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

Optical microscopy is fundamental to modern life-science research, yet interpreting its results requires precise modelling of point spread functions (PSFs) within complex environments. This manuscript introduces a versatile and efficient approach to wave-optical PSF calculations that extends existing frameworks by incorporating detection PSF modelling through the principle of reciprocity. Accompanying this work is a free MATLAB software package centred on a single, minimalistic core function, PlaneWaveExc.m, which utilizes a plane-wave superposition based on the Richards-Wolf model. Despite its simplicity, the framework accounts for "real-life" complexities such as systemic aberrations, arbitrary amplitude and phase modulations, and stratified media with complex-valued refractive indices. We demonstrate the softwares broad applicability through diverse case studies, including single-molecule imaging, STED microscopy, the segmented aperture of the James Webb Space Telescope, and coherent wide-field iSCAT microscopy. Each example is supported by dedicated scripts to facilitate adaptation for specific research needs.

Optogenetics enables experiments in out-of-equilibrium conditions to clarify biological mechanisms and quantify biophysical parameters. However, modelling and control techniques to study mammalian cell biology under optogenetic perturbation remain underutilised. Here, we benchmark these methods within mammalian cells by steering nucleocytoplasmic transport via the optogenetic LEXY protein in outcome-driven microscopy. First, we employ system identification to obtain models that predict transport dynamics by minimising the prediction error. We quantify this prediction accuracy for one biophysical model and two black-box models. Second, we evaluate closed-loop control efficacy by steering transport along a predefined trajectory using model-free Proportional Integral (PI) control, model-based Linear Quadratic Regulation (LQR) and Model Predictive Control (MPC). Both the predictive models and the applied control techniques demonstrate robust performance against cell-to-cell variation. This biological variation is quantified by the parameter distributions obtained from model identification with single-cell trajectories. While we show that model-free techniques such as PI and gain-scheduled PI achieve steering without explict model knowledge, predictive architectures offer better performance under this cell-to-cell variation and time-varying setpoints. Moreover, black-box predictive accuracy suggests that this model-based control is possible, even when explicit mechanistic understanding is missing. Ultimately, we demonstrate that predictive modelling and optogenetics enable quantitative characterisation and precise manipulation of mammalian cells, while offering practical guidelines for the implementation of these techniques.

We introduce a workflow to identify oligomeric structures that are recorded with single-molecule localization microscopy (SMLM) under cryogenic conditions. Typically, these oligomers are assumed to consist of protomers arranged as equilateral two-dimensional polygons and every protomer is labeled with a dye molecule for visualization. Unlike previous work, we consider scenarios in which the sample plane has an unknown orientation relative to the focal plane. Our contribution is a high-precision plane-fitting algorithm to determine the sample plane, combined with geometrical transformations and two circle-fitting algorithms to identify the oligomeric structures. Our simulations on synthetic data demonstrate that the proposed workflow achieves high accuracy in estimating both the unknown tilted plane and the oligomer size.

Superspreading events (SSEs) produce extreme, rare bursts of disease transmission that standard compartment models, which assume population homogeneity, fail to capture. This inability to model heterogeneity in transmission rates can result in biased estimates of transmissivity. To address this limitation, we present a modular framework that treats SSEs as statistical outliers in case count time series and incorporates them into SIR-type models via pulse terms that transfer SSE cases directly from susceptible to infected compartments. This separation isolates anomalous SSE-driven transmission from background spread, which reduces bias when estimating mean transmission rates. We validate the approach on synthetic data generated by a stochastic model with embedded SSEs, demonstrating accurate recovery of the true non-SSE transmission parameter. We then apply the method to COVID-19 outbreaks in Hong Kong and the German district of Gutersloh, showing improved model fits and more robust estimates of background transmissivity both for a period with constant transmission and for a period with temporally structured NPI-driven heterogeneities. The framework's interchangeable outlier-detection, compartment, and SSE modules make it adaptable to diverse diseases and data contexts.

The spatial resolution of optical imaging systems is fundamentally restricted by the diffraction limit. However, in widefield live-cell microscopy, the achievable resolution is further constrained by the specimen motion, which indicates the existence of a fundamental spatio-temporal resolution trade-off between signal accumulation during the full frame integration and the resulting motion blur. To improve the fidelity with which moving objects can be imaged, a quantitative understanding of this spatio-temporal trade-off is necessary. Here, we present a systematic analysis of motion-induced resolution dynamics measured with spectral signal-to-noise ratio (SSNR). We developed a simulation framework which models the image formation of objects undergoing arbitrary motion, to evaluate the degradation of the spatial resolution under translational and rotational dynamics. Our results demonstrate that for translating objects, the spatial resolution is anisotropically reduced as a function of the orientation of the object relative to the motion vector, leading to the spectral signal-to-noise ratio degrading by up to 50% and the resolution by up to 40% for a 90{degrees} change in the motion direction. Furthermore, we show that for rotational motion, conventional radially averaged metrics such as the Fourier Ring Correlation are not able to quantify the effects of angular blur. On the other hand, the SSNR is able to accurately quantify this degradation. These findings underscore the necessity of an object-oriented imaging approach, in which acquisition parameters such as exposure time are tuned to specific biological spatio-temporal characteristics to optimize the trade-off between motion blur and spatial fidelity.

Approximate Bayesian computation sequential Monte Carlo (ABC-SMC) propagates its particles with a perturbation kernel, and with the standard Normal kernel it degrades sharply as the parameter dimension grows, a failure usually attributed to dimension itself. We show instead that it is governed by the quality of the summary statistics, with dimension entering only through a separate and milder mechanism, and that the two must act together for the Normal kernel to break. The first ingredient is covariance overinflation: the kernel covariance, estimated from the particle cloud, overshoots the true posterior covariance by a factor set by information loss in the summary statistics. We derive this overscaling factor in closed form for a Gaussian model with sufficient statistics and show that it stays modest at any dimension, shrinking toward its baseline value as the tolerance tightens; the extreme values seen in practice (of order 103) are a signature of insufficient summaries, not of dimension. The second ingredient is perturbation overconcentration: the normalised Normal step size concentrates around one as the dimension grows, so every proposal overshoots by the same factor. Either ingredient alone is harmless; only their combination breaks the Normal kernel. A Cauchy kernel (multivariate t with one degree of freedom) removes the concentration, keeping a positive acceptance rate under arbitrary overscaling at a bounded worst-case cost of 1.87x in expected squared jump distance. In a Metropolis-Hastings framework we derive closed-form acceptance rates for both kernels that illustrate the advantage of the Cauchy kernel in this limit. A series of full ABC-SMC computational experiments on five problems at d = 12, including a hierarchical gene-expression model, show the Cauchy reducing the sliced Wasserstein distance to the reference posterior by factors of up to 50 with the same simulation budget. Since the summary statistics are commonly insufficient for the models that require ABC, overinflation is structural and the Cauchy perturbation kernel is the right default for problems in higher dimensions.

Surface electromyography (sEMG) is the most practical non-invasive interface for myoelectric prostheses, exoskeletons, and rehabilitation systems, but power-line interference (PLI) contamination and excessive digital pipeline group delay still limit its clinical adoption. This paper proposes a co-designed analog-digital correction system combining a high-CMRR front-end with an exponentially-windowed RMS (EMRMS) envelope estimator and a recursive single-tone PLI canceller. We present a closed-form CMRR model capturing the electrode-skin imbalance, and provide a complete stability analysis of the LMS canceller. The EMRMS estimator reduces the computational overhead from[O] (L) to strictly[O] (1) in both time and space complexities. Featuring no data-dependent branching, the algorithm achieves deterministic algorithmic execution time (zero jitter under an RTOS environment) and is natively compatible with fixed-point arithmetic on microcontrollers lacking a hardware Floating-Point Unit (FPU). A reference implementation reaches an 8.2 {micro}s median per-sample latency, yielding an end-to-end delay of[~] 30 ms -- leaving a generous >90 ms budget for electromechanical actuation -- while requiring an active CPU duty cycle of merely 1.6%, enabling prolonged deep-sleep intervals. Validation on the public Ninapro DB2 dataset demonstrates a 13.9 dB mean SNR improvement (averaged across 12 channels; single-channel comparison: 9.7 dB, Table 3) and a 70.0 {micro}V envelope RMSE against a length-200 rectangular reference. Paired Wilcoxon signed-rank tests confirm statistical significance (p < 0.001) over static baselines, and Pearson correlation analysis ({rho} = 0.993 {+/-} 0.0002) confirms strict morphological fidelity. The full open-source codebase and benchmarks are publicly released. O_TBL View this table: org.highwire.dtl.DTLVardef@299dc5org.highwire.dtl.DTLVardef@3519a0org.highwire.dtl.DTLVardef@2586aborg.highwire.dtl.DTLVardef@1ac5610org.highwire.dtl.DTLVardef@1465c46_HPS_FORMAT_FIGEXP M_TBL O_FLOATNOTable 3:C_FLOATNO O_TABLECAPTIONQuantitative comparison on a common 60 s segment of Ninapro-like synthetic sEMG (single channel) with a 3 mV 50.3 Hz mains tone slightly drifted from the static notchs design centre at 50.0 Hz, stress-testing the adaptive corrector under a frequency mismatch. The Ninapro multi-channel aggregate (13.9 dB) reported in Section 3.4 uses mains exactly at 50 Hz (matched notch) and so achieves a higher {Delta} SNR. "MAC/sample" excludes the EMRMS square root and the pre-computed LMS sine/cosine. C_TABLECAPTION C_TBL

Stochastic epidemic models are a cornerstone of infectious disease epidemiology and are often used to study intervention scenarios. However, large run-to-run variability can make intervention effects difficult to estimate precisely. We revisit the epidemic Sellke construction, which assigns each individual an infection threshold for the cumulative infection hazard such that, conditional on the thresholds, the epidemic trajectory becomes deterministic. This enables coupling of simulations with and without an intervention, yielding low-variance effect estimates even when outcomes such as final size or peak incidence vary widely between runs. We develop an exact, event-driven implementation that maintains infection and recovery events in priority queues. Cumulative infection-hazard updates require O(log N) time per event, yielding overall complexity O(Elog N) for E events in a population of size N. The implementation achieves computational performance comparable to the classical Gillespie algorithm while naturally accommodating non-Markovian infectious periods and complex infectiousness profiles. We illustrate the approach using distance-dependent spread of avian influenza between poultry farms in the Netherlands and a multilayer population with households, schools, and workplaces. In both examples, coupling enables efficient within-run comparisons of intervention scenarios across stochastic realisations.

Parameter estimation in nonlinear biological dynamical systems is a difficult inverse problem because the governing equations are often stiff or oscillatory, the data are sparse and noisy, and the objective landscape is non-convex. Physics-informed neural networks (PINNs) offer an alternative to purely simulation-based calibration by representing state trajectories with neural networks while penalizing violations of the governing equations. This paper studies the empirical reliability of PINNs for recovering the parameters of the repressilator, a synthetic genetic oscillator formed by three cyclically repressive genes. We use synthetic time-series generated from the standard ordinary differential equation model and train inverse PINNs to estimate the production parameter {beta} and the Hill coefficient n. The study varies observation noise, partial observation of repressors, sampling density, sensitivity to initial parameter guesses, and the difference between stable and oscillatory regimes. The results show that PINNs can reconstruct trajectories accurately when the model structure is correct and the three repressors are observed, but parameter recovery is more fragile than trajectory fitting. Noise, sparse sampling, unobserved variables, and unfavorable initial guesses increase the risk of biased estimates. The stable regime is easier to reconstruct, whereas the oscillatory regime provides richer information but also exposes optimization sensitivity. These findings support PINNs as a useful reverse-engineering tool for small gene-regulatory ODE models, while highlighting the need for repeated runs, uncertainty reporting, and experimental designs that improve identifiability.

Ordinary differential equation models of biochemical reactions are often formulated as stoichiometric systems in which the dynamics arise from a collection of interacting processes. A central challenge is that the functional form of each process is rarely known a priori and may be difficult to infer from data. We propose biochemically informed neural ordinary differential equations (BINODEs), a neural-ODE framework that retains the stoichiometric structure of mechanistic models while representing individual processes by neural networks. In BINODEs, the outputs of neural network processes (NNPs) are mapped to state derivatives through a linear layer analogous to a stoichiometric matrix. This architecture allows biological side information, such as process-specific inputs, sign constraints, and monotonicity assumptions, to be built directly into the model. We characterize the approximation properties of NNPs for several standard biochemical rate laws and show that the proposed framework recovers both trajectories and process-level structure in Monod, Lotka-Volterra, pharmacokinetic, and ultradian endocrine models. These results suggest that BINODEs offer a useful compromise between mechanistic interpretability and data-driven flexibility for modeling partially known biochemical or biological dynamical systems.

Three-dimensional fluorescence microscopy often exhibits anisotropic resolution because axial information is poorly sampled and more blurred than lateral information, which complicates quantitative interpretation of fine 3D structures. Although optical remedies and computational restoration have been explored, many approaches require demanding system calibration or rely on accurate PSF models and assumptions that are difficult to satisfy across all samples and modalities. Here we present DeepIso, a self-supervised isotropy restoration framework that couples supervised pretraining with an internal-learning inference stage to estimate degradation directly from the measured volume. Without explicit PSF specification or enforced lateral-axial structural equivalence, DeepIso recovers axial frequency content and improves the continuity of elongated structures while retaining fine features, with superior performance over existing computational approaches in terms of both visual inspection and quantitative metrics. The method is validated on synthetic benchmarks and experimental datasets, demonstrating isotropy enhancement across confocal, light-sheet, and 3D structured illumination microscopy, thereby supporting downstream volumetric analysis including segmentation and tracking.

AO_SCPLOWBSTRACTC_SCPLOWEarly tumor detection is critical for improving patient survival and recovery. Clinically, tissue palpation is routinely used to identify regions of abnormal stiffness, a hallmark of many pathological conditions. However, palpation is restricted to anatomically accessible sites and remains highly operator dependent. Here, we introduce a method for real-time quantitative stiffness mapping using an unmodified commercial endoscope, with the goal of enhancing diagnostic capabilities and restoring mechanical feedback during endoscopic procedures. Our approach combines shear wave elastography with speckle imaging and an innovative synchronization strategy that enables the measurement of shear wave propagation using an unmodified commercial endoscope. The resulting wave fields are analyzed with the noise-correlation-inspired (NCI) method[1], providing pixel-wise estimates of shear wave velocity and, consequently, quantitative maps of local tissue stiffness. The method demonstrated robust performance in both benchtop and endoscopic configurations. Validation was achieved on polymer phantoms as well as on ex vivo and in vivo biological tissues, highlighting its potential for minimally invasive biomechanical imaging and real-time tissue characterization.

Quantum kernel methods offer a potential advantage for classification tasks in high-dimensional feature spaces, yet their practical benefit critically depends on how input features are prepared. We compare five dimensionality reduction strategies--principal component analysis (PCA), Gaussian random projection (RP Gaussian), sparse random projection (RP Sparse), partial least squares (PLS), and uniform manifold approximation and projection (UMAP) -- as pre-processing steps for quantum kernel support vector machines (SVMs) applied to trabecular bone classification from synthetic micro-computed tomography (micro-CT) data. Using a custom procedural generator based on Gaussian random field zero-crossings, we produced 500 synthetic trabecular bone volumes with controlled morphometric properties such as bone volume fraction (BV/TV), trabecular thickness (Tb.Th), number (Tb.N) and spacing (Tb.Sp). Texture features extracted from grayscale slices are reduced to 8-dimensional quantum circuit inputs via each method, then classified using both classical radial basis function (RBF)-SVMs and quantum kernel SVMs with ZZ feature maps on a statevector simulator, both evaluated with 5 x 5 repeated stratified cross-validation (25 folds). Our results show that UMAP is the only reduction method where the quantum kernel remains competitive with the classical baseline. Under repeated cross-validation, UMAP showed a +0.032 accuracy gap favouring the quantum kernel (Dietterich 5 x 2 CV p = 0.177); however, validation on 10 fully independent datasets--each with independently generated samples, separate reduction fits, and separate kernel matrices -- reversed the sign to -0.030 (paired t-test p = 0.123; Wilcoxon p = 0.193; quantum wins 3/10 datasets), indicating that the apparent advantage was likely inflated by fold dependence. Nevertheless, UMAPs gap remains small and non-significant in both analyses, whereas all linear methods (PCA, RP Gaussian, PLS) show substantial quantum deficits of -0.090 to -0.116 across BV/TV classification, with PCA and PLS remaining significant under corrected tests (5 x 2 CV p = 0.004 and p = 0.007 respectively). We additionally evaluate quantum kernel ridge regression for continuous morphometric prediction, finding that ZZ quantum kernels fail uniformly at regression (negative R2 for all methods except PLS at 4 qubits), suggesting that the ZZ kernel captures decision boundaries but not smooth metric structure. These findings provide practical guidance for feature engineering in near-term quantum machine learning pipelines and demonstrate that the choice of dimensionality reduction can determine whether quantum kernels remain competitive with classical baselines.

Infectious disease dynamics can be inferred from pathogen genomic data using phylodynamic methods, but the applicability of many such approaches to large data sets is constrained by computational cost. Recent deep-learning approaches to phylodynamics have improved scalability, yet challenges remain when genetic divergence is limited during fast spreading outbreaks. To address this, we use pathogen-specific models to show that deep-learning models trained on outbreak-like phylogenies can accurately estimate the reproductive number (R) when both the birth-death model and the expected phylogenetic resolution are matched to the target pathogen, highlighting the importance of realistic training conditions. Focusing on three major respiratory pathogens of public health importance (SARS-CoV-2, seasonal human influenza virus, and respiratory syncytial virus (RSV)), we introduce PhyloRt, a scalable framework for estimating the time-varying reproductive number (Rt) from large outbreak phylogenies. PhyloRt decomposes large trees into overlapping subtrees and applies a hierarchical deep-learning-based inference strategy to classify subtrees as exhibiting constant or time-varying reproduction numbers, enabling identifiable and computationally efficient estimation of Rt as a piecewise-constant trajectory through time. Applications to SARS-CoV-2 and influenza outbreaks show that PhyloRt recovers transmission dynamics consistent with estimates derived from mathematical epidemiological and Bayesian phylodynamic analyses. Our work enables scalable and rapid estimation of time-varying transmission dynamics from very large-scale outbreak genomic data sets, supporting real-time genomic epidemiology of emerging pathogens. SignificanceEstimating changes in transmission dynamics over time is important for responding to infectious disease outbreaks. Current methods mostly rely on reported case data from epidemiological surveillance, which can be biased or incomplete due to variable testing capabilities, particularly in resource-limited settings. A complementary approach is to use viral genomes as an alternative data source. However, inferences from genomic data can be computationally intensive and have mainly been applied retrospectively. We present PhyloRt, a scalable deep-learning-based phylodynamic framework that enables fast inference of the time-varying reproductive number (Rt) from large outbreak phylogenies. Our approach is widely applicable and provides a practical approach to monitoring epidemic dynamics, complementing traditional surveillance and supporting timely public health decision-making.

Microscopes are essential tools for discoveries on a scale invisible to the unaided human eye. The development of immuno-fluorescence followed by molecular biology techniques and fluorescent fusion proteins have revolutionised the use of optical microscopy in bioscience. The quality of the data produced is dependent upon the sample, its preparation and the instrument used. However, instruments can degrade over time without easily visible changes to the produced images and, in turn, negatively impacts results. By testing instruments and doing comparisons between results over time and between different instruments, problems can be highlighted and corrective action can be taken. Using small fluorescent beads the point spread function (PSF) of the microscope can be recorded and the image resolution measured. Beads were prepared in a concentration matched to the field of view size and dried onto coverslips and mounted on slides. The beads were then imaged as 3D Z-stacks of sufficient size to fully enclose the PSF of the system. This data was uploaded to OMERO and processed using OMERO-metrics, an OMERO plugin developed for this purpose. This paper summarizes the development of workflows and protocols to enable this process, presents the results obtained and demonstrates the detection of significant instrument issues.

Optical fluorescence microscopy enables visualization of biological structures and dynamics. However, the intrinsic diffraction limit, especially axially, and depth-related scattering noise compromise the image resolution and fidelity. Computational 3D deconvolution is a promising approach for mitigating these issues, yet its execution is hindered by inaccurate and cumbersome theoretical modeling or experimental measurement of 3D point spread function (PSF), as well as ineffective 3D noise regularization. Furthermore, in the 3D super-resolution regime, there remains a lack of standardized tools for evaluating 3D super-resolution fidelity. Here, we present the 3D adaptive deconvolution and evaluation (3D-ADE) toolkit, which comprises 3D-Ada deconvolution with physics-oriented automatic 3D-PSF calibration, and 3D-SQUIRREL for 3D super-resolution quality assessment. It effectively resolves noise instability, eliminates the need for 3D-PSF calibration, and reliably assesses the fidelity of 3D resolution extension via deconvolution, physical, and deep-learning-based methods. Accessible via multiple software platforms, 3D-ADE enhances the versatility of 3D deconvolution and fills the gap in 3D super-resolution evaluation tools, and thereby advances volumetric fluorescence imaging applications.

The incidence rate ratio R is the standard measure for comparing event rates in clinical trials and epidemiology. In vaccine trials, the vaccine efficacy is VE = 1 - R. When events are rare, the two arm counts are Poisson. The estimator of R is heteroskedastic: its sampling variance changes with the data. So no fixed-width interval covers correctly everywhere. The usual log-Wald interval is undefined at zero events and covers poorly at small counts. Early vaccine and drug-safety readouts fall in exactly this regime. We show that a single reparameterization collapses this bivariate problem to an effective one-parameter family with a quadratic variance function, whose variance-stabilizing transformation is 2 arcsinh(sqrt(R)). The reduction yields a closed-form confidence interval for R. Its two leading errors, a curvature bias and the variability of the estimated scale, each admit a closed-form correction with no tuning constants. In a Monte Carlo study of our seven arcsinh variants and five competitors, the +Curve+Stu variant covers within 0.002 of the nominal 0.95 for about 50 control and 5 treatment events. Its width is on par with the best competitor. It avoids the conservatism and zero-count breakdown of log-Wald and MOVER. For moderate counts, we recommend this interval; for sparser data, our Bar-Lev and Enis count-shift variant is more robust. The result is a ready-to-use, closed-form interval for the low-count regime. We illustrate it on early Covid-19 vaccine-efficacy readouts and provide reference implementations in R and Python.

Uncertainty quantification (UQ) in computational heart models is essential for reliable cardiac digital twins (DTs) in personalized medicine, yet remains challenging. Traditional Monte Carlo and stochastic Galerkin methods often become impractical in the high-dimensional, nonlinear state variable and parameter spaces of cardiac electrophysiology and mechanics. This article introduces a framework for learning a joint probability density over cardiac observables and model parameters, enabling the characterization of statistical dependencies across a large number of variables in patient-specific cardiac DTs. By sampling from this density and conditioning on available data, useful predictive distributions can be constructed, allowing uncertainty to be propagated through the model and quantified in terms of variability. Conditional regression can then be performed directly on this learned density, enabling systematic exploration of interdependencies among observables for both predictive inference and model design. The statistical methodology adopts a geometry-aware generative learning framework, recently introduced by the authors, that decouples the learning of data geometry from sampling. First it identifies a low-dimensional latent representation that captures the intrinsic structure of the data and its multiscale geometric features. A stochastic differential equation is then formulated directly in the low-dimensional latent space to generate samples efficiently; these are subsequently mapped back to the high-dimensional space of cardiac states and parameters through a smooth lifting operator. We demonstrate the approach on a ventricular arrhythmia prediction benchmark, where the learned joint probability density enables the construction of predictive distributions over key parameters (e.g., conductivities, fibrosis patterns) through sampling and conditioning. This enables uncertainty to be propagated and quantified through sampling and conditioning on the learned joint density, with substantially fewer model evaluations than conventional UQ methods.

For decades, the photon counting histogram (PCH) was used as the sole method to quantify fluorophore numbers in a diffraction-limited focal volume. This technique combines spatial excitation profiles, and the distribution of photon counts to register the photon emission statistics of individual fluorophores. However, this approach has not yet been transferred to widefield fluorescent imaging due to the lack of fast and single photon sensitive camera sensors which can capture the photon emission statistics of a single fluorophore. Here, we explore avenues towards quantitative analysis of the active fluorophore number by leveraging recent advancements in single photon avalanche diode (SPAD) array technology. Binary exposures of a SPAD array can be synchronized with picosecond laser pulses to measure the PCH in a widefield setting. Then, by modeling the statistical relationship between the active fluorophore number and the PCH in a region of interest following a laser pulse, we can perform Bayesian inference of this number. The model is demonstrated experimentally by counting quantum dots and various numbers of fluorescent dye molecules bound to DNA origamis. We find that this method has several important applications in widefield microscopy, including enhanced localization microscopy and constrained fitting of multiple unresolvable fluorescent emitters.

Quantifying the diagnostic dispersion of inferred parameter distributions is a challenge in uncertainty-aware modeling. Scalar summaries such as credible interval width are topology-blind; fundamentally different posterior morphologies can yield identical scores, obscuring whether a parameter is precisely estimated or constrained to a range. We propose a Composite Certainty Framework that addresses this metric degeneracy by aggregating five complementary uncertainty metrics including interquartile range, standard deviation, full width at half maximum, Shannon entropy, and mass width. These metrics are aggregated through non-parametric Borda rank voting into a single, unitless consensus certainty score. Applied to a simulation-based inference pipeline for a finite-element model of the human middle ear tuned to cadaveric acoustic measurements, the framework reveals parameter-specific identifiability profiles invisible to any individual metric. It produces two actionable clinical thresholds: (1) the maximum tolerable measurement noise for reliable parameter recovery, and (2) the minimum simulation budget for posterior convergence. We demonstrated that no single metric captures all aspects of posterior dispersion, as spread-based metrics and entropy diverge systematically for clinically critical parameters, whereas their aggregation produces a consensus reflecting genuine diagnostic certainty. The framework is generalizable to any model-based diagnostic pipeline where posterior distribution not merely its coverage, but determines clinical certainty.