Personalizable Models of Cardiac Elasticity with Physics-informed Symbolic Regression
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Introduction to the show: ident: Genomics Radio. Generated commentary on the latest computational biology and genomics papers.
Ines: I'm Ines, and with me are Marcus and Yuki, guest researcher.
Marcus: Today's paper: "Personalizable Models of Cardiac Elasticity with Physics-informed Symbolic Regression".
Ines: Cardiac Hyperelastic Evolutionary Symbolic Regression Algorithm (CHESRA) introduces a physics-informed machine learning framework that automatically derives simple strain energy functions from multiple experimental data sources to create parsimonious models for…
Marcus: First, who's behind it and why it matters.
Title and authors: Ines: We're moving into the title and authors of this paper, "Personalizable Models of Cardiac Elasticity with Physics-informed Symbolic Regression." It’s clear they are focusing on making these cardiac models personal and physically constrained from the start.
Marcus: The authors are a team from several different institutions across medicine, computer science, and physics, which is kind of what you expect when you're blending those two worlds—biology and computational modeling.
Yuki: I’m interested in seeing how they connect the structural biology insights with the machine learning side to create these personalized models.
Ines: They are essentially proposing this framework as a way to build digital twins that aren't just complex, but are also uniquely parameterizable for an individual patient's physiology.
Marcus: The paper focuses heavily on how the AI discovers these functions using evolutionary processes guided by physical principles like frame-invariance and material symmetry, which restricts the search space considerably.
Yuki: So they’re not just throwing a black-box model at the data; they are using physics as a guide to discover biologically plausible mathematical forms.
Ines: That's the main point of this specific work: leveraging biophysical constraints alongside data-driven discovery to generate accurate, personalizable models for cardiac digital twins, which is what they call CHESRA.
Marcus: It’s about moving away from models that are over-parameterized and instead finding those low-complexity polynomial functions that maintain high data fitting accuracy while keeping the parameter count manageable.
The paper's summary: Ines: So, what does the actual summary of "Personalizable Models of Cardiac Elasticity with Physics-informed Symbolic Regression" boil down to? It’s about introducing CHESRA, a physics-informed machine learning framework that automatically derives simple strain energy functions from multiple experimental data sources.
Marcus: They use a normalizing loss function in their fitness evaluation formula, ffit(, x, y, alpha) = fGoF(, x, y) + alpha at most, where fGoF measures how well the function fits and alpha at most counts the total number of nodes in the expression tree.
Yuki: That structure—balancing a goodness-of-fit metric against model complexity—is a very common challenge when you try to find any simple biological rule from messy experimental data.
Ines: Exactly, because they are systematically exploring space using initialization, selection, and evolutionary operators like mating and mutation to minimize that complexity count.
Marcus: The paper highlights that by combining mechanical data with physical principles like frame-invariance and material symmetry, they restrict the space of possible strain energy functions to only those that are physically admissible.
Yuki: That's a huge part of it; it means they are not just finding any mathematical curve that fits, but ones that respect the basic laws of elasticity and symmetry in tissue.
Ines: The key result here is the discovery of two new functions, psi CH1 and psi CH2, which fit data from four different experimental studies with high accuracy using significantly fewer free parameters than existing state-of-the-art orthotropic SEFs.
Marcus: And they specifically note that these functions are simpler than those in the literature because they avoid exponential terms and use fewer invariants, which speaks to their parsimony.
The paper's improvements: Ines: Now we look at what the paper actually suggests as improvements over what was available before, and it seems to be centered on addressing the issues of complexity and parameter reliability.
Marcus: They point out that by using this physics-informed approach, they manage to achieve high data fitting accuracy while simultaneously enabling more consistent parameter estimation than state-of-the-art approaches, both in tissue benchmarks and three dee simulations <ref:2508.09772#pg1>.
Yuki: That consistency in parameter estimation is what makes the models useful for personalized medicine; it means you can trust the numbers you get when you try to update a digital twin with new patient data.
Ines: They also show that this method provides more consistent parameter estimations in tissue data settings compared to those state-of-the-art SEFs, which is a direct improvement in reliability for clinical use.
Marcus: Furthermore, they address the issue of parameter non-uniqueness inherent in some models by producing SEFs with unique and stable parameter estimates across repeated optimizations, which reduces uncertainty when you're trying to personalize them.
Yuki: That stability is key; without it, every little tweak to the input data could lead to a totally different model structure for the same underlying biology.
Ines: The paper shows how embedding mechanistic insight into this machine learning process accelerates the development of transparent and clinically actionable digital health technologies by focusing on parsimony and identifiability.
Conclusion: Marcus: So, to wrap up, the main implication here is that CHESRA provides low-complexity models designed a-priori to balance accuracy with personalizability, which directly mitigates the risk of parameter non-uniqueness in clinical personalization.
Ines: It’s about merging symbolic learning with physical laws of elasticity to achieve a better balance between accuracy, generalizability, and interpretability for cardiac tissue mechanics.
Yuki: For me, it means that we are getting tools that aren't just fitting noise; they are finding the fundamental structural rules that govern how cardiac tissue behaves across different conditions.
Marcus: And looking at the results with psi CH1 and psi CH2, these functions offer a pathway to building more reliable digital twins where parameter estimation is consistent and stable across repeated simulations.
Ines: The paper demonstrates how embedding mechanistic insight into machine learning can accelerate the development of transparent, data-efficient, and clinically actionable digital health technologies by focusing on these parsimonious structures.
Yuki: It’s a solid step forward in using physics-informed methods to build models that are both accurate enough for the lab and general enough for personalized medicine in practice.
Marcus: That’s what we have on "Personalizable Models of Cardiac Elasticity with Physics-informed Symbolic Regression." We'll be back next time to discuss how these findings fit into the broader landscape of personalized cardiac modeling.
Sophia Ohnemus, Kristin Fullerton, Leto L. Riebel, Mary M. Maleckar, Andrew D. McCulloch, Viviane Timmermann†, Gabriel Balaban†
Institute for Experimental Cardiovascular Medicine, University Heart Center Freiburg – Bad Krozingen, Medical Faculty and Medical Center – University of Freiburg, Freiburg im Breisgau, Germany. · Speemann Graduate School of Biology and Medicine, University of Freiburg, Freiburg im Breisgau, Germany. · Faculty of Mathematics and Physics, University of Freiburg, Freiburg im Breisgau, Germany. · Physiology Biophysics and Systems Biology Program, Weill Cornell Graduate School of Medical Sciences · Department of Computer Science, University of Oxford · Department of Computational Physiology, Simula Research Laboratory, Oslo · Faculty of Medicine, University of Freiburg
q-bio.TO
Submitted: 2025-08-13
Updated: 2026-10-05
Code: https://github.com/GabrielBalabanResearch/CHESRA
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Importance score: 91/100
The gist: Cardiac Hyperelastic Evolutionary Symbolic Regression Algorithm (CHESRA) introduces a physics-informed machine learning framework that automatically derives simple strain energy functions from
Key concepts
- Strain Energy Function (SEF)
- The mathematical function that describes the elastic energy stored in a material when it is deformed. In this context, it's used to model how cardiac tissue stretches and contracts under different loads.
- Physics-Informed Machine Learning
- A machine learning approach that incorporates known physical laws, like elasticity principles, directly into the learning process. This ensures the resulting models are not just statistically accurate but also physically plausible and constrained by real-world mechanics.
- Symbolic Regression
- An AI technique that automatically searches for mathematical formulas (symbolic expressions) that best fit a given set of data. CHESRA uses this to discover the simplest, most elegant mathematical representations of cardiac tissue mechanics.
- Parsimony
- The principle of simplicity in modeling. In this study, parsimony means finding the simplest possible strain energy function that still accurately describes the complex behavior observed in cardiac tissue, avoiding unnecessary complexity.
Terminology
Summary
Cardiac Hyperelastic Evolutionary Symbolic Regression Algorithm (CHESRA) introduces a physics-informed machine learning framework that automatically derives simple strain energy functions from multiple experimental data sources to create parsimonious models for cardiac tissue mechanics. This framework is crucial for advancing cardiac digital twins by balancing high data fitting accuracy with model simplicity and generalizability
How it works
CHESRA utilizes a physics-informed evolutionary framework that manipulates symbolic representations of cardiac strain energy functions to fit experimental observations while minimizing SEF complexity
The evolutionary process in CHESRA is structured as follows:
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Initialization involves generating a set of random SEFs, where each SEF has a function tree representation with nodes being operators, exponential functions, material parameter symbols p1, …, pk, or invariant symbols ˜I1 to ˜I8 f s
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Fitness evaluation is performed using the formula ffit(Ψ, x, y, α) = fGoF(Ψ, x, y) + αleq (Ψ), where fGoF quantifies the goodness of fit and leq counts the total number of nodes in the expression tree
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Selection involves using a combination of elitism and random tournament to select a new SEF population for breeding, ensuring that the best solutions are preserved
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Evolutionary changes are applied via mating, mutation, reduction, and extension operators with specified probabilities (pmate, pmutate, preduce, pextend) to explore the space of SEF designs
Model Discovery and Simplification
CHESRA is designed to discover parsimonious SEFs from heterogeneous experiments by combining mechanical data with physical principles like frame-invariance and material symmetry The framework restricts the space of possible SEFs to physically admissible models, which is a key strength as it avoids the issues of high dimensionality and parameter interdependence found in human expert-designed SEFs
The algorithm specifically targets low-complexity polynomial cardiac SEFs, identifying two novel functions, psiCH1 and psiCH2, that fit data from four experimental studies with high accuracy while using fewer free parameters than state-of-the-art orthotropic SEFs These discovered SEFs are notably simpler than those in the literature, as psiCH1 and psiCH2 include no exponential terms and use fewer invariants
Validation and Parameter Estimation
The efficacy of CHESRA is validated through several rigorous tests:
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Cross-validation tests confirm the utility of CHESRA’s SEFs for generalizing to novel data, showing that leave-one-out SEFs achieved superior fits (fGoF ≤ 0.026) compared to single-fit SEFs under certain penalty values
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In a parameter variability benchmark using 3D ventricular simulation models, psiCH1 provided the most consistent and accurate parameter estimates, with markedly reduced parameter variability relative to state-of-the-art SEFs
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The quality assessment of strain energy functions showed that CHESRA generated SEFs (psiCH1, psiCH2) provide more consistent parameter estimations in the tissue data setting as compared to the state-of-the-art SEFs
Clinical Implications
The resulting CHESRA SEFs, psiCH1 and psiCH2, are promising for developing personalized cardiac digital twins because they provide low-complexity models designed a-priori to satisfy an optimal balance between accuracy and personalizability The parsimony and identifiability of these SEFs mitigate the risk associated with parameter non-uniqueness, which is critical for reliable clinical personalization Furthermore, the framework’s invariant-based symbolic structure allows it to be applied to other soft tissues and disease contexts where mechanics play a diagnostic or prognostic role
The study concludes that CHESRA embodies the principles of physics-informed machine learning for personalized digital medicine by merging symbolic learning with physical laws of elasticity to achieve a balance between accuracy, generalizability, and interpretability The parsimony and identifiability of CHESRA-derived SEFs mitigate the risk associated with parameter non-uniqueness, which is critical for reliable clinical personalization The study demonstrates how embedding mechanistic insight into machine learning can accelerate the development of transparent, data-efficient, and clinically actionable digital health technologies
The gist
CHESRA is a novel physics-informed machine learning framework that automatically derives simple strain energy functions from multiple experimental data sources to create parsimonious models for cardiac tissue mechanics.
Validation and Parameter Estimation
The efficacy of CHESRA is validated through several rigorous tests:
Improvements for AI systems
- Bold Header: Physics-Informed Symbolic Regression for Elasticity Modeling
This framework allows AI systems to automatically derive simple strain energy functions from multiple experimental data sources,
enabling high data fitting accuracy while maintaining more consistent parameter estimation than state-of-the-art approaches.
- Bold Header: Automated Discovery of Low-Complexity Constitutive Laws
The system can be used to generate low-complexity polynomial cardiac SEFs
that fit experimental data with fewer free parameters, addressing the problem where human expert designed SEFs are quite complex [9–12]
and improving the feasibility of parameter identification.
- Bold Header: Robustness Against Data Noise and Artifacts
By utilizing a normalizing loss function
and combining multiple datasets, CHESRA is designed to be a form of regularization, reducing the effect of lab-specific artifacts,
which helps in developing models that are more generalizable
for diverse patient populations.
- Bold Header: Enhanced Personalization Reliability
The system can produce SEFs where parameter estimates are more reliable; specifically, for the discovered functions, the CHESRA-derived SEFs (psiCH1 and psiCH2) provide more consistent parameter estimations in the tissue data setting,
which translates to improved personalization reliability and predictive stability
in digital twins.
- Bold Header: Identification of Unique Parameter Estimates
The algorithm avoids the problem of parameter non-uniqueness
inherent in state-of-the-art models by producing SEFs with unique and stable parameter estimates across repeated optimizations,
which mitigates uncertainty in clinical personalization.