device and should NOT be used for clinical decision-making. The Oura Ring is a consumer wearable; its measurements have known limitations in accuracy. All state estimates are model-dependent and should be interpreted with appropriate uncertainty. Consult qualified healthcare professionals for medical decisions.