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

The osteocyte network in bone is believed to play an important role for how bone tissues sense and respond to mechanical stimulation. Yet, bone adaptation to mechanical loads is often conceptualised as a simple response to mechanical stimuli, such as Wolffs law, which is based on mechanical variables only and takes no account of the cellular basis of mechanosensation. Wolffs law presumes the existence of a reference mechanical stimulus, the mechanical setpoint, above which bone is consolidated, and under which bone is removed. In this paper, we develop a theory of bone tissue sensing and adaptation based on osteocytes to provide new understanding of the role played by osteocyte signals in mechanical adaptation. In this theory, the mechanical setpoint of Frosts mechanostat is explicitly embodied as osteocyte properties involved in mechanotransduction. The mechanical setpoint is allowed to adapt due to the replacement of osteocytes during remodelling, making the setpoint space and time dependent. We propose a mathematical model to implement this new theory of bone adapation and present numerical simulations of this model to explore how mechanobiological response curves (effective Wolffs laws) are modulated by setpoint adaptation during remodelling. By accounting for varying osteocyte populations within bone tissue, we explore bone adaptation under osteocyte disruptions, which is particularly relevant to age-related bone loss. Our model suggests that biological disruptions of remodelling balance cannot always be compensated by mechanical feedback, and that setpoint adaptation during remodelling may have significant observable consequences, such as hysteresis in bone response signatures that resemble lazy zones.

The study of tissue dynamics has been stimulated during the last decades thanks to the use of quantitative descriptions, with the development of several theoretical and computational frameworks, many of them revolving around the notion of reaction-diffusion systems, eventually with additional structure variables beyond time and space. The use of structure variables can accommodate phenotypic traits. In this work, we study a family of competition models, where a given population depends on a resource (e.g. oxygen) and several populations are competing for it. Our quantitative description incorporates phenotypic traits and heterogeneity at the level of cell cycle variations, which influence replication rates via oxygen consumption. This enables us to replicate the fitness of specific subpopulations to environmental conditions (e.g. oxygen shortage or external influences). Using numerical simulations, we show that such models display dynamical pattern formation in the form of coupled travelling wave profiles that expand or retreat at the same wave speed. The full theoretical analysis of such dynamics is quite involved; to circumvent this difficulty, we introduce a quasi-stationary approximation for the resource dynamics. We find that this approximation can reproduce the overall behaviour very accurately, with the additional benefit of allowing theoretical treatment of the reduced model. In this way, we provide estimates on the wave speed which are numerically shown to be robust across a wide range of macroscopic parameters of the full model. The wave speeds are thus found to depend strongly on the proliferation rate of the fittest population, resembling a winner-takes-all dynamics.

BackgroundPlatelet activation in flowing blood is a multiscale process in which vessel-scale hemodynamics, red blood cell (RBC) mechanics, adhesive receptor interactions, and intracellular signalling jointly determine thrombotic risk. Individual components are well studied, but a single reduced description that carries each explicitly from vessel-scale flow to mechanosensitive calcium entry, with dimensionally consistent couplings, remains uncommon. ObjectivesWe develop and analyse a reduced, six-module mechanobiological framework for platelet priming spanning the cascade from hemodynamic shear to mechanosensitive calcium entry, and we delineate which elements are supported by existing evidence and which are new, testable hypotheses. MethodsThe framework comprises six coupled modules: (I) hemodynamic forcing from the incompressible Navier-Stokes equations, with an objective principal-strain-rate measure for extensional flow; (II) RBC-mediated platelet margination and near-wall delivery, closed by a near-wall arrival flux; (III) von Willebrand factor (VWF) activation with a bounded kernel and glycoprotein Ib (GPIb) catch-slip capture, resolved through an explicit contact area and a bond-dependent mobility that progressively immobilises wall-interacting platelets; (IV) a single-load membrane-stimulus formulation; (V) mechanosensitive gating and a dimensionally consistent cytosol-store calcium model with extracellular influx; and (VI) a phenomenological mechanical-memory state. We formally derive that the single-platelet stochastic dynamics and the continuum population balance form a Fokker-Planck pair, with the spatially varying diffusivity handled by an explicit drift correction. ResultsThe framework yields a family of mechanochemical dimensionless groups delineating priming regimes. Its central prediction is reformulated as a falsifiable, history-sensitive signature: in a conditioning-test protocol, a low-tension conditioning block charges the memory state, and a fixed sub-threshold test pulse then reports a delay-dependent calcium facilitation that decays on the memory time{tau} m and is distinguishable from no-memory gating, channel adaptation, and residual-calcium priming. We show explicitly that the previously proposed pulsatile-versus-monotone contrast is a nonlinear convexity/thresholding effect of the gating nonlinearity--its difference-in-differences is approximately zero-- and is therefore not a valid test of memory; the conditioning-test signature is. A second prediction links RBC stiffening to reduced near-wall delivery and captured-platelet calcium response, upstream of intrinsic platelet signalling. ConclusionsThe framework provides a dimensionally consistent, mechanistically grounded and hypothesis-generating description linking hemodynamic forcing to mechanosensitive calcium entry. It demonstrates how history-dependent platelet priming may arise from a phenomenological sensitisation state and proposes a conditioning-test protocol for comparison against adhesive, channel and intracellular-store persistence. The framework is calibratable rather than validated, and the quantitative outputs shown use representative uncalibrated parameters.

Structural network representations of metastatic dissemination typically focus on static topology without resolving transport dynamics, relaxation timescales, or steady-state behaviour. Here, we formulate a discrete Markovian transport model on a directed higher-order network with transition rates derived from qualitative clinical affinity classes. By constructing a non-Hermitian row-stochastic transfer operator, we characterise the relaxation dynamics through its spectral decomposition. The system exhibits a fast-mixing regime characterised by a spectral gap of {gamma} {approx} 0.67, corresponding to a characteristic relaxation timescale of {tau} {approx} 1.49 discrete steps, with the influence of the primary tumour origin progressively attenuated during dissemination. Convergence towards a non-equilibrium steady state (NESS) is accompanied by a reduction in Shannon entropy, concentrating probability mass within specific topological sinks. This spectral relaxation delineates two distinct dynamical regimes: early transient dissemination (n < {tau}), dominated by local organ-specific transition probabilities (organotropism), and the asymptotic regime (n > {tau}), determined increasingly by the global transport architecture of the network. Comparison with independent clinical and autopsy observations across 21 primary tumours and 23 target organs indicates that the predicted stationary distribution is consistent with the observed hierarchy of metastatic organ involvement.

Type 2 diabetes is characterized by progressive aggregation of islet amyloid polypeptide (IAPP) within the islets of Langerhans, a process strongly implicated in beta-cell dysfunction and loss. Although oligomeric IAPP intermediates are widely considered the principal cytotoxic species, the relative contributions of the many biological and kinetic processes governing their formation, clearance, and conversion into fibrils remain poorly quantified. Here, a mathematical model of IAPP aggregation is developed that incorporates the physiology of beta-cell secretion and the microanatomy of the islet, including capillary-mediated clearance, enzymatic degradation, and the kinetics of oligomer and fibril formation within a well-mixed control volume. Building on the hypothesis that oligomers are the major cytotoxic species, the concept of accumulated cytotoxicity is introduced, defined as the time integral of the oligomer concentration, and a systematic sensitivity analysis of this quantity with respect to all model parameters is performed. The results reveal a striking hierarchy: only two parameters, the basal rate of IAPP monomer secretion and the rate constant for spontaneous oligomer dissociation, exert a first-order influence on long-term accumulated cytotoxicity, with dimensionless sensitivities approaching +1 and -1, respectively, while the effect of all other parameters remains subordinate and decays at long times. The model further shows that capillary clearance, owing to the physical exclusion of oligomers from fenestrated capillaries, selectively reduces fibril accumulation and amyloid deposition without affecting oligomer-mediated cytotoxicity, indicating that amyloid area fraction, the standard histological metric of disease severity, may not be a reliable surrogate for cytotoxic burden. The model predicts that approximately 48% of the islet area is replaced by amyloid after 30 years, broadly consistent with histological observations of advanced disease. These findings identify monomer secretion and oligomer dissociation as the most promising therapeutic targets to limit cytotoxic damage in type 2 diabetes and provide a quantitative framework for evaluating candidate intervention strategies.

Mechanical properties of biological tissues, driven by passive and active forces, play a vital role in several processes ranging from development to cancer metastasis. However, the dynamical responses of cells in tissues, subject to mechanical deformations such as shear and the associated rheological properties, are not well characterized. Here, we use three-dimensional agent-based models for normal and cancer tissues to investigate their responses to simple shear as a function of cell stiffness and stochastic active forces. In the normal epithelium, with uniform strength of active force, the yield stress as a function of shear rate follows the Herschel-Bulkley form over a range of cell volume fraction. Strikingly, the shear rate dependence and the elasticity-dependent changes in the yield stress fall on master curves upon suitable scaling. To model cancer-like behavior, a certain fraction (Np) of cells was chosen to have enhanced activity and decreased stiffness. As Np increases, the extent of collective cell movement decreases, transitioning from affine (collective) to non-affine (individualistic) movement, a finding that is in accord with imaging experiments. Simulations of a model of a stiff solid tumor, with radius Rs embedded in normal tissue, show that as Rs increases, the yield stress increases. Interestingly, the cells migrate collectively as Rs increases. A Gaussian Mixture Model (GMM) and a mean field theory quantitatively account for the simulation as well as experimental results on cancerous, non-cancerous, and a mixture of these two types. The combined theoretical and experimental study establishes that heterogeneity in stiffness and activity determines non-affine movements in normal and cancer tissues.

A fundamental biological process of transcription occurs in the cell nucleus, which is a complex medium that also contains multiple heterogeneous structures known as biomolecular condensates. Interestingly, some of these condensates contain mRNA molecules in addition to proteins, suggesting an important cellular role in transcription that is not yet well understood. In this work, we develop a minimal theoretical framework for quantitative investigation of the role of reversible mRNA condensation in transcription. Our discrete-state stochastic approach accounts for the most relevant processes, allowing us to explicitly evaluate the properties of the system and clarify the effects of condensation. Analytical calculations supported by computer simulations suggest that reversible mRNA condensation influences the transcription processes by maintaining a constant level of free mRNA in the nucleoplasm while lowering the degree of stochastic noise and increasing the robustness against external perturbations. Physicochemical arguments are presented to explain these observations. The proposed theoretical framework elucidates important microscopic aspects of transcription, providing a convenient quantitative tool for investigating complex biological phenomena.

Diffuse gliomas are deadly because the individual tumor cells invade - they travel far from the imageable mass, so it is impossible to remove the tumor completely. On the cellular level, glioma cells seem to be in either a "go" state (in which they do not divide) or a "grow" state (in which they do not migrate). We investigate what this tiny choice has to say about the large-scale speed of the invasion front and whether the implication is sufficiently strong to rule out the classical description of the Fisher-Kolmogorov-Petrovsky-Piskunov (Fisher-KPP) type, in which a single phenotype migrates and proliferates. We derive a two-phenotype reaction-diffusion model with density-dependent switching, and we prove the cooperative (quasi-monotone) structure and the associated comparison principle and study travelling-wave solutions of the model. A leading-edge linearization gives minimal front speed as minimizer of an explicit dispersion relation, and direct simulation verifies the predicted speed. In the experimentally relevant fast switching limit, we find a closed-form expression for the speed, that is, we obtain an effective Fisher-KPP equation with rescaled diffusivity and growth rate, with the fractions of the phenotypes. The "go-or-grow" (GoG) front can move at a maximum speed of half the Fisher speed for the same single-cell motility $D$ and proliferation rate $r$, which occurs only when the cells divide their time equally between the two phenotypes. This bound is directly testable: measurement of the front speed, plus independent determination of $D$ and $r$, discriminates the two hypotheses, and in the GoG case, yields recovery of the phenotype balance. We then extend the result to anisotropic (DTI-informed) invasion along white-matter tracts and discuss implications for understanding clinical measurements of growth rate.

Tumor spheroid mechanics arise from both the mechanical properties of individual cells and the adhesive interactions that organize them into tissues. The relative contribution of these two factors to the bulk mechanical behavior, however, remains difficult to disentangle experimentally. Here, we develop a computational model of micropipette aspiration to compare the mechanical response of isolated cells and multicellular spheroids within a common computational framework. By independently varying single-cell stiffness and cell-cell adhesion, we quantify their effects on aspiration dynamics, effective elastic modulus, and viscoelastic relaxation. Our results show that increasing single-cell stiffness substantially alters the mechanics of isolated cells but has limited influence on the effective elastic modulus of multicellular spheroids. In contrast, changes in cell-cell adhesion produce pronounced effects on spheroid effective elastic modulus. Nevertheless, both parameters increase the retardation time governing the transition from the initial elastic response to long-time viscous deformation. These findings suggest that multicellular elasticity is governed primarily by intercellular mechanical coupling, whereas the dynamical response to applied stress depends jointly on cell-scale mechanics and cell-cell adhesion.

Contact inhibition of proliferation (CIP) enables epithelial tissues to self-regulate growth and maintain tissue homeostasis. However, how cell-level mechanical contact, tissue-scale structural order, and proliferation kinetics interplay remains a fundamental open question in living matter physics. Here, we present a particle-based model of a confluent epithelial monolayer governed by overdamped dynamics, where individual cells interact via a two-dimensional hard core- soft shoulder potential. By comparing structural evolution during quasistatic densification with previously reported experimental division kinetics, we find that the dynamics of proliferation arrest mimics the onset of direct steric contacts between the hard cores of the shell. Identifying hard core contacts as the physical driver of CIP, we couple our mechanical model with a stochastic Monte Carlo division scheme in which the instantaneous division rate decreases to zero from an intrinsic value as the number of hard core contact increases to six from zero. We demonstrate that for high intrinsic division rates, the cellular densification outpaces mechanical relaxation. This kinetic mismatch drives premature hard-core contact formation, shifts the onset of jamming and contact inhibition to lower packing fractions, and induces increasingly disordered transient configurations before the tissue universally converges to a hexagonal close-packed limit. Our model's predicted division kinetics and structural order evolution are consistent with epithelial monolayer experiments, both reported and our own. This minimal physical framework links single-cell steric contact mechanics directly to tissue-scale growth regulation and structural evolution.

Microbial populations generally evolve in fluctuating environments under time-varying conditions. These are often described by binary switching models, sometimes seen as coarse-grained feast-famine cycles, in which resource availability switches abruptly between abundant and scarce conditions. However, experimental studies suggest that feast-famine environments actually exhibit more complex temporal dynamics. Here, we study how two strains, one growing slightly slower than the other, compete for the same resources in fluctuating environments comprising a finite number of intermediate states, each having its own carrying capacity. Environmental switching between these states and their carrying capacities represents gradual changes in nutrient availability. This class of multi-state stochastic switching models can be interpreted as a coarse-grained description of feast-famine cycles and allows us to investigate strain competition under the gradual recovery and depletion of resources. By computational and analytical means, we characterise the population dynamics in these multi-state fluctuating environments. In particular, we study how the switching rates and distribution of carrying capacities affect the population-size statistics, fixation probability, and mean fixation time. By comparing these results with their counterparts in binary environments, we clarify how the frequency and amplitude of environmental fluctuations influence population dynamics in coarse-grained feast-famine cycles.

Since the earliest microscopic observations, the geometric organisation of cells has captured biologists interest. Recent work by Gorgi et al. showed that bacterial colony organisation, including biofilms, can be explained across diverse species by radial expansion from fixed initial seeding sites and contact-inhibited growth, with little need for species-specific mechanisms. Here, we extend this geometric framework by incorporating seeding time as an additional driver of colony organisation. Using simulations and analytical models for expected colony size, we show that staggered seeding yields order of magnitude increases in the expected size of early seeded founder colonies. At realistic biofilm growth rates, a 2-day lag between founder and subsequent colony seeding produces an approximately 10-fold increase in expected founder size, while a 1-week lag produces a 25-fold increase. These findings provide a simple geometric basis for biological priority effects, illustrating temporal advantage alone can generate substantial spatial dominance, with implications for cardiovascular devices where host and bacterial cells compete in a race for the surface.

A classical study found no excitation transfer when isolated cardiomyocytes were placed side by side, whereas a recent paper reported action potential transfer in carrdiomyocytes placed end to end. We use nanoscale numerical simulations based on the full Poisson-Nernst-Planck equations to investigate whether these apparently opposing observations can be explained by the different geometrical configurations. The computations show that in the end-to-end configuration, ephaptic coupling occurs when the intercellular cleft is sufficiently narrow and a sufficiently large fraction of the sodium channels is localized at the intercalated disc. Coupling is strengthened when the sodium channels are concentrated in fewer clusters and when ionic diffusion within the cleft is reduced. Under these conditions, excitation transfer occurs on a timescale consistent with rapid cell-to-cell activation. Conduction depends biphasically on cleft width and terminates abruptly beyond a critical width. Localization of potassium channels at the intercalated disc has only a moderate effect, whereas gap junctions substantially improve conduction and reduce the relative contribution of ephaptic coupling. In the side-by-side configuration, excitation transfer does not occur under physiological conditions and requires highly flattened cells, minimal separation, and unrealistically strong sodium-channel clustering. The different outcomes of the side-by-side and end-to-end experiments can therefore be explained by the fundamentally different geometrical conditions for ephaptic coupling.

Within the studies of stochastic gene expression, apart from the variability of copy number of gene products, the problems of threshold crossing of those products are biologically important as they often lead to terminal cellular events. Here, we study the threshold crossing problem of the messenger ribonucleic acid (mRNA) and present an exact probability distribution of first passage times in Laplace space. The function furnishes moments of any order and also predicts the characteristic time of the exponential tail of the distribution, which we match against Gillespie simulations. We find that all the measures of relative fluctuations of the threshold crossing times show U-shapes within this simple model of mRNA, as was found earlier in more mathematically involved models of threshold crossing time statistics of proteins. Furthermore, we extend the exact formula to include the phenomenon of DNA duplication and the corresponding doubling of transcription rate. As expected, the distribution varies considerably depending on the onset of the duplication stage within the cell cycle.

Repetitive low-intensity blast (LIB) exposure has been identified as a probable cause of mild blast-induced traumatic brain injury (mbTBI) and a chronic injury risk to U.S. military personnel. However, the human brains biomechanical response to this loading regime remains poorly characterized. Using blast-exposure-validated 3D models of human anatomy, we simulated the intracranial tissue response to blast pressure typically experienced by Warfighters during weapons training. Two scenarios were evaluated, a single-dose exposure and a repetitive-dose exposure, to study intracranial pressure (ICP), shear strains, and spectral content. Ansys LS-DYNA was used to generate planar blast waves with peak overpressures of 4-90 kPa and positive phase durations of 2.2-10 ms. Single exposures produced ICP ranging from 4.7-112.7 kPa, dependent on dose and positive phase duration. Under repetitive LIB exposure, peak ICP increased by 8-26% relative to single exposures, with an increase of high-frequency components (>2 kHz). These results demonstrate that LIB can produce measurable intracranial responses that are amplified through repetition, producing pronounced spectral content and elevated pressures despite low strain levels. This study underscores the need to further investigate cumulative dose effects and the value of computational approaches to clarify hypothesized mbTBI mechanisms in operationally relevant conditions.

Biomolecular condensates are dynamic assemblies whose functions depend on continuous exchange of molecular components with the surrounding environment. While scaffold molecules drive phase separation and condensate architecture, many functional components are clients that are recruited through interactions with the scaffold-rich environment. Despite their prevalence, how client-scaffold interactions shape client exchange dynamics remains poorly understood. Here, we develop a reaction-diffusion model for client exchange in scaffold-driven condensates, in which clients switch between a scaffold-bound state and an unbound state. Bound clients exchange through scaffold-mediated transport, whereas unbound clients diffuse through the pore space of the condensate. Using the fluorescence recovery of fully photobleached condensates as a measure of client exchange, we compare transport through these two pathways with bound-unbound conversion and identify three limiting regimes. In the slow-conversion regime, bound and unbound clients recover through distinct scaffold- and pore-mediated pathways. In the intermediate-conversion regime, recovery of bound clients becomes limited by client unbinding. In the fast-conversion regime, local equilibrium between bound and unbound clients produces an effective single-state recovery. We further propose a unifying description that connects these regimes and quantitatively captures the apparent recovery timescales extracted from numerical simulations across condensate sizes. Our results provide a framework for interpreting component-specific exchange dynamics, and highlight client size, client-scaffold binding, and condensate porosity as key regulators of client turnover in multicomponent condensates.

AO_SCPLOWBSTRACTC_SCPLOWCellular automata and graph reaction-diffusion systems encode local spatial interactions in different mathematical forms. We develop a cochain-operator calculus for these two settings. Over a finite field Fq, every local rule on a finite neighborhood has a unique reduced polynomial representative. On an oriented line, the coboundary and endpoint maps recover the left and right shifts. Our main theorem shows that these operators, together with linear operations, constant cochains, and the degree-zero cup product, generate every finite-radius polynomial cellular automaton. Explicit formulas for Rules 30, 110, and 22 show how reflection-invariant linear coupling, directed transport, and nonlinear neighbor interactions enter the calculus. On a general graph, d*d is the unweighted combinatorial Laplacian and enters a graph reaction- diffusion recurrence. Over [R], the term - Dd*d with D [&ge;] 0 admits the usual diffusion interpretation; over Fq, the corresponding expression defines modular coupling without an intrinsic order. In the morphogenetic examples, we therefore distinguish pattern-generating dynamics from finite-state observation and use the Betti numbers of active induced subcomplexes to summarize observed patterns. This yields a common algebraic representation without identifying real-valued diffusion with finite-field dynamics.

We present a quantum-enhanced version of the classic k-Nearest Neighbors (kNN) classification algorithm, applied to the prediction of arterial hypertension. The traditional Euclidean distance metric of the kNN algorithm is replaced with a Fidelity-derived quantum dissimilarity measure to evaluate the similarity between data samples. We map classical real-world clinical and ECG-derived data features into quantum states via the Dense-Angle Encoding, which efficiently utilizes parameterized rotation gates to pack multiple features into minimal qubits while maintaining pure states. We evaluate the performance of the dissimilarity measure using both the noiseless state vector Simulator and the IBM Qiskit Estimator primitives. The quantum circuit demonstrates robust predictive capabilities comparable to the classical model. While it does not claim computational supremacy over the classical baseline, the framework proves that fidelity-based similarity is a physically meaningful and efficient approach for hybrid quantum classical classification.

Purpose Prevention and early detection of osteoporosis remains a global challenge, more so in regions like the Philippines where screening barriers exist. Chest x-rays meanwhile are relatively inexpensive, and more frequently done, and therefore can be used for opportunistic screening. This study aimed to develop a deep learning model for osteoporosis detection from chest x-rays using DXA as the gold standard. Methods A convolutional neural network called Osteo-AI was developed using 406 pairs of chest x-rays and DXA scans of Filipino patients aged 50 and above. With data augmentation, the training set expanded to 6,300 pairs. Gradient-weighted class activation mapping technique was applied to localize and identify patterns and areas in the chest x-ray images correlating with osteoporosis. Results Training data consisted of 369 female patients and 37 males. Ages of the patients ranged from 50 to 89 with a mean age of 63 years old. Initial testing yielded promising results, with Osteo-AI achieving a diagnostic accuracy of 85.71%, easily outperforming a benchmark of 33.33% Conclusion Our findings suggest the potential of Osteo-AI to enhance osteoporosis screening accessibility, aiding in early intervention to prevent fragility fractures. Further research involving larger datasets is warranted to refine and optimize the model, potentially improving detection accuracy and expanding its utility in global healthcare settings.

In the current clinical practice, the diagnosis of spinal disorders and their surgical planning are critically based on imaging data. To complement this data, patient-specific finite element models have been developed and showed to be powerful tools for evaluating spine mechanics. Most of them rely on Computational Tomography (CT) scans - which have a high resolution but are seldom available in routine clinical practice - while only a recent few models are on less invasive Magnetic Resonance Imaging (MRI). Yet, despite the proliferation of these computational models, encompassing detailed anatomical and functional information, the rheological assumptions they are built upon are based on tissue-sample mechanical response data, which leaves a gap in the quantitative analysis on how such assumptions influence the macroscopic response of a functional spinal unit. Aiming at addressing these shortcomings, the main purpose of this work is to introduce a quantitative computational assessment of the macroscopic impact of commonly adopted rheological models - from linear elasticity to fiber-reinforced nonlinear hyperelasticity - in several loading conditions, focusing on a lumbar unit which is considered as a typical benchmark system. We also propose a reconstruction procedure to accurately describe subject-specific anatomy from MRI data, including the intervertebral disc and its nucleus pulposus. Bones are modeled as linear elastic media, whereas for the AF, we consider three different mechanical models - namely, isotropic linear elasticity and the Holzapfel-Gasser-Ogden model with and without fiber reinforcement. Model verification on an idealized geometry demonstrates numerical consistency, while parametric orthostatic simulations highlight the need for nonlinear formulations to capture anisotropy and strain-stiffening behavior of the intervertebral disc. Then, we carry out flexion, lateral bending, and torsion tests on a subject-specific reconstructed functional unit, for which we provide parametric analysis in terms of momentum magnitude and resulting range of motion. These tests further confirm the need for a nonlinear rheology of the annulus fibrosus and provide a quantitative assessment of the differences between the constitutive laws considered. Moreover, successful comparisons with the literature, in terms of macroscopic deformation under several loading conditions, serve as partial validation for our computational model.