전산의학연구실 - Human Digital Twin

Topic: Inverse Problem

A digital twin is a computational model of one person, updated with that person's own measurements. Our cardiovascular models already run in the forward direction: given parameters such as vascular resistance, cardiac contractility or ionic conductances, they simulate blood pressure, body-surface ECGs and cellular action potentials. A twin needs the opposite direction. From signals measured non-invasively, often far from the tissue that produced them, we must infer the parameters that explain them. This is the inverse problem.

Inverse problems in physiology are ill-posed. Different parameter sets can produce nearly the same signal, small measurement noise can cause large errors in the estimate, and wearable or body-surface sensors give only a sparse, indirect view of the heart and vessels. A useful twin therefore combines a trustworthy forward model with prior knowledge, regularization, optimization and an honest estimate of uncertainty.

In short: given measured signals y and a forward model F, find the parameters θ for which F(θ) matches y, and state how certain that estimate is. Three questions guide our work:

• Which parameters can be identified from which signals?

• How much noise and model error can each inverse step tolerate?

• How should uncertainty be reported so that a clinician or a drug developer can trust the twin?

We study the inverse problem along three pathways that span the scales of the cardiovascular system: the circulation (Pathway 1), the whole heart (Pathway 2) and lab-grown cardiac organoids (Pathway 3). Each starts from measurements our own devices can record and ends in a personalized mechanistic model.

Pathway 1: Circulatory Digital Twin

From biosignals to a personalized circulation. We describe the circulation with a lumped-parameter model: the left ventricle as a pump whose stiffness rises and falls in every beat (a time-varying elastance), connected to arteries and veins represented as resistances and compliances. Three parameters shape a person's blood pressure most strongly:

R scale multiplies the model's vascular resistances. Together with cardiac output, it sets mean arterial pressure.
C scale multiplies the arterial compliances. Stiffer arteries (lower C) widen the pulse pressure.
Emax, the end-systolic elastance, is the slope of the end-systolic pressure–volume relation: a load-independent index of left-ventricular contractility.

Inverse problem: CMA-ES. The fitting target is the measured arterial blood pressure (ABP) waveform. The Covariance Matrix Adaptation Evolution Strategy (CMA-ES) searches for the combination of R scale, C scale and Emax whose simulated ABP best matches it. CMA-ES needs no gradients, which suits a stiff, nonlinear circulation model: each generation it samples candidate parameter sets, simulates them, and shifts and reshapes its search distribution toward the best.

Forward: mechanical simulation. The estimated parameters personalize the model, which then runs forward to give pressure–volume loops, stroke volume, cardiac output and cardiac work, and to test what-if scenarios such as a change in vascular tone or contractility.

Open challenges. From the ABP waveform alone, the three parameters can trade off: a stronger heart pumping into more compliant, less resistive vessels can produce the same pressure as a weaker heart pumping into stiffer ones. A measure of flow or stroke volume, or cardiac timing from ECG and PCG such as the pre-ejection period and ejection time, can break this trade-off. Next come beat-to-beat tracking from wearable data and an uncertainty range for each parameter.

Pathway 2: Cardiac Digital Twin

From body-surface potentials to ion channels. Electrocardiographic imaging (ECGI) combines many ECG leads recorded over the chest and back, the body-surface potential map (BSPM), with the geometry of the torso and heart. We follow the signal back toward its cellular source in three inverse steps.

BSPM → heart-surface potentials. The torso acts as a volume conductor: heart-surface potentials map linearly to body-surface potentials through a transfer matrix computed from the torso and heart meshes, for example with the boundary element method. Inverting this matrix is severely ill-posed, because the torso smooths away detail, so we reconstruct heart-surface potentials with regularization (Tikhonov and related methods) that balances data fit against smoothness.
heart-surface potentials → action potentials. From the reconstructed electrograms we extract local activation and recovery times, whose difference approximates the local action-potential duration, and we work toward reconstructing the transmembrane potential itself.
action potentials → ionic conductances. A human ventricular cell model, such as the O'Hara–Rudy model used in CiPA, is calibrated until its action potential matches the reconstructed one. This yields conductances for the sodium (INa, INaL), potassium (IKr, IKs, IK1) and L-type calcium (ICaL) currents.

Where we are. The forward chain is in place: we generate BSPMs in silico from simulated cardiac activity, with torso and heart meshes. Our immediate focus is the first inverse problem, reconstructing heart-surface potentials from these simulated BSPMs, where the true answer is known.

Open challenges. Each step loses information, so errors compound along the chain. Clinical ECGI systems use more than a hundred electrodes; reconstructing from BioPulse's 16-channel body-surface map will need stronger priors, such as physiology-based or learned regularization. The last two steps face non-uniqueness, because different combinations of conductances can produce similar action potentials; pacing at several rates and adding drug responses help separate them.

Pathway 3: Organoid Digital Twin

From organoid recordings to ion channels. Cardiac organoids grown from human induced pluripotent stem cells beat on their own, and multi-electrode arrays (MEAs) record their extracellular field potentials without harming them. The field potential carries the cells' electrophysiology in indirect form: its sharp initial spike reflects the sodium-driven upstroke, and the field-potential duration tracks the action-potential duration.

field potential → action potential. We reconstruct the organoid action potential from its field potential, using a forward model of how cell currents produce the potential at each electrode, together with learned mappings trained on simulated pairs.
action potential → ionic conductances. We calibrate stem-cell-specific cardiomyocyte models, such as the Paci and Kernik models, to estimate the conductances of INa, INaL, IKr and ICaL. These models capture the immaturity of stem-cell-derived cells, such as spontaneous beating and a weak IK1.
Validation by design. Unlike a patient's heart, an organoid can be perturbed on purpose. Exposing it to known channel blockers at several doses tells us which conductance should fall and by how much: a direct test of whether the inverse steps recover the truth.

Why this pathway matters. Pathway 3 is our controlled testbed. The cell-model calibration of Pathway 2 can be checked here against known drug effects before it is applied to patients. It also links to our QSAR work: channel block predicted by Cardiosim-Tox can be compared with the conductance changes estimated from drug-treated organoids

Topic: Breast Cancer

A digital twin is a computational model of a single patient's tumour, built from that patient's own images. It is not a statistical model trained on a population, and nothing is carried over from other patients. The model describes the tumour mechanistically, through the processes that actually govern it: cells moving through the surrounding tissue, dividing, and being killed by chemotherapy.

Building one has two stages :

Calibration : The model's free parameters are adjusted until the simulation reproduces the tumour burden recorded by the patient's own scans.
Forecasting : The calibrated model is then run forward past the last scan used in fitting, producing a forecast for that patient alone.

The value of such a forecast depends on when it arrives. Neoadjuvant chemotherapy runs for months before surgery, and whether it has worked is confirmed only at the end, when the removed tissue is examined. We therefore build the twin in two configurations that differ in how much of the treatment the model is allowed to see before it commits to a prediction: one calibrated on the early part of the course, and one calibrated across the full course up to surgery.

Every digital twin in this project is run by solving the equation above. It states how the density of tumour cells at a given point in the breast changes from one moment to the next, as the combined result of three processes acting at the same time: cells spreading into less crowded tissue, cells dividing until the tissue reaches its capacity, and cells being killed by the drug that has reached that point.

What distinguishes one patient's twin from another is not the equation, which is the same for everyone, but the values its parameters take. Those values are estimated for each patient from their own scans. Once fixed, the equation is advanced in small time steps, yielding the patient's predicted tumour state at any point in the treatment course.

This figure shows two patients side by side, each from two perspectives: what the scans measured and what the model predicted. Each row is one examination in the treatment course, running from before treatment at the top to just before surgery at the bottom. Colour indicates the density of tumour cells, from dark blue, where few cells remain, to red, where the tissue is densely packed. Only the segmented tumour carries colour; the rest of the breast is shown in greyscale. The patient on the left achieved a complete response. Both columns tell the same story: a dense lesion at baseline, most of it gone by the second examination, and nothing detectable by the end. The patient on the right did not respond completely. The model follows the early decline correctly, but the enlarged panels at the bottom show where it falls short. Disease is still present at the final examination, and the model predicts a lower cell density than the scan actually recorded. Capturing residual disease that persists to the end of treatment remains harder than capturing disease that disappears.

Page updated

Google Sites

Report abuse