Evaluating a Distributed HPC Workflow for Mechanistic Simulation and Neural Surrogate Modelling of Diabetic Wound Healing

Revised proposal draft

P001 Abstract: Diabetes mellitus is a major contributor to chronic ulcer formation, delayed healing, disability and lower-limb amputation. This research will develop a patient-specific computational framework for modelling diabetes-associated chronic ulcer healing using mechanistic modelling, high-performance computing and neural operator learning. A simplified three-dimensional model of the diabetic ulcer microenvironment will represent key processes such as inflammation, oxygen transport, extracellular matrix remodelling and tissue regeneration. Routinely available clinical and wound variables, including HbA1c, haemoglobin concentration, smoking history, wound size and wound depth, will be used to initialise patient-specific simulations. The mechanistic model will be accelerated using HPC to generate synthetic wound-healing trajectories across diverse diabetic ulcer scenarios. These simulations will be used to train a neural operator surrogate capable of rapidly approximating healing trajectories. The project is a computational proof-of-concept and will not claim clinical diagnostic or treatment capability. The expected contribution is a reproducible simulation-to-surrogate workflow that supports future research into diabetic ulcer digital twins and computational precision medicine in South Africa.

Project Outline

P002 Diabetes mellitus is a major contributor to chronic foot ulcer formation, lower-limb amputation and long-term disability worldwide, with a particularly significant impact in South Africa's resource-constrained healthcare system. Healing of diabetic foot ulcers is governed by complex interactions between inflammation, oxygen transport, angiogenesis, extracellular matrix remodelling and tissue regeneration, all of which are influenced by patient-specific factors such as glycaemic control, vascular health and smoking history. Mechanistic computational models provide an interpretable means of studying these biological processes; however, as model complexity increases, particularly in three-dimensional simulations, computational cost becomes a major limitation. This restricts the number of patient scenarios that can be explored and limits large-scale parameter studies needed to better understand wound-healing behaviour. Recent advances in scientific machine learning have shown that neural surrogate models can approximate expensive numerical simulations with significantly lower computational cost. However, surrogate models require large, diverse and high-quality simulation datasets for training. Generating these datasets using computationally expensive mechanistic wound-healing models remains a significant bottleneck. While distributed high-performance computing (HPC) provides a potential solution, there is limited understanding of whether multi-node simulation workflows can efficiently generate sufficiently rich mechanistic datasets for surrogate modelling while preserving the biological fidelity of the original simulations. Furthermore, it remains unclear whether such workflows can support broader analyses, including parameter exploration, optimisation and the identification of recurring wound-healing patterns across diverse patient conditions. This research therefore investigates whether a distributed HPC simulation-to-surrogate workflow can improve the computational scalability of mechanistic diabetic wound-healing simulations while maintaining acceptable surrogate accuracy and biological fidelity. Rather than developing a clinical prediction tool, the research uses diabetic wound healing as a representative biomedical application through which to evaluate the effectiveness of combining mechanistic modelling, distributed HPC and scientific machine learning within a unified computational workflow. The proposed methodology will begin with the development or adaptation of a bounded three-dimensional mechanistic model of the diabetic wound microenvironment representing key biological processes, including inflammation, fibroblast migration, oxygen diffusion, angiogenesis and extracellular matrix remodelling. Patient-specific variables, such as HbA1c, haemoglobin concentration, smoking status and wound geometry, will be incorporated to initialise biologically meaningful simulation scenarios. The mechanistic model will then be parallelised using a hybrid MPI/OpenMP approach to enable efficient execution across multiple compute nodes. Large numbers of simulations will subsequently be performed to generate synthetic wound-healing trajectories representing diverse physiological conditions. The resulting simulation dataset will be used to train a neural operator surrogate model that learns the temporal evolution of the mechanistic simulations. The research will evaluate two principal questions. First, whether distributed HPC significantly improves computational performance compared with conventional simulation workflows, using metrics such as runtime, scalability, speed-up and parallel efficiency. Second, whether the surrogate model can accurately reproduce the behaviour of the mechanistic simulator while substantially reducing computational cost. Surrogate performance will be assessed using measures of predictive accuracy, biological plausibility and agreement with independent mechanistic simulations. The proposed Master's research is a computational proof-of-concept and does not seek to demonstrate clinical effectiveness or develop a deployable clinical decision-support system. Instead, the contribution is an evaluation of a scalable simulation-to-surrogate workflow for mechanistic biomedical modelling, using diabetic wound healing as the test application. The outcomes of this work will provide evidence on the trade-offs between computational efficiency and simulation fidelity, establish a reproducible HPC workflow for scientific machine learning, and lay the computational foundations for future patient-specific digital twin research in computational medicine.

Aim

P003 To investigate whether a distributed HPC simulation-to-surrogate workflow can improve the scalability of mechanistic diabetic wound-healing simulations while maintaining sufficient surrogate fidelity and biological plausibility for future patient-specific biomedical modelling.

Research Objectives

P004 To achieve the proposed aim, the study will pursue the following objectives: 1. Represent the diabetic wound microenvironment by developing a three-dimensional mechanistic model that captures key cellular, biochemical and structural interactions involved in wound repair, including inflammatory response, fibroblast migration, angiogenesis, oxygen transport, extracellular matrix remodelling and tissue regeneration. 2. Incorporate patient-specific clinical information into the mechanistic model by mapping routinely available variables, such as age, diabetes status, HbA1c, haemoglobin concentration, smoking history and wound dimensions, to biologically meaningful model parameters. 3. Develop a scalable HPC implementation of the mechanistic model using hybrid parallel computing and optimisation techniques to enable efficient simulation of large numbers of patient-specific diabetic wound-healing scenarios. 4. Generate a synthetic dataset of patient-specific diabetic wound-healing trajectories representing diverse physiological conditions and wound presentations. 5. Train and evaluate a neural operator-based surrogate model capable of learning the temporal evolution of the simulated wound microenvironment and producing rapid predictions of healing trajectories. 6. Quantify the trade-off between computational efficiency and surrogate fidelity by comparing the HPC-enabled mechanistic simulations against baseline simulation workflows, and comparing surrogate predictions against independent mechanistic simulation outputs using runtime, scalability, accuracy and biological plausibility metrics.

Methodology Planning Notes

P005 • Research approach: This research will adopt a computational modelling and simulation approach to investigate whether a distributed HPC simulation-to-surrogate workflow can improve the scalability of mechanistic diabetic wound-healing simulations while maintaining surrogate fidelity. A bounded three-dimensional mechanistic model of the diabetic wound microenvironment will be developed or adapted as the representative biomedical test case. Patient-specific clinical variables will be incorporated to initialise biologically meaningful simulation scenarios. • Model development: The mechanistic model will represent key wound-healing processes, including inflammatory response, fibroblast migration, angiogenesis, oxygen transport, extracellular matrix remodelling and tissue regeneration. Biological complexity will be deliberately bounded to ensure computational feasibility while retaining the essential wound-healing dynamics required for meaningful evaluation. • Patient-specific parameterisation: Routinely available clinical information, including diabetes status, HbA1c, haemoglobin concentration, smoking history and wound characteristics (e.g., wound area, depth and anatomical location), will be mapped to biologically meaningful model parameters using published physiological and clinical literature. These parameters will define diverse simulation scenarios rather than represent individual clinical patients. • High-performance computing: The mechanistic model will be parallelised using a hybrid MPI/OpenMP implementation. Computational performance will be evaluated against a serial implementation using runtime, speed-up, scalability, parallel efficiency and resource utilisation metrics. Optimisation techniques will be investigated to improve computational performance where appropriate. • Synthetic dataset generation: Large numbers of mechanistic simulations will be performed across diverse physiological conditions and parameter combinations to generate a synthetic dataset describing the temporal evolution of diabetic wound healing. The resulting dataset will support parameter exploration, pattern recognition and surrogate-model development. • Neural operator surrogate modelling: A neural operator-based surrogate model will be trained using the synthetic simulation dataset to learn the temporal evolution of the mechanistic wound-healing model. The surrogate will be evaluated against independent mechanistic simulations to determine its predictive accuracy, computational efficiency and ability to reproduce biologically plausible wound-healing trajectories. • Validation strategy: The research will evaluate two principal aspects of the proposed workflow: Computational performance, by comparing serial and distributed implementations using runtime, scalability, speed-up and parallel efficiency. Surrogate fidelity, by comparing neural surrogate predictions against independent mechanistic simulations using appropriate accuracy metrics, biological plausibility and computational cost. The study will not claim clinical validity or diagnostic capability. • Data source: The primary data source will consist of simulation-generated synthetic data. No patient data will be collected during this Master's project. Any future incorporation of clinical data would require appropriate ethical approval, clinical collaboration and data governance. • Software and computational platform: The mechanistic model, HPC implementation and neural surrogate will be developed using appropriate scientific computing and machine learning frameworks. Simulations will initially be developed and tested on local computational resources before being executed on institutional or national HPC infrastructure, such as the Centre for High Performance Computing (CHPC), where available. • Expected outputs: The project is expected to deliver: - A bounded three-dimensional mechanistic model of diabetic wound healing. - A distributed HPC implementation of the mechanistic model. - A synthetic dataset of mechanistic wound-healing trajectories. - A neural operator surrogate model. - A quantitative evaluation of the trade-off between computational scalability and surrogate fidelity. - A reproducible simulation-to-surrogate workflow that can support future research in computational medicine and patient-specific digital twin development.

Expected Contribution

P006 • This Master’s research will contribute an evaluation of a scalable HPC simulation-to-surrogate workflow for mechanistic modelling of diabetes-associated chronic ulcer healing. The contribution is not the development of a clinical diagnostic tool, but an investigation of whether distributed simulation can generate sufficiently rich wound-healing data for accurate and efficient neural surrogate modelling. • The expected output is a reproducible computational workflow comprising a bounded mechanistic wound-healing model, an HPC-enabled simulation implementation, a synthetic wound-healing dataset, and a neural operator surrogate model. The framework will be evaluated using runtime, scalability, parallel efficiency, surrogate accuracy, biological plausibility and computational cost. • The main research contribution is the quantification of the trade-off between computational efficiency and surrogate fidelity. A successful project would show whether HPC-enabled mechanistic simulation and neural surrogate modelling can reduce computational cost while preserving the wound-healing dynamics needed for future patient-specific modelling, pattern recognition and digital twin research. National Imperatives Alignment • This research aligns with South Africa’s national priorities in health innovation, digital transformation, artificial intelligence, high-performance computing and advanced ICT skills development. Diabetes-associated chronic ulcers place pressure on resource-constrained healthcare systems through delayed healing, repeated interventions and long-term disability. This project addresses the problem at the research level by investigating computational workflows that may support future biomedical modelling of diabetic ulcer healing. • The project contributes to national computational capability by developing and evaluating methods in mechanistic modelling, distributed HPC, optimisation, synthetic data generation, pattern recognition and neural surrogate modelling. These skills are directly relevant to South Africa’s broader goals of strengthening advanced digital research capacity and applying computational engineering to socially relevant problems. • At Master’s level, the work will remain a computational proof-of-concept. It will not claim to be a clinical tool or provide diagnostic or treatment recommendations. Future translation into clinical decision support would require biomedical collaborators, patient data, ethical approval, clinical validation, data governance and regulatory assessment.

Science Engagement

P007 The proposed science engagement activity will involve a short public-facing seminar, presentation or digital explainer on how computational modelling, high-performance computing and artificial intelligence can be used to study complex biomedical problems. Using diabetic wound healing as an accessible example, the engagement will explain how simulations can help researchers explore biological processes that are difficult to observe directly, such as inflammation, oxygen transport and tissue regeneration. It will clearly communicate that the project is a computational research workflow, not a clinical diagnostic or treatment tool. The aim is to improve public understanding of computational medicine and show how advanced engineering methods can support future health research in South Africa.

National Infrastructure Platform

P008 The proposed research will require access to high-performance computing resources for large-scale mechanistic simulations, parameter exploration and surrogate-model training. Initial model development and testing will be conducted on available local or institutional computing resources. Once the workflow has been validated at smaller scale, larger simulation runs may be executed using institutional HPC facilities at the University of the Witwatersrand or, where required, national infrastructure such as the Centre for High Performance Computing, Lengau, through the appropriate application processes. This staged approach ensures that the project remains feasible even before large-scale HPC access is secured.

P009 Technology Transfer or Commercialisation Route

P010 The proposed research is an early-stage computational proof-of-concept and is not intended to produce a commercial product or clinical tool within the scope of the Master’s degree. The primary outcome will be a reusable simulation-to-surrogate workflow that demonstrates the feasibility of combining mechanistic modelling, high-performance computing and neural surrogate modelling for diabetes-associated chronic ulcer research. The longer-term translation pathway could include development into computational research software or, with appropriate clinical collaboration, future decision-support technologies. Such translation would require access to patient data, ethical approval, clinical validation, regulatory assessment, intellectual property evaluation and deployment-focused software engineering. This Master’s will therefore focus on generating research knowledge, evaluating the computational workflow and establishing a platform that can support future interdisciplinary development.

Publication Angle

P011 The anticipated publication arising from this research will focus on the development and evaluation of a scalable HPC simulation-to-surrogate workflow for mechanistic modelling of diabetes-associated chronic ulcer healing. The principal contribution is expected to be the evaluation of whether distributed mechanistic simulation can generate sufficiently rich synthetic wound-healing data for accurate neural surrogate modelling while reducing computational cost. Depending on the final results, the work may contribute to computational bioengineering, HPC for biomedical simulation, scientific machine learning and computational medicine. The specific publication venue will be determined following completion of the literature review and final evaluation of the research contribution.

Aatikah's literature-review note

P012 Below, I have pasted the literature review I conducted, which highlights the research gaps I would like to investigate: (I can email the pdf if needed)

Literature Review

P013 Diabetic Foot Ulcers Diabetic foot ulcers (DFUs) are open wounds of the foot or lower limb that arise in patients with diabetes mellitus through the convergence of peripheral neuropathy, peripheral arterial disease, and impaired immune function, with severity conventionally staged using the Wagner or University of Texas classification systems. Neither classification, however, predicts how an individual wound will actually progress. The reason DFUs resist healing lies in the disruption of every phase of normal repair: sustained hyperglycaemia drives persistent macrophage-mediated inflammation, impairs the angiogenic signalling required to revascularise the wound bed, accelerates advanced-glycation-end-product cross-linking of collagen, and generates oxidative stress that suppresses fibroblast and keratinocyte proliferation [1]. This burden is amplified in South Africa, which carries both the highest national HIV prevalence in the world, 12.7% of the population, and 16.68% among adults aged 15–49 [2], and the highest diabetes prevalence on the African continent, rising from approximately 7% in 2010 to 13% by 2019 [3], against a continental diabetic population projected to grow 129% by 2045 [4]. Across 19 African countries, DFU prevalence is 13%, with 15% of affected patients undergoing major amputation and 14.2% dying during hospitalisation [5]; within South Africa, infected ulcers were the primary cause in 75% of 1,862 amputations recorded across KwaZulu-Natal and Gauteng between 2017 and 2019 [6]. Globally, five-year mortality following ulceration approaches 50%, a figure comparable to several aggressive cancers [7], and the economic toll is similarly severe: South African public-sector diabetes costs are projected to reach ZAR 35.1 billion by 2030, with complications including DFU accounting for nearly half [8], while the wider sub-Saharan regional cost is estimated at USD 19.5 billion annually [9]. Current clinical management, debridement, infection control, offloading, and standardised but retrospective tools such as PUSH and BWAT, characterises a wound's present state without predicting its trajectory. No tool currently available to South African clinicians indicates, at first presentation, whether a given wound is heading toward chronicity.

P014 Mechanistic Modelling of Wound Healing Mechanistic models simulate the biological processes of healing rather than learning statistical patterns, offering interpretability and the capacity to test hypothetical interventions in silico. The earliest tradition is continuum modelling, treating cells and growth factors as density fields governed by reaction–diffusion partial differential equations, beginning with Sherratt and Murray's model of epidermal re-epithelialisation [10] and extended to dermal wound contraction [11] and angiogenesis [12]; Vermolen provides a comprehensive review of this PDE-based tradition [13]. Continuum models are mathematically tractable but cannot represent the discrete, stochastic behaviour of individual cells. Cellular automaton (CA) and agent-based models (ABMs) close this gap by representing each biological entity explicitly. Parallelised CA approaches have been used for clinically-scaled tumour simulation, establishing that domains of clinical relevance require parallel computing even for cell-based formalisms [14]. Among ABM platforms, CompuCell3D implements the Cellular Potts formalism on a lattice [15]; PhysiCell is an off-lattice, physics-based simulator that scales linearly with cell count under OpenMP, supporting up to 10⁶ cells on a single compute node [16]; and the Wound Environment Agent-Based Model (WEABM) is the most biologically complete wound ABM published to date, modelling macrophage polarisation and fibroblast-to-myofibroblast transition at voxel resolution for volumetric muscle loss injury [17]. The general-purpose platforms BioDynaMo and TeraAgent demonstrate that agent-based simulation scales to roughly 1.7 billion agents under OpenMP and 500 billion agents under MPI respectively [18], [19], but neither implements wound biology. Across these platforms, the biological processes consistently modelled are fibroblast chemotaxis and proliferation, parameterised by a measured PDGF diffusion coefficient of approximately 0.01 mm² h⁻¹ and a maximum migration speed of 0.1 mm h⁻¹ [20]; macrophage-mediated inflammatory signalling, governed by cytokine diffusion on the order of 10⁻⁸ cm² s⁻¹ [21]; angiogenic sprouting; and collagen deposition and remodelling. The shared strength of this body of work is mechanistic fidelity; its shared weakness is computational cost. A three-dimensional, cellular-resolution simulation of a clinically relevant 2 mm × 2 mm × 0.5 mm wound contains approximately two million agents and requires roughly 90 minutes of wall-clock time per run on a single workstation [16], a cost that has confined essentially all published wound ABMs to small, two-dimensional domains and prevented the generation of the large, diverse simulation ensembles a clinical prediction tool would require.

P015 High-Performance Computing in Computational Biology High-performance computing removes precisely this constraint by distributing both memory and computation across many nodes. HemeLB, a lattice-Boltzmann blood-flow solver for patient-specific vascular geometries, illustrates the scale this enables: near-linear strong scaling to 32,768 CPU cores and a peak throughput of 29.5 billion lattice-site updates per second [22], [23], with GPU acceleration extending this toward full human-scale, exascale simulation [24]. In computational oncology, Cytowski and Szymanska's Timothy framework uses MPI domain decomposition with ghost-cell halo exchange to simulate approximately 10⁹ cells across tissue volumes of roughly 1 cm³ [25], a communication pattern structurally identical to that required for a distributed wound-healing ABM. Within South Africa, the most directly relevant precedent is the NRF-funded, Stellenbosch-based agent-based model of tuberculosis granuloma infection [26], which establishes both the scientific legitimacy and the funding precedent for mechanistic ABM research nationally, and which runs on the same CHPC Lengau infrastructure, over 33,000 CPU cores on FDR/EDR InfiniBand, freely available to South African academic researchers, that a distributed wound-healing simulator would target. HPC matters here for two compounding reasons: it removes the runtime wall, reducing the single-machine ensemble-generation taskfrom roughly a month to under a day across a few dozen distributed ranks, and it removes the memory wall, since the aggregate RAM of even a modest cluster exceeds what any single workstation can offer, enabling the full three-dimensional, cellular-resolution domains that current wound ABMs cannot reach.

P016 Surrogate Modelling Even HPC-accelerated mechanistic simulation is too slow, minutes, not milliseconds, for real-time clinical use; surrogate models close this final gap by learning a fast approximation of the simulator from its own output. Physics-informed neural networks (PINNs), introduced by Raissi et al., embed the governing partial differential equation directly into the network's loss function, constraining predictions to remain physically consistent and reducing the volume of training data required [27]. Where governing equations are not fully known, or are agent-based rather than continuum, neural operators offer an alternative: rather than mapping fixed-size vectors, the Deep Operator Network (DeepONet) of Lu et al. learns a mapping between function spaces directly from input–output simulation pairs, via a branch network encoding the input condition and a trunk network encoding the spatiotemporal query point [28]. DeepONet has already been applied to wound contraction: Husanovic et al. trained a surrogate on finite-element post-burn contraction simulations, achieving R² = 0.99 and speedups of up to 128× on CPU and 235× on GPU, but using only three distinct training wound shapes, a narrow basis for clinical generalisation [29]. Papapanagiotou et al. evaluated neural-network surrogates, including PINN variants, for a single-machine, two-dimensional burn-immune-response ABM [30], while Comlekoglu et al. demonstrated a U-Net surrogate for a Cellular Potts vasculogenesis model achieving a 590-fold speedup over native execution [31]. The Fourier Neural Operator of Li et al., which learns input–output mappings directly in frequency space, offers a natural architectural comparator to DeepONet for problems with rich spatial structure [32]. Collectively, this literature establishes that operator-learning surrogates can reproduce complex biological simulation dynamics at a fraction of the runtime cost, but no published surrogate has yet been trained on an HPC-generated, three-dimensional, diabetes-parameterised wound ensemble.

P017 Research Gap Three research traditions therefore each stop short of what a clinically usable tool requires. Mechanistic wound models are biologically expressive but computationally confined to small, single-machine domains; even WEABM, the most complete of them, models volumetric muscle loss rather than diabetic ulceration and has no surrogate coupling [17]. HPC-scale agent-based platforms prove that MPI-distributed biological simulation is feasible at enormous scale, but BioDynaMo and TeraAgent implement no wound biology at all [18], [19]. Surrogate models prove that fast, accurate operator-learning approximations of biological simulators are achievable, but existing wound surrogates are trained on narrow, single-machine, non-diabetic datasets [29]–[31]. No published work integrates patient-specific calibration, mechanistic three-dimensional modelling, distributed HPC, and surrogate learning within a single workflow for diabetic wound healing, and, to the author's knowledge, no computational wound-healing research of any kind has yet been conducted in South Africa, despite the country possessing the infrastructure, the methodological precedent [26], and arguably the world's most acute combined diabetic and HIV-related wound burden in which to apply it. This Masters aim to address that integration directly: developing an MPI+OpenMP-parallelised, three-dimensional, diabetes-parameterised wound-healing ABM on CHPC Lengau or the Wits cluster, using the resulting simulation ensemble to train a DeepONet surrogate, and validating both against clinical data. The gap identified here is not merely academic, every percentage point in the amputation and mortality statistics represents a patient for whom an earlier, evidence-based intervention might have changed the outcome.

References

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