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The functional impact of myofiber macroscopic organization and disarray in computational models of the murine heart

This study demonstrates that while microscopic fiber disarray has minimal impact on passive mechanics and electrophysiology, accurate macroscopic fiber architecture is critical for realistic active contraction, revealing that excessive smoothing or rule-based surrogates lead to unphysiological results and that current surrogate methods for modeling disarray have significant limitations.

Original authors: Carlo Guastamacchia, Roberto Piersanti, Francesco Giardini, Raffaele Coppini, Cecilia Ferrantini, Luca Dede', Leonardo Sacconi, Francesco Regazzoni

Published 2026-04-02

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CC0 1.0

Original authors: Carlo Guastamacchia, Roberto Piersanti, Francesco Giardini, Raffaele Coppini, Cecilia Ferrantini, Luca Dede', Leonardo Sacconi, Francesco Regazzoni

Original paper dedicated to the public domain under CC0 1.0 (http://creativecommons.org/publicdomain/zero/1.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Building a Digital Heart

Imagine you want to build a perfect, working model of a human heart on a computer to test new drugs or plan surgeries. This is called a "Digital Twin." To make this model work, you need to know exactly how the heart muscle is built.

The heart isn't just a bag of mush; it's made of millions of tiny muscle fibers (like strands of spaghetti) that twist and turn in a very specific, complex pattern. These fibers are the engine of the heart. If they are aligned just right, the heart pumps efficiently. If they are messy, the pump might struggle.

The Problem: We can't easily see these tiny fibers inside a living human heart. It's like trying to map the individual threads inside a sweater without taking it apart. Because we can't measure them directly, scientists usually have to guess the pattern using math rules (like drawing a perfect spiral).

The Goal of this Study: The researchers wanted to find out: Does the messy, real-world arrangement of these fibers actually matter for how the heart works? And if we use a "perfect" math guess instead of the messy reality, how wrong are we?

The Experiment: The "Perfect" vs. The "Messy" Heart

To answer this, the team didn't use a human heart. They used a mouse heart. Why? Because they had a special microscope that could see the fibers of a mouse heart in incredible detail (like seeing every single thread in that sweater). This gave them a "Ground Truth"—the real, messy reality.

They then created three versions of a computer simulation:

The Real Mess: Using the actual, high-resolution data from the mouse (with all its tiny twists and turns).
The Smoothed Version: They took the real data and "smoothed it out" like ironing a wrinkled shirt. This removed the tiny messiness but kept the big, overall spiral shape.
The Rule-Based Guess: They used the standard math rules scientists usually use (the "perfect spiral" guess).

What They Found: The Three Rules of Heart Fibers

1. The Electrical Signal (The Spark)

Analogy: Think of the electrical signal as a message being passed down a line of people.
The Result: The researchers found that whether the "people" (fibers) are standing in a perfect line or slightly jumbled, the message gets through almost the same speed.
Takeaway: For the electrical spark that tells the heart to beat, the tiny messiness of the fibers doesn't matter much. The standard "perfect spiral" math guesses work fine here.

2. The Passive Stretch (The Balloon)

Analogy: Imagine blowing air into a balloon. How hard is it to stretch?
The Result: When the heart is just filling with blood (relaxing), the fibers act like the rubber of the balloon. Whether the fibers are perfectly aligned or slightly messy, the balloon stretches about the same amount.
Takeaway: The "messiness" of the fibers doesn't change how easy it is to fill the heart with blood.

3. The Active Squeeze (The Pump)

Analogy: This is the most important part. Imagine a team of rowers in a boat.

The Real Mess: The rowers are all facing slightly different directions. Some are rowing forward, some are rowing sideways.
The Smoothed Version: Everyone is facing the same general direction, but not perfectly locked in.
The Rule-Based Guess: Everyone is facing the exact same perfect direction, rowing in perfect unison.

The Result:

The Real Mess (and the Smoothed Version): The boat moves forward well. The "Smoothed Version" was actually the most efficient. By removing the tiny, useless sideways movements (the mess) but keeping the big spiral shape, the heart pumped better than the raw, messy data.
The Rule-Based Guess: This was a disaster. Because the "perfect" math guess made the fibers too organized, the heart squeezed so hard it essentially broke the computer simulation (the "boat capsized"). The heart contracted too violently because the model didn't account for the natural "wobble" or messiness that actually exists in real tissue.

The "Fix-It" Strategies

Since we can't measure real fibers in humans, scientists often try to "fake" the messiness in their models. They tried two common tricks:

Turning down the volume: They told the muscle to just be weaker overall (like telling the rowers to row less hard).
Adding sideways force: They told the muscle to push sideways as well as forward (like telling the rowers to row diagonally).

The Verdict:

Turning down the volume worked surprisingly well. It made the heart pump with the right amount of force and the right shape.
Adding sideways force looked okay from a distance (like looking at the boat from far away), but up close, the movement was wrong. It didn't match the real shape of the heart squeezing.

The Bottom Line

This paper teaches us three main things:

The Big Picture Matters Most: The overall spiral shape of the heart muscle is the most important thing for making it pump.
Perfection is Unrealistic: If you build a heart model that is too perfect (using standard math rules), it will squeeze too hard and give you wrong answers. Real hearts are a little messy, and that messiness actually helps them function safely.
How to Fix the Models: If you are building a heart model and can't measure the real fibers, don't try to simulate the messy angles. Instead, just make the muscle slightly weaker in your model. This simple trick mimics the effect of the real-world messiness much better than trying to add complex "sideways" forces.

In short: To build a good digital heart, you need the right big shape, but you also need to remember that real life is a little messy. Trying to make it too perfect breaks the simulation.

1. Problem Statement

Cardiac computational models are increasingly used for clinical decision-making and the development of "digital twins." However, a critical bottleneck remains the accurate reconstruction of myocardial fiber architecture.

The Challenge: Direct in vivo measurement of fiber orientation at high resolution is currently infeasible. Consequently, models rely on Rule-Based Methods (RBMs) (e.g., Laplace-Dirichlet RBMs) which generate idealized fiber fields based on geometry.
The Gap: These surrogate methods typically neglect fiber disarray (local microscopic deviations of fibers from the mean direction). While RBMs capture the macroscopic helical organization, they fail to represent the physiological heterogeneity found in real tissue.
The Question: What is the specific functional impact of macroscopic fiber architecture versus microscopic fiber disarray on cardiac electromechanics? Furthermore, are current surrogate strategies (like adding cross-fiber stress or reducing stiffness) sufficient to compensate for the lack of real disarray data?

2. Methodology

The authors developed a high-fidelity, biventricular electromechanical model of a murine heart to decouple and analyze these factors.

A. Data Acquisition and Reference Ground Truth

Imaging: Used mesoscopic optical imaging (mesoSPIM) on an ex-vivo mouse heart to obtain a high-resolution (3.25 µm isotropic) 3D map of cardiomyocyte organization.
Processing: Applied Structure Tensor Analysis (STA) to extract longitudinal fiber and sheet directions at a resolution of 96 µm. This dataset serves as the experimental ground truth.

B. Decoupling Macroscopic Architecture from Microscopic Disarray

To isolate the effects of disarray, the authors introduced a spatial smoothing strategy based on a Helmholtz filter:

Coordinate Transformation: Fiber angles ( $\alpha, \gamma$ ) were mapped to a circular coordinate system $(\sin(2\alpha), \cos(2\alpha))$ to handle angular periodicity and directional invariance.
Filtering: A Helmholtz filter with a regularization radius ( $\ell$ $ℓ$ ) was applied.
- Low-frequency content: Represents the macroscopic fiber architecture (smoothed field).
- High-frequency residuals: Represent microscopic fiber disarray.
Comparison: Simulations were run using:
1. The raw experimental field (Baseline).
2. Regularized fields (varying $\ell$ from 0 to 1.0 mm).
3. A standard LDRBM (Laplace-Dirichlet Rule-Based Method) field.

C. Electromechanical Model

Electrophysiology: Eikonal-diffusion formulation for activation times; transversely isotropic conductivity.
Mechanics: Hyperelastic passive behavior + Active stress model (RDQ20-MF).
Surrogate Strategies Tested: To mimic disarray in smoothed/RBM fields, two common approaches were tested:
1. Reduced Contractility: Lowering the cross-bridge stiffness ( $a_{XB}$ ).
2. Cross-Fiber Activation: Introducing active stress components in sheet ( $s$ ) and normal ( $n$ ) directions via Stress Factors ( $m_s, m_n$ ).

3. Key Contributions

First High-Resolution Validation: This is the first study to validate RBMs and disarray modeling strategies using a fully coupled electromechanical model against a high-resolution (96 µm) experimental fiber field.
Decoupling Framework: Introduced a novel mathematical framework to separate macroscopic organization from microscopic disarray, allowing for the independent assessment of their functional roles.
Critical Evaluation of Surrogates: Systematically evaluated the efficacy of "effective contractility reduction" vs. "cross-fiber stress" in reproducing the effects of real disarray.

4. Key Results

A. Electrophysiology

Low Sensitivity: Activation patterns are only weakly affected by fiber disarray.
Anisotropy: Disarray makes propagation slightly more isotropic, but the macroscopic architecture (captured well by LDRBM) is the dominant factor.
Conclusion: RBMs are sufficient for reproducing global activation maps; microscopic disarray has a negligible impact on signal propagation speed in healthy ventricles.

B. Passive Mechanics

Weak Sensitivity: Passive inflation (diastolic filling) is minimally affected by disarray.
Stiffness: Removing disarray (smoothing) slightly increases myocardial stiffness (reducing volume variation by ~4% when switching from experimental to LDRBM).
Conclusion: Passive mechanics are dominated by the bulk material properties and macroscopic geometry rather than local fiber misalignment.

C. Active Mechanics (Electromechanics)

High Sensitivity: Active contraction is highly sensitive to both macroscopic architecture and disarray.
The "Sweet Spot" ( $\ell \approx 0.25$ mm):
- Moderate smoothing (removing noise/disarray while keeping macro-helix) maximizes Ejection Fraction (EF).
- Excessive smoothing (destroying the helical structure) or using idealized RBMs leads to unphysiologically strong contraction (causing mesh collapse in simulations) or inefficient pumping.
Surrogate Strategy Performance:
- Contractility Reduction: Reducing $a_{XB}$ by ~13% in a smoothed field provided the best match to the baseline Pressure-Volume (PV) loops and strain distributions.
- Cross-Fiber Stress: While adjusting Stress Factors ( $m_s, m_n$ ) could match global PV loops, it failed to reproduce local strain patterns. It created uniform contraction that suppressed epicardial dilation and introduced spurious distortions, unlike the heterogeneous strain seen in the experimental data.

5. Significance and Implications

Dominance of Macro-Architecture: The study confirms that the macroscopic helical organization is the primary driver of cardiac function. Accurate reconstruction of this global structure is more critical than explicitly modeling microscopic disarray.
Limitations of Current Surrogates:
- Standard RBMs (without smoothing) often overestimate contractility because they assume perfect alignment.
- Simply adding cross-fiber active stress is insufficient to model the local mechanical effects of disarray; it distorts local strain fields even if global hemodynamics look correct.
- Phenomenological reduction of contractility is a more robust, albeit less mechanistic, approach to compensating for missing disarray data in smoothed models.
Clinical Relevance: For the development of cardiac digital twins, prioritizing the reconstruction of the macroscopic fiber field (e.g., via advanced imaging or improved RBMs) is essential. Relying solely on rule-based methods without accounting for the "loss of efficiency" caused by missing disarray can lead to significant errors in predicting mechanical function and local tissue deformation.

Conclusion: The paper establishes that while microscopic disarray has a minor role in electrophysiology and passive mechanics, it plays a crucial regulatory role in active mechanics. Current modeling practices that ignore disarray or attempt to mimic it via simple cross-fiber stress terms fail to capture the true local mechanical behavior of the heart, highlighting the need for better upscaling procedures or more accurate macroscopic fiber reconstruction.