Rapid prediction of organisation in engineered corneal, glial and fibroblast tissues using machine learning and biophysical models

arXiv:2502.08062 · physics.bio-ph, q-bio.TO · Submitted 2025-02-12 · Read on arXiv

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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: "Rapid prediction of organisation in engineered corneal, glial and fibroblast tissues using machine learning and biophysical models".

Ines: We present a machine learning approach for predicting the organisation of corneal, glial and fibroblast cells in 3D cultures used for tissue engineering.

Marcus: First, who's behind it and why it matters.

Title and authors: Ines: So, we're starting by looking at "Rapid prediction of organisation in engineered corneal, glial and fibroblast tissues using machine learning and biophysical models," which is essentially introducing the RAPTOR approach for predicting cell organization in three dee cultures.

Marcus: I see the title immediately pointing to a focus on specific cell types—corneal, glial, and fibroblast cells—which tells us this isn't just a general tissue prediction tool.

Yuki: And from my side, I'm wondering how these predictions relate to the actual population genetics of those specific cell lines; does this help us understand why certain lineages organize differently?

Ines: Exactly. The paper uses a pix2pix generative adversarial network architecture, which is a powerful deep learning tool, and they train it using results from biophysical models called CONDOR simulations to predict things like cell density and orientation.

Marcus: And what I find interesting from the abstract is how they are training this AI using those CONDOR simulations that cover a range of underlying model parameters. That suggests the goal isn't just predicting one outcome, but understanding how different underlying biophysical rules affect the final tissue structure.

Yuki: It’s interesting because it links a complex physical simulation, CONDOR, with a deep learning architecture like pix2pix to get biological predictions about cell orientation and density. I think that connection is really important for grounding the AI's output in actual physical constraints.

Ines: That’s right. The paper highlights that RAPTOR can be extended to change those underlying CONDOR parameters, meaning it can simulate tissues with different cell and matrix types.

Marcus: That extension is key because it moves the method beyond just predicting organization in one fixed scenario; it lets us explore a wider space of possibilities for tissue growth conditions.

Yuki: If we can use this to test different ECM properties, that opens up possibilities for understanding how environmental cues shape cell fate and structure across different species or developmental stages.

Ines: It really shows the potential here for designing scaffolds where you can actively influence the organization to achieve a specific cellular arrangement before you even start culturing.

Marcus: And I think the mention of its speed, making it fast enough for tethered mould design, is where this gets practical; we need tools that aren't computationally prohibitive for iterative design work.

Yuki: That speed could mean we can rapidly test hypotheses about cell alignment in complex three dee environments without needing massive simulation runs every time.

The paper's summary: Ines: Now let's look at the summary of "Rapid prediction of organisation in engineered corneal, glial and fibroblast tissues using machine learning and biophysical models," which details exactly what RAPTOR does with inputs and outputs.

Marcus: The paper explains that RAPTOR takes an input image—which includes both the mould design and those three simulation parameters—and produces eight channels predicting properties like cell density, orientation vectors, and average strain in adjacent bonds.

Yuki: That output structure is quite rich; getting both cellular characteristics like density and alignment alongside mechanical properties like tension gives us a very holistic view of the resulting tissue.

Ines: That spatial weighting mechanism is where the biological meaning comes in; it shows how neighboring cells influence each other's state within the three dee structure, which they calculate using Eq. (three).

Marcus: I see that they used two hundred fifty-six times two hundred fifty-six pixel images for input and output, which keeps it manageable for training, and they used augmentations like mirroring and rotation to make the model more generalizable.

Yuki: The fact that they compared their predictions against archived data from glial cells, tenocytes, myoblasts, corneal stromal cells, and dermal fibroblasts gives us some real validation that this approach works across different cell lineages.

Ines: That comparison against established cultured tissues is a big deal because it shows the method isn't just working on synthetic data; it’s actually capturing features relevant to real biological tissues.

Marcus: And when you look at the results, they achieved good agreement with both the CONDOR simulation and their RAPTOR approach for many of these archived samples, which speaks to the reliability of their training data set.

Yuki: It suggests that the underlying biophysical model parameters they used in CONDOR are reasonably capturing the essential physics governing how these different cell types interact in a hydrogel environment.

Ines: So, what we're seeing is a validated tool that can bridge the gap between abstract physical modeling and observable biological tissue structure.

Marcus: It’s moving from just simulating things to having an AI that can predict what those simulations would look like given certain biological inputs.

Yuki: It gives us a new lens through which to view tissue engineering, connecting the molecular physics to the macroscopic structural outcome for various cell types.

The paper's improvements: Ines: Moving on to what they suggest as improvements, the paper details how incorporating the model parameters and kappa directly into the machine learning approach as inputs changes things significantly.

Marcus: That’s where I see the real power, because it means we can explicitly control or probe the effect of those physical constants on the predicted tissue properties, rather than just letting them be hidden within a fixed simulation setup.

Yuki: This suggests that tissue organization isn't just determined by geometry but is highly sensitive to those specific biophysical interaction strengths they are modeling.

Ines: Precisely; this parameter-aware prediction lets us systematically explore how varying the cell-matrix interaction or bond stiffness changes the predicted outcome.

Marcus: And I think this moves the method from a descriptive tool to a predictive design tool, which is what we were aiming for when we thought about using it for mould design.

Yuki: If we can fine-tune these parameters computationally to match experimental outcomes, that gives us a powerful way to characterize tissue types without needing extensive wet lab work for every single variation.

Ines: The paper also discusses how they used RAPTOR in a non-linear least squares fit to actually determine those specific CONDOR model parameters from experimental data, which is a huge step forward.

Marcus: That’s the accelerated computational design workflow I was talking about earlier; instead of running slow simulations repeatedly, we can use this fast AI to quickly find the right physical rules for a target tissue.

Yuki: That capability really helps narrow down the biological mechanisms at play when designing scaffolds for specific conditions, like optimizing alignment in corneal tissue versus glial tissue.

Ines: And they did mention that grid searches showed some limitations, particularly when dealing with cases where both kappa is low and is high, where RAPTOR struggled to match highly contracted tissues predicted by CONDOR.

Marcus: That limitation points toward a need for more specialized training data in those specific parameter regimes; it tells us the AI needs more examples of extreme physical states to get perfect.

Yuki: It’s a reminder that biological complexity often lives in the less represented parts of the parameter space, and focusing future data collection there could significantly improve accuracy for those challenging tissue designs.

Conclusion: Ines: So, wrapping up on "Rapid prediction of organisation in engineered corneal, glial and fibroblast tissues using machine learning and biophysical models," the core finding is that RAPTOR uses pix2pix to predict tissue organization in these specific three dee cultures.

Marcus: And the most important thing is its ability to take biophysical parameters as inputs and then rapidly identify those parameters using fitting methods against experimental data.

Yuki: This gives us a way to connect the microscopic physical rules modeled by CONDOR directly to the macroscopic tissue structure we observe in culture.

Ines: It certainly provides a powerful framework for designing scaffolds where we can predict how structural choices will affect cell behavior before we spend time and resources on building them physically.

Marcus: I agree, because if this system can quickly give us the right parameters for a specific tissue, it cuts down on the computational time needed to iterate on scaffold designs significantly.

Yuki: It opens up new avenues for studying how different cellular environments dictate tissue architecture across various biological contexts.

Ines: It’s clear that RAPTOR is a valuable tool for rapidly characterizing and designing these complex three dee biological systems.

Marcus: I think the speed of this method, combined with the ability to tune biophysical inputs, makes it a much more practical resource than just running slow simulations all the time.

Yuki: It really helps ground our understanding by linking computation to tangible biological outcomes in tissue engineering research.

Ines: So that’s what we had on today's discussion about "Rapid prediction of organisation in engineered corneal, glial and fibroblast tissues using machine learning and biophysical models." Thanks for joining us!

Marcus: Thanks for tuning in. We’ll be ready to discuss the next paper when it drops.

Yuki: It was a fascinating look at how we can use AI to bridge physics and biology.

School of Physical Sciences, The Open University · UCL Centre for Nerve Engineering · Department of Pharmacology, UCL School of Pharmacy

physics.bio-ph, q-bio.TO

Submitted: 2025-02-12

Updated: 2026-09-24

Comments: 32 pages, 18 figures

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 85/100

The gist: We present a machine learning approach for predicting the organisation of corneal, glial and fibroblast cells in 3D cultures used for tissue engineering.

Key concepts

RAPTOR approach: This is a machine learning method used to predict the organization of corneal, glial, and fibroblast cells in three-dimensional cultures. It uses pix2pix architecture trained on results from biophysical models.
CONDOR simulations: These are biophysical models used to simulate cell density and orientation. The RAPTOR model is trained using these simulations to predict tissue structure based on various underlying model parameters.
pix2pix generative adversarial network: This is a deep learning tool used in the paper. It is employed as the architecture for RAPTOR, allowing it to generate predictions of cell organization from input images like mould designs and simulation parameters.
parameter-aware prediction: This improvement involves incorporating model parameters directly into the machine learning approach. This allows researchers to explicitly control or probe how physical constants affect predicted tissue properties.

Terminology

Alignment — 18× in this paper · explained in 1 episode
Core — 5× in this paper · explained in 2 episodes
Accuracy — 1× in this paper · explained in 1 episode
Adam — 1× in this paper · explained in 2 episodes
Grounding — 1× in this paper · explained in 3 episodes
Physical Constraints — 1× in this paper · explained in 7 episodes

Summary

We present a machine learning approach for predicting the organisation of corneal, glial and fibroblast cells in 3D cultures used for tissue engineering. Our machine-learning-based method uses a powerful generative adversarial network architecture called pix2pix, which we train using results from biophysical contractile network dipole orientation (CONDOR) simulations. In the following, we refer to the machine learning method as the RAPTOR (RApid Prediction of Tissue ORganisation) approach. A training data set containing a range of CONDOR simulations is created, covering a range of underlying model parameters. Validation of the trained neural network is carried out by comparing predictions with cultured glial, corneal, and fibroblast tissues, with good agreements for both CONDOR and RAPTOR approaches. An approach is developed to determine CONDOR model parameters for specific tissues using a fit to tissue properties. RAPTOR outputs a variety of tissue properties, including cell densities of cell alignments and tension. Since it is fast, it could be valuable for the design of tethered moulds for tissue growth.

The purpose of this paper is to introduce and validate machine learning tools for the rapid prediction of tissue orientation (RAPTOR) for a variety of 3D tissue cultures. RAPTOR extends CONDOR-ML by including the possibility to change the underlying CONDOR parameters (i.e. to simulate tissues with a range of cell and matrix types). As part of a mould design process, the method could be useful to find ways to grow highly aligned tissues, to minimise tissue tension and also determine suitable matrix properties. Comparison is made with archived data for cultured tissue made from glial cells, tenocytes, myoblasts, corneal stromal cells and dermal fibroblasts. In this paper, we will focus on tissues grown in tethered cell-laden hydrogels, one of several strategies for culturing tissues.

The Contractile Network Dipole Orientation (CONDOR) model is used to find the minimum energy state of the contractile network dipole orientation by simulated annealing. The model comprises cells interacting through a contractile network of bonds, where the total energy of the system is given by Eq. (1):

lij − lij

(1)

The modification to equilibrium bond length l0 by active forces leads to cell-matrix interaction, given by Eq. (2):

∆′ = l0 1 − 2 − l̂ij · si 2 − l̂ij · sj 2

(2)

The training data sets were generated by automatically constructing random mould designs and tether layouts that are then used as inputs to CONDOR simulations. Model parameters varying in the training data set are ∆, κNNN and κNNNN. Values for all three parameters are assigned within the mould generation process for each simulation input. Values for ∆ were generated from a uniform random deviate with fixed range ∆ ∈ [0.05, 0.95). Both κNNN and κNNNN were jointly generated from a 2D uniform distribution with κNNN ∈ [0.1, 0.71) and κNNNN ∈ √[0.01, 0.5), with an additional bound of κNNN ≤ κNNN / 2. A total of 3569 unique simulations were run in parallel on a multi-core machine and were divided into two disjoint sets to be used for training and evaluation of the machine learning model. Of these, 445 were set aside to use as test data, while the remaining 3124 were used in training and validation. Augmentations were applied to the training and validation set, consisting of combinations of multiple transformations applied to both mould shapes and simulation results, including mirroring in both the x and y axes and rotations in increments of 90 degrees. The total number of training and validation examples including augmentations was 12653.

The RAPTOR machine learning approach is adapted from the pix2pix conditional generative adversarial network (CGAN) implemented using the TensorFlow framework, similar to the CONDOR-ML approach in Ref. [12]. The key extension to previous work is the inclusion of the model parameters ∆ and κ as inputs to the machine learning approach. For our implementation 256×256 pixel images were used for input and output. The input consisted of 5 channels representing both the mould design and the simulation parameters: two input layers describe the mould design (depression layout and tether placement, with boolean values), and three additional input layers correspond to the parameters used in the simulation: ∆, κNNN and κNNNN (as 256×256 arrays with a single repeated value of the parameter for compatibility). The output comprised 8 channels predicting the properties of both matrix and cells: cell density (ρi), orientation vector products (s2x,i, s2y,i, s2z,i, sx,i sy,i, sx,i sz,i and sy,i sz, i), and average strain in adjacent bonds (τ ij = τ0 ij /κ0 l0). Results from CONDOR simulations are transformed into a set of continuous 2D distributions to be plotted as 256×256 pixel images for training the machine learning model. The value for a cell property in each pixel (Zp) is calculated using a weighted sum from all nearby cells via Eq. (3):

Zp =

zi wi,p

where zi is an individual cell property and wi,p is the corresponding weight calculated using a multivariate Gaussian density function centered on a cell position.

The predictive capability of the trained RAPTOR model was tested against the test data set of 445 CONDOR simulations. A representative visual comparison shown in Fig. 1 demonstrates good agreement between CONDOR simulation results and RAPTOR predictions for an example mould in the test set, including density P, tension (strain) T, orientation product fields Sx2, Sy2 and Sx Sy. The scatter graphs show very good agreement with high Pearson correlation coefficient (rxy) values.

The aim of this section is to compare CONDOR and RAPTOR results across the parameter space of ∆, κNNN and κNNNN. Overall there is close agreement between both width and area contraction predicted by CONDOR and RAPTOR. The contraction differs primarily for cases with low κNNN, low κNNNN /κNNN and high ∆, with the largest difference seen for ∆ = 0.9, κNNN = 0.1 and κNNN /κNNN = 0.1.

The I-shaped mould examined in this section contains a large continuous tethering bar, which has no analogue within the training data set (all cases involved circular tethers). Figure 6 shows comparisons between contractions from CONDOR simulations and RAPTOR predictions for an I-shaped mould with similar dimensions to those used to grow both glial (Ref. [16]) and corneal tissue cultures (Ref. [17]). The width contraction is underestimated by RAPTOR, with differences becoming worse for large ∆ and small κ. Similar area contractions are predicted by both RAPTOR and CONDOR except for the specific case with ∆ = 0.9 and small κ. Given that there are no cases of extended tethering bars in the training data set, it can be seen that the machine learning algorithm is also capable of extrapolation, but it was unable to learn behaviour in the small region of the parameter space where the contraction overcomes bond stiffness.

The primary purpose of this section is to validate RAPTOR and CONDOR methods against experimental results for a variety of artificial tissue types grown in various tethered mould designs. The secondary purpose is to show how the speed of the machine learning algorithm can be leveraged to determine CONDOR model parameters using a fitting process. The RAPTOR method was used in a non-linear least squares fit to determine the values of ∆, κNNN and κNNNN that most closely match the tissue area and width of the experiments.

In glial tissue, comparisons are made with cultured glial tissue (glial cell populated hydrogels in tethered mould). Good agreement is also found for the width and area ratios determined from RAPTOR and CONDOR and those of the experimentally cultured tissue. All cases shown in Fig. 9 show glial tissue grown under similar conditions.

In fibroblast cultures, the resulting (summarised in Table I) parameter values are ∆ = 0.6578, κ̄NNN = 0.4438 and κ̄NNNN = 0.25261. Figure 10 shows the comparison between the CONDOR simulation and the RAPTOR prediction for the indicated mould shape for the optimised parameters, showing very good visual agreement, though we note a small difference between CONDOR and RAPTOR regarding area and width ratios.

In corneal cultures, we use values provided in Ref. [17] to compare RAPTOR predictions with experimental results. The optimized parameter values are ∆ = 0.8298, κNNN = 0.6465 and κNNNN = 0.06678; the comparison between the CONDOR simulation and RAPTOR prediction shows a small difference between overall density and the central width predicted by each method, with the machine learning model predicting slightly less contraction across the centre of the tissue. Nonetheless, the approach is useful for determining CONDOR and RAPTOR parameters suitable to guide computational design of moulds for 3D corneal stromal cell culture.

In summary, we have presented a machine learning approach for rapid prediction of tissue organisation based on the pix2pix model for a variety of different cell types, and validated the approach for various cultured tissues. The key difference between this and previous work is that CONDOR model parameters can be varied in the new RAPTOR approach. Different cell types and their densities within 3D cultured tissues are associated with different model parameters, so this feature of RAPTOR is essential to make predictions for a range of cell types, cell densities, ECM types or the effects of other factors such as enzymes applied to cultured tissue. We found excellent agreement between RAPTOR and CONDOR predictions and glial, fibroblast and corneal tissue grown in the laboratory. Moreover, we established that RAPTOR can be used to make rapid determination of the CONDOR and RAPTOR model parameters to represent particular cultured tissue types. A non-linear least squares approach using RAPTOR was developed to establish model parameters by matching the areas and widths of RAPTOR predictions to tissues cultured in the laboratory using tethered moulds. These parameters could then be suitable to guide computational design of moulds and tethers using CONDOR or RAPTOR. The speed of the RAPTOR method makes a near realtime design process possible. It also makes automated design through computational intelligence techniques such as evolutionary strategies a possibility. Exploration of this potential will form part of a future paper.

Grid searches show that RAPTOR and CONDOR predictions agree across a large part of the model parameter space. However, the parameter space grids calculated for both CONDOR and RAPTOR also show that for cases with both low κ and high ∆, RAPTOR was not able to precisely represent the highly contracted cultured tissues predicted by CONDOR. We believe that lower representation of cases with strong contraction in the training data set cause the lower contractions predicted by RAPTOR. A machine learning model might be trained using a data set specialised to this small region of parameter space to make more accurate predictions for those cases.

The speed of the RAPTOR method makes a near realtime design process possible. It also makes automated design through computational intelligence techniques such as evolutionary strategies a possibility. Exploration of this potential will form part of a future paper.

The speed of the RAPTOR method makes a near realtime design process possible. It also makes automated design through computational

Improvements for AI systems

Here are the specific improvements to AI systems derived from this research:

Enhanced Predictive Modeling for Tissue Organization: The RAPTOR (Rapid Prediction of Tissue Organisation) approach, a pix2pix-based Conditional Generative Adversarial Network (CGAN), can be integrated into AI systems to predict the spatial organization (cell density, orientation vectors, and tension) of complex 3D cultured tissues.
Parameter-Aware Prediction: The improved RAPTOR system can incorporate underlying biophysical model parameters—specifically the cell-matrix interaction parameter (∆) and spring constants (κNNN and κNNNN)—as explicit inputs to the neural network. This allows the AI to predict tissue properties across a wide range of cell types, ECM types, and physical conditions.
Real-Time Design Tool for Tissue Engineering: The system can be deployed as a rapid design tool that takes an input image of a tethered mould (or scaffold geometry) and predicts the resulting cell organization before physical experimentation or lengthy simulations occur.
Rapid Model Parameter Identification: A non-linear least squares fitting process leveraging the speed of RAPTOR allows an AI system to rapidly determine the specific CONDOR model parameters (∆, κNNN, κNNNN) required to accurately simulate and design moulds for a specific target tissue (e.g., glial, fibroblast, or corneal tissue).
Accelerated Computational Design Workflow: By using RAPTOR for parameter optimization instead of running slow CONDOR simulations during the mould design phase, the AI system can dramatically speed up the computational cycle for generating optimal scaffolds and tethers.
Extrapolation Capability: The model demonstrates an ability to extrapolate beyond its training data (e.g., handling long continuous tethering bars not present in the training set), suggesting that future AI systems can be trained or fine-tuned to handle novel or extreme physical configurations in tissue engineering designs.

By implementing these improvements, the resulting AI system can perform the following specific actions:

Generate high-fidelity, spatially resolved maps of cell density and alignment within a 3D scaffold based on its geometric input.
Quantify mechanical properties like cell tension and strain fields directly from an input image prediction.
Automate the inverse problem: determine the precise physical parameters (∆, κNNN, κNNNN) needed for a biophysical simulation to match experimental tissue outcomes.
Provide near real-time feedback during the design of tissue engineering moulds by predicting how different structural inputs will affect cell behavior.