Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Advances in single-photon sensitive detectors are rapidly expanding the adoption of photon-counting fluorescence microscopy. Under the Poisson photon-counting statistics, iterative Richardson-Lucy (RL) -type algorithms are statistically optimal for image deconvolution but suffers from a fundamental semi-convergent behaviour: prolonged iterations inevitably amplify noise, requiring heuristic early stopping or regularisation typically based on assumptions about object morphology. Here we present a morphology-agnostic regularisation framework for RL deconvolution that exploits independent noise realisations instead of structural object priors. Preserving the Poisson statistics of the acquisition process, we formulate the Regularized by Noise (RbN): a regularized variational framework and its corresponding iterative minimization algorithm that exploit the statistical consistency of independent noise realisations to distinguish reproducible image features from stochastic noise. The regularisation strength is selected automatically using the Poisson residual whiteness principle, resulting in a fully data-driven reconstruction without heuristic parameter tuning. Photon-timing-resolved systems naturally provide the independent noise realisations exploited by our framework, whereas computational photon splitting provides a statistically equivalent implementation for photon-counting systems. We validate the approach experimentally using photon-timing-resolved confocal microscopy and image scanning microscopy across eight morphologically distinct subcellular targets, and further demonstrate its applicability to photon-counting microscopes through computational photon splitting. Across imaging modalities, detector technologies, biological structures and signal-to-noise regimes, our method eliminates RL semi-convergence, removes sensitivity to the stopping criterion, and consistently outperforms conventional RL while preserving fine structural detail. More broadly, our results establish independent noise realisations as a general source of morphology-agnostic regularisation. Although demonstrated here for SPAD-based laser-scanning microscopy and Poisson statistics, the underlying principle could be extended to other imaging modalities and, more generally, to statistical inverse problems through appropriate noise-specific formulations.

Abstract: Compartmental epidemic models conventionally treat the probability of moving between dis ease states as fixed over time, an assumption that sits uneasily with the reality of a pandemic in which lockdowns, mask mandates, vaccination roll-out, and the arrival of new variants continually reshape transmission. This paper develops a time-inhomogeneous Markov chain framework for the Susceptible-Exposed-Infectious-Removed (SEIR) process, in which each transition probability pab(t) is allowed to vary with calendar time while respecting the struc tural zeros implied by the SEIR compartmental flow. We derive the constrained maximum likelihood estimator of pab(t) under these structural constraints, establish its finite sample efficiency, asymptotic normality, and Wilson score confidence intervals, and construct a like lihood ratio test of the null hypothesis that a compartments exit probability is constant over time. We further propose a stochastic machine learning hybrid extension in which the raw, kernel smoothed transition probabilities are regressed on policy and mobility covariates using both a logistic generalized linear model and a random forest, allowing the framework to attribute time-inhomogeneity to observable interventions. The methodology is applied to a compiled daily, district level COVID-19 surveillance panel for Sierra Leone spanning March 2020 to December 2023 (16 districts, 1,401 days). The likelihood ratio test rejects time-homogeneity of the exposed to infectious transition in 15 of 16 districts and of the infectious-to-removed transition in 8 of 16 districts ( = 0.05), and the covariate augmented logistic model achieves an out of sample Brier score roughly 76 times smaller than a time homogeneous pooled baseline, with healthcare capacity and the time trend emerging as the most influential predictors in the random-forest component. These results provide statisti cal evidence that time-inhomogeneous, covariate informed Markov models offer a materially better description of district-level COVID-19 transmission in Sierra Leone than classical time homogeneous compartmental models, with implications for sub-national outbreak monitoring in resource constrained settings

Scientific image sequences often feature recurring structures with unknown appearance and dynamics. While traditional methods using predefined templates, noise models, or motion classes work well when targets are known, such assumptions can hinder exploratory analysis where discovering that knowledge is the primary goal. This work presents a self-supervised framework that maps noisy video into a discrete vocabulary of local states and their spatiotemporal relationships. The method operates without clean targets, pretrained representations, semantic labels, feature templates, or prescribed trajectories, assuming only that informative structures recur for a finite duration within a bounded spatial neighborhood. A temporally masked vector-quantized network predicts the missing central frame from its neighbors, while a masked Transformer refines token assignments by weighing encoder evidence against contextual compatibility. Project-specific token sets define the feature family, while a support model quantifies the temporal evidence for individual occurrences, facilitating optional conservative suppression. The framework is first demonstrated on synthetic videos of moving particles. Without access to clean frames or particle coordinates during learning and selection, the learned states recover compact, point-spread-function-like structures. Tests on low-signal particle-tracking benchmarks yield frame-wise component precision between 87.0% and 94.5%, with recall decreasing as particle density rises. An experimental example using E. coli further shows that discrete states can separate biological structures from illumination and acquisition artifacts. In all cases, the primary outputs are interpretable state, activity, support, and component maps; rendered images serve as diagnostics rather than optimization targets.

The measurement of light received at the cornea of the eye is a paramount consideration for the understanding of the relation between environmental illumination and the non-image-forming effects of light. The field of view (FOV) at the cornea is less than a full hemisphere, because it is partially occluded by human facial morphology. The International Commission on Illumination (CIE) has defined a standard model of human FOV. A suitably designed physical occluder attached to the sensor (of a light meter) has been proposed as a means of incorporating the effect of human FOV when taking measurements. Similarly, when using simulation to predict light received at the cornea, a geometrical description of the occluder at the eye point(s) can be added to the 3D model of the scene. The first occluder model proposed to represent CIE human FOV was enumerated in terms of: the CIE definition; the radius of the occluder; and, the radius of the light sensor disc. We present a simpler model based only on the CIE definition and the occluder radius. Both models were tested using a virtual goniophotometer. Various sensor response functions describing the spatial sensitivity across the sensor disc, including several we characterized through laboratory measurements, were included in the test. For all functions considered, the performance of the simpler occluder model was equivalent to or better than the model first proposed.

Fluorescence lifetime imaging microscopy provides quantitative, concentration-independent contrast for probing molecular interactions, biochemical environments and cellular physiology. However, the requirement to acquire sufficient time-resolved photon statistics makes FLIM inherently slow, limiting its application to dynamic biological processes. In live-cell applications, including calcium signalling and vesicular trafficking, acquisition times can exceed the timescale of the underlying biology, causing temporal averaging, motion artefacts and loss of transient information. Methods that increase FLIM acquisition speed while preserving quantitative lifetime accuracy are therefore required. We report on a high-speed, compressive, multiphoton fluorescence lifetime imaging technique (TomoFLIM). Two-photon fluorescence is excited using a line focus projected tomographically across the sample, while time-tagged fluorescence is acquired using time-correlated single-photon counting. Time-resolved fluorescence data are reconstructed using Lucy-Richardson deconvolution followed by a computationally efficient centre-of-mass method lifetime estimator. In addition, TomoFLIM Net, a physics-informed neural-network, directly reconstructs fluorescence intensity and lifetime from compressed time-resolved tomographic data. TomoFLIM was benchmarked against raster-scanned fluorescence lifetime measurements using calibrated fluorescence lifetime beads and biological specimens. We demonstrate imaging at compression ratios exceeding 90%, with Pearson correlation coefficients above 80% relative to reference images. A raster-scanned FLIM dataset acquired in 60 s was reproduced using TomoFLIM in 3.75 s, representing a 16-fold increase in frame rate and equivalent reduction in accumulated dark counts. TomoFLIM Net recovered distinct experimental bead lifetime populations, demonstrating a direct route from compressed measurements to quantitative lifetime maps. TomoFLIM therefore offers significant potential for rapid live-cell imaging of dynamic biological processes, including deep within turbid biological specimens.

Simulation models are widely used to support counterfactual inference in settings where direct experimental validation is difficult or infeasible. However, for phenomenological models calibrated to observational time series, goodness-of-fit does not necessarily establish that the structural assumptions underlying such inferences are uniquely supported by the data. Here, we examine this issue using a published COVID-19 transmission model for Japan that incorporates empirical inputs including human mobility, variant prevalence, and vaccination and has been used to estimate the effects of alternative vaccination scenarios. Using the publicly archived code together with a reconstructed substitute for a restricted-access input file required by the released implementation, we first reproduced the published model behaviour. We then performed two complementary computational stress tests. First, the vaccination-related input was suppressed and the remaining parameters were re-estimated against the original epidemic trajectory. Second, as a complementary test of trajectory-level flexibility, the model was refitted to synthetic target series with qualitatively different temporal structures while retaining the empirical mobility and variant inputs. The model retained substantial fitting capacity in both tests: suppression of the vaccination-related input caused only a limited deterioration in fit to the original trajectory, while qualitatively different synthetic trajectories could also be reproduced through parameter adjustment. Variation in fitted parameters across these conditions was also consistent with compensatory parameter behaviour. These results do not imply that vaccination had no effect or that the original model is invalid. Rather, they provide empirical evidence that, in this case, goodness-of-fit to the observed epidemic trajectory alone does not uniquely support the structural interpretation required for vaccination-related counterfactual inference. The study illustrates the value of reproducible computational stress testing as a complement to, rather than a substitute for, formal identifiability or model-comparison analyses.

Host immunity acquired through prior infections is a key factor shaping the spread of emerging variants. However, accounting for complete infection histories in mathematical models is challenging because the number of possible histories grows exponentially with the number of variants. Here, we present a flexible framework for modeling the co-circulation of multiple variants emerging at arbitrary times while incorporating cross-immunity and variant-specific characteristics. We introduce three tractable approximations: truncation, which retains only infection histories up to a given number of strains; one variant at a time, which is exact when variants circulation does not overlap; and two variants at a time, which is exact when at most two strains co-circulate. We systematically evaluate these approximations across a range of cross-immunity levels and inter-variant emergence delays. Truncation approximations perform best under short emergence delays and strong cross-immunity, whereas the other approaches outperform them at longer delays. When applied to SARS-CoV-2 variant dynamics, the second-order truncation and the two variants at a time approximation accurately capture incidence patterns, whereas the other approaches perform well only for specific subsets of variants. These results identify the parameter regimes in which simplifying assumptions remain valid, provide guidance for model selection, and highlight the key role of infection history in shaping epidemic trajectories.

Cardiac blood flow is a regulator of several important developmental and remodelling processes in the heart, including through fluid shear forces sensed by the endothelial cells lining the heart. However, optically mapping these flow fields in the complex 3D geometry of the heart is challenging even in transparent animal models such as the zebrafish. One of the main challenges is the difficulty in measuring the out-of-plane (axial) velocity component, preventing accurate mapping of the complete 3-component-3-dimension (3C-3D) blood flow velocity field; image-based techniques such as microscopic particle image velocimetry ({micro}PIV) traditionally only provide the in-plane flow components. Here we present a computational approach to achieve full time-varying 3C-3D blood flow vector mapping using a standard selective plane illumination microscope (SPIM), based on robust cardiac phase assignment, precise measurement-driven registration of sequentially acquired z-stacks, and PIV data fusion from multiple sample orientations. Our approach holds the key to understanding the complex dynamic flow fields within the developing heart, and their role in shaping cardiac development.

Magnetic field effects (MFEs) in biological systems are typically small and experimentally challenging to measure reproducibly across large sample populations. Existing approaches to measure such effects often rely on low-throughput microscopy or custom-built magnetic stimulation systems that provide limited control over magnetic field geometry, synchronization, or experimental automation. Here, we present an open-source magnetofluorescence imaging platform designed for bacterial plate-scale screening of MFEs in live colonies. The instrument integrates a programmable three-axis vector electromagnet, synchronized fluorescence excitation and imaging, and integrated acquisition software with per-frame metadata logging on a hardware-synchronized data acquisition card. An extensive calibration procedure enables accurate generation of arbitrary magnetic field vectors, while synchronized triggering ensures deterministic alignment between field application, illumination, and image acquisition. The system images an entire 100 mm Petri dish in a single acquisition. Typical experiments monitor hundreds of bacterial colonies simultaneously over multi-hour acquisition sequences. Control software, calibration routines, mechanical design files, and acquisition workflows are provided openly to facilitate replication. Instrument performance is demonstrated through detection of magnetic field-dependent fluorescence changes in E. coli expressing the engineered magnetosensitive fluorescent protein MagLOV2. This instrument provides a flexible and scalable platform for high-throughput magnetobiology, synthetic biology, and quantum biology experiments.

The mechanical properties of red blood cell (RBC) membranes are critical to their function in oxygen delivery, and changes to these properties as RBCs age affect their journey around the circulatory system, including clearance by the spleen. Such changes can also have significant health effects,including in cardiovascular disease and on the interactions between RBCs and malaria parasites. The function of RBCs requires them to be very soft, which together with the small size of the cells brings the energy required for measurable deformation of the membrane into the range of typical thermal energies. Red Blood Cells can be observed to flicker under optical microscopy, and these shape fluctuations can be quantified and used to obtain key biophysical parameters such as the tension and bending modulus of the membrane. Typically the shape of the cell's equator is extracted, and the mean power spectrum is obtained by time-averaging the power present in the normal modes of the thermal fluctuations. Flickering spectroscopy has been used extensively on RBCs, but has so far been very low throughput and with some technical limitations. Here we address issues related to active versus passive fluctuations, focusing and optics, camera exposure and sampling, and fast contour detection. In combination with an automated imaging system it is possible to measure thousands of cells in one day, with no user input. We validate this new pipeline by chemical modification of RBC mechanics, and by comparison with simulated fluctuations including each confounding effect. The methods and codes for this robust flickering analysis will allow consistent measurements across labs.

Fourier light field microscopy (FLFM) enables high-speed volumetric imaging by encoding multiple angular perspectives of a three-dimensional sample onto a single image. For this reason, FLFM is well-suited to sparse and rapidly evolving biological systems. To aid in the adoption of FLFM, we present OpenFLR, an open-source software framework for real-time volumetric reconstruction, three-dimensional particle tracking, and calcium image processing using FLFM. OpenFLR reconstruction is distributed as four interchangeable interfaces: a Python library, a command-line script, an interactive web application, and an ImageJ/micromanager plugin, so that the pipeline is accessible to both developers and bench biologists. Building on established Richardson-Lucy deconvolution, we use a hybrid experimental-computational PSF calibration strategy and a triangulation approach to tracking to extract particle positions in 3D directly from raw light field frames, bypassing reconstruction. We validate the complete pipeline on GCaMP6s recordings of freely behaving Hydra vulgaris, tracking sparse populations of neurons as they undergo large three-dimensional displacements.

Disease surveillance data are often sparse, irregularly timed and heterogeneous across observational units, creating challenges for inference in mechanistic epidemiological models. We present observation-masked neural posterior estimation (OM-NPE), a simulation-based Bayesian inference framework for such settings. The approach represents observations on a common temporal grid and records observation availability through a binary mask, enabling heterogeneous surveillance records to be analysed using a single amortised neural posterior estimator. We demonstrate OM-NPE using two contrasting epidemiological systems. First, we fit an effective SEIR model of Zika virus transmission to weekly sentinel surveillance data from six French Polynesian archipelagos during the 2013-14 outbreak. Second, we fit a stochastic compartmental model of Xylella fastidiosa spread to annual disease-severity observations from 17 olive groves in Apulia, Italy, each surveyed only two or three times over seven years. In both applications, OM-NPE recovered epidemiological parameters consistent with the assumed epidemiological and observation models, appropriately represented uncertainty, and generated posterior distributions in well under one second without retraining or Markov chain Monte Carlo sampling. Observation masking extends amortised Bayesian inference to heterogeneous longitudinal surveillance systems and supports rapid evaluation of alternative monitoring schedules.

Chromosome segregation is vital. Its disruption can cause aneuploidy, a hallmark of cancer. Centromere protein A (CENP-A) is an important protein during the segregation as it marks the location of the centromere, where the kinetochore assembles for microtubule attachment. Each mammalian centromere contains hundreds of CENP-A nucleosomes, whose spatial arrangement is expected to be critical for kinetochore function and error-free chromosome segregation. However, previous studies--mostly in fixed cells and focused on metaphase--have yielded conflicting results on CENP-A organization. Given the centromere's sub-diffraction size, we used stimulated emission depletion (STED) super-resolution microscopy to visualize the CENP-A organization in both living (about 45 nm resolution) and fixed (about 30 nm resolution) immortalized human retinal pigment epithelial cells (hTERT RPE-1). We found that CENP-A organization does not adopt a single architecture but spans a spectrum from dense clusters to fragmented subclusters, with mitotic stage-dependent abundance and morphology. CENP-A chromatin is most dispersed in prophase, and progressively compacts during prometaphase and metaphase as microtubules attach. In meta- and anaphase predominantly dense organizations are formed, often with a plate-like morphology. Yet, non-dense and non-plate-like organizations persist through metaphase and anaphase, suggesting CENP-A spatial reorganization is heterogeneous during cell division.

Inferring "whether a change in the expression of a given gene causally affects the disease state" from observational single-cell transcriptomic data is one of the central problems in single-cell biology. The difficulty lies in confounding: cell state, batch, cell cycle, and the co-expression of other genes may all simultaneously influence the target gene (treatment variable T) and the disease label (outcome variable Y), so that naive correlation analysis cannot distinguish causation from covariation. Double machine learning (DML), via orthogonal scores and cross-fitting, allows machine learning to estimate high-dimensional nuisance functions, thereby addressing the causal inference problem in high-dimensional data. Constrained by computational resources, this study takes a small-sample dataset with p{approx}n (2,120 cells, 1,999 background genes) as the experimental testbed and systematically compares three nuisance function construction strategies under this critical condition; strategies for the n>>p regime are then addressed by theoretical argument. Using systemic lupus erythematosus (SLE) peripheral blood memory B cells (GSE189050, 2,120 cells), we construct a three nuisance function construction strategies x (in-sample / cross-fitting) 2x3 factorial experiment and compare them in terms of resolution, biological plausibility, stability, and deconfounding ability in causal effect estimation. The three strategies are: (S1) direct linear nuisance regression on the high-dimensional background genes without dimensionality reduction; (S2) learning a shared low-dimensional representation with an unsupervised autoencoder, with the treatment and outcome residuals sharing that representation; (S3) fitting the treatment and outcome with two independent deep networks. The results yield a clear three-part pattern with mechanistic meaning: (1) both modes of S1 fail; (2) S2 achieves the optimum in-sample and requires no cross-fitting; (3) S3 is "rescued" under cross-fitting and becomes effective. We explain this pattern starting from the convergence rate condition of DML (Sec.5 Theoretical Foundations) and give the applicability boundaries of the two strategies: S2 (shared unsupervised deep learning) achieves estimation quality comparable to standard cross-fitted DML at a tiny fraction of the computational cost, making it a feasible scheme for large-scale screening; S3 (dual networks + cross-fitting), as the standard DML recipe, can serve as a broad-spectrum reference control for S2 results.

This paper presents a two-stage pipeline for implicit feature engineering in time series-based physiological stress detection using electrodermal activity (EDA) signals. In the first stage, we forecast three descriptive statistics of future EDA signals over short horizons (3, 5, and 10 seconds) based on a 60-second context window. In the second stage, a lightweight linear classifier detects stress from these predicted statistics. We evaluate three forecasting architectures spanning the domain expertise spectrum: a domain-specific bidirectional long short-term memory (BiLSTM) recurrent neural network, zero-shot and fine-tuned variants of Amazon Chronos T5 time series foundation model, and the Tabular Prior-data Fitted Network (TabPFN) applied to engineered physiological features. Experiments on the publicly available Wearable Stress and Affect Detection (WESAD) dataset, comprising chest-worn multimodal physiological signals from 15 subjects under baseline and stress conditions, demonstrate that the domain-specific BiLSTM achieves the highest classification performance, with area under the receiver operating characteristic curve (AUC) values ranging from 0.913 to 0.962. TabPFN follows with AUC values of 0.853-0.869, while Chronos variants yield 0.528-0.744. Notably, models using predicted features consistently outperform those using oracle features derived from the true future signals--the theoretical upper bound--suggesting effective noise filtering through learned sequence representations. Chronos models quickly reach performance saturation regardless of training depth, highlighting challenges in tokenizing continuous physiological time series. The proposed approach advances implicit feature engineering for wearable stress monitoring by leveraging forecasting as a powerful inductive bias, thereby improving robustness and providing insights into the limitations of the foundation model for physiological signals.

The lifetime of fluorescent molecules provides an orthogonal readout to fluorescence intensity, opening experimental possibilities of measuring changes in local molecular environments, mechanical tension, and metabolism, among other factors. These changes are best studied live and in vivo; however, limitations of slow imaging speeds, high phototoxicity, and increased data size and complexity have significantly impeded progress on this front. Here, we present a complete and transferable pipeline consisting of a light sheet FLIM microscope and an accompanying machine learning model for data processing that renders long-term and/or high-speed volumetric FLIM (vFLIM) tractable in living systems. We benchmark this pipeline across several biological use cases, model systems, lifetime ranges, and spatiotemporal scales, showcasing a suite of possibilities that our workflow enables. This comprehensive pipeline from imaging to analysis is a crucial step forward towards disseminating the power of live vFLIM to the broader bioimaging community.

Diffusion within the cytoplasm is fundamental to numerous biological processes. Fluorescence recovery after photobleaching (FRAP) is one of the most common method for quantifying molecular diffusivity in living cells using standard laser scanning confocal microscopy (LSCM). However, accurately measuring fast cytoplasmic diffusion (typically >10 m^2/s) is challenging due to rapid recovery kinetics, weak signal-to-noise ratios, post-bleach signal artifacts, and spatial restrictions affecting normalization. While individual challenges have been addressed in specific contexts, a simple and robust framework to quantify cytoplasmic diffusivity remains elusive. Here, we present a FRAP methodology specifically designed to overcome these obstacles. By utilizing the Gaussian function -- the impulse response (ImpRes) of the diffusion equation in an infinite medium -- our approach leverages the full spatiotemporal dataset through a single-equation three-parameter fitting procedure, thus releasing restrictions to small regions of interest and arbitrary initial time-points. The methodology was validated on three datasets of increasing complexity: in silico simulated recovery profiles, in vitro data from FITC-dextran in glycerol solution, and live-cell imaging of free cytoplasmic GFP. Systematic comparison with existing models demonstrates that the ImpRes approach significantly reduces sensitivity to noise and imperfect fluorescence normalization, while remaining robust against short-term biases, such as transient probe photo-activation. Given its robustness under realistic experimental conditions and its ease of implementation, the proposed FRAP methodology provides a reliable tool for quantitative cytoplasmic analysis.

Continuous neural decoding is fragile under nonstationary neural recordings because unconstrained sequence regressors can turn small mapping errors into temporally inconsistent and physically implausible motion. We propose Neural State-Space Dynamic Movement Primitives (Neural SS-DMP), which shifts the inductive bias from the neural encoder to the decoded output space: instead of directly predicting kinematics, the model infers low-dimensional movement-primitive controls and realizes them through a differentiable second-order dynamical generator. This reframes decoding as structured control inference, shrinking the set of admissible trajectories while retaining expressivity through learned forcing inputs. Because a universal motor prior cannot capture subject-specific movement dynamics, we form a personalized generator by blending the base DMP dynamics with behavior-derived subject dynamics estimated solely from training kinematics. Across ECoG and multi-session spiking benchmarks, Neural SS-DMP improves strong offline baselines in accuracy, consistently improves trajectory smoothness, and shows slower degradation on chronologically held-out sessions under an offline window-causal protocol.

The Transport-of-Intensity Equation (TIE) and polarization differential phase contrast (pDPC) exhibit transfer characteristics that limit their use as standalone quantitative phase imaging modalities. TIE provides stable recovery of low spatial frequencies but attenuates fine structure, while pDPC enhances phase gradients but is intrinsically insensitive near zero frequency. We present a hybrid reconstruction framework that combines a single-shot pDPC measurement with an in-focus-defocused TIE image pair and fuses the resulting phase estimates in the Fourier domain using frequency-selective weighting. The illumination geometry is co-designed to enforce angular separation between modalities, enabling high-frequency phase-gradient acquisition in a single exposure while preserving low-frequency sensitivity through low-numerical-aperture symmetric illumination. The proposed method requires three intensity measurements without requiring interferometric stability or sequential asymmetric illumination. Experimental results demonstrate improved phase fidelity across spatial frequencies, reduced halo artifacts, and enhanced recovery of both smooth and fine structural features. This approach provides a compact and robust method that moves towards extended spatial-frequency phase imaging for dynamic and resource-constrained applications.

Background and ObjectiveSimulation of diffusion MRI signals from tissue microstructure is a fundamental problem in quantitative imaging, as it enables controlled study of how cellular architecture influences measured signals. However, physics-based simulations at clinically relevant scales are challenging due to a scale mismatch between imaging and histology: clinical diffusion MRI spans centimeter-scale fields of view with millimeter-scale voxels, whereas histology resolves structure at micrometer scales. Capturing voxel-wise signal formation therefore requires repeated simulations over heterogeneous microstructure, which becomes computationally and memory intensive in classical solvers. We propose a neural operator framework that amortizes this cost by learning local microstruc-ture-signal mappings once and applying them across large tissue regions. MethodsWe train a Fourier Neural Operator on finite-element simulations of histology-derived cell segmentations to predict magnetization fields from diffusivity and permeability maps. The model is embedded in a subdomain tiling strategy that enables scalable inference over whole-slide histology images. Unlike most conventional simulation pipelines, inference operates directly on regular grids derived from cell segmentations and does not require meshing. ResultsThe proposed framework enables simulation of apparent diffusion coefficient maps over 2D liver histology spanning 28.224 mm x 18.144 mm. It achieves over 2,600-fold acceleration compared with CPU-based finite-element simulation, reducing runtime from an estimated 217 days to under 2 hours. The network yields mean relative signal errors of 0.34%-0.43% at high diffusion weighting and 0.03% at low diffusion weighting, with maximum errors below 5%. On manually segmented datasets with greater morphological variability, mean errors increased slightly to 1.37%-1.79%. ConclusionsNeural operators enable computationally practical, mesh-free diffusion MRI simulation by amortizing expensive physics-based computation into a reusable operator applied across local sub-domains. This makes large-scale histology-based diffusion MRI modeling feasible while preserving high accuracy.