The mechanistic model of AD (mAD) progression developed in this study integrates four main components:

For each Aβ peptide, the aggregation pathway model is represented by six species: monomer (M), dimer (D), small oligomer (o), large oligomer (O), protofibril (F) and plaque (P), as indicated in Figure 2. In addition, mAD validation was conducted by comparing simulation outputs to clinical neuroimaging data, specifically evaluating Aβ plaque burden using Standardized Uptake Value Ratio (SUVR) and Centiloid scales (Figure 2).

The mAD model was implemented using multiscale Computational Biology (CoBi) software version 2023.1.1, which enables physics-based numerical solutions of coupled ordinary and partial differential equations (ODEs, PDEs) for biology applications (Przekwas et al., 2006). Source coding of the pathway mechanics and parameters used in the model are available in the Supplementary material.

Aβ is a 38–43 amino acid peptide derived from APP through sequential cleavages by β- and γ-secretase enzymes in an amyloidogenic pathway. Aβ generation was accounted for based on an APP processing model adapted from the work of Madrasi (Madrasi et al., 2021). However, APP is also processed in parallel by α-secretase to generate soluble APPα in a non-amyloidogenic pathway (Figure 3) (Chow et al., 2010). When APP is cleaved by α-secretase (αS) followed by γ-secretase (γS), this results in a hydrophobic p3 peptide release (also known as Aβ_{17 − 40/42}). Therefore, the Madrasi model was extended in this work to also include the non-amylogenic processing of APP. In the present mAD model, equations for all species were formulated to achieve molar balance according to the reaction mechanisms defined in Table 1. These reactions were used by the CoBi ODE-Gen module to automatically generate ODEs. A two-way arrow indicates a reversible reaction, and a one-way arrow indicates an irreversible reaction at a known rate. Both pathways accounting for APP and Aβ homeostatic biogenesis are essential for synaptic function.

Various length Aβ isoforms in the human brain appear to have neuroprotective properties at low concentrations where the length of the Aβ species affects their physiological and biophysical properties. Among the various Aβ isoforms, Aβ₄₀ (~4.3 kDa) and Aβ₄₂ (~4.5 kDa) are most relevant due to their roles in AD pathology and diagnostics. These two isoforms were therefore selected for inclusion in the model.

Once Aβ_x monomers are generated, they become involved in a complex aggregation process forming dimers, oligomers, protofibrils, fibrils, and ultimately plaques. The cascade involves a large number of steps including primary and secondary nucleation, oligomerization, breakup, catalytic growth, and formation of insoluble fibrils and large plaques. Assumptions for this aggregation model are based on the peptide properties.

For both Aβ₄₀ and Aβ₄₂, the N-terminal is hydrophilic while most amino acid residues in C-terminal region (originating from the transmembrane region of APP) are more hydrophobic. Under physiological conditions, the Aβ hydrophobic C-terminal region forms a folded structure and exposes the hydrophilic N-terminal region (Song et al., 2022). In its native conformation (folded) the monomer exists as a stable structure without self-aggregation. Under certain conditions Aβ unfolds and forms a thermodynamically unstable morphology, leading to the binding of two hydrophobic C-terminals to form a more stable, aggregated dimer. This aggregation process continues, leading to higher-order aggregates.

An Aβ generation/aggregation kinetics model was recently developed by Geerts et al. (2023b), which employed a 25-step aggregation pathway for both Aβ₄₀ and Aβ₄₂. However, the Geerts model contained a large number of parameters that had to be calibrated from limited clinical data. In this case, the large number of assumptions on aggregate size and morphology is unlikely to benefit mechanistic understanding at such a high resolution without proper calibration. In contrast, our Aβ agglomeration reduced order model (ROM) was formulated using only six Aβ species: monomer (M), dimer (D), small oligomer (o), large oligomer (O), protofibril (F) and plaque (P). A schematic of the simplified, linear, reversible aggregation pathway is shown in Figure 4A followed by the reaction kinetics for the full aggregation pathway model assumptions (Figure 4B). Model aggregation assumptions were consistent for Aβ₄₀ and Aβ₄₂, however, since Aβ₄₂ is more hydrophobic and more prone to aggregate compared to Aβ₄₀, it was assumed to form fibrils significantly faster. The kinetic rate constants were derived from the previously reported 25 step Aβ aggregation model (Geerts et al., 2023b). Rate constants for the monomer (M) and dimer (D) were the same as the reference model such that generation of monomers and dimerization of two monomers into a dimer were treated with full stoichiometry consistency. Rate constants for the larger species (o,O,F,P,) were calibrated to match trends in ISF and CSF in reported results (Karelina et al., 2021; Geerts et al., 2023b). Note that to create the ROM, the higher order aggregates (o, O, F, and P) were treated as assemblies where the composite rate constants limit pure simplification into stoichiometric relationships.

The Aβ aggregation model involves several additional steps observed in in vitro and preclinical models, such as plaque catalyzed secondary nucleation, fragmentation, dissociation of oligomers, protofibril breakup, protofibril and plaque growth saturation and microglia clearance. Individual steps of the Aβ aggregation reaction mechanisms were formulated using published mechanisms (Scheidt et al., 2019; Rinauro et al., 2024; Niu et al., 2024) and the reference 25-step model (Geerts et al., 2023b). These main components were accounted for based on reaction mechanisms depicted in Figure 4B.

Note that M appears in Figure 4B in five boxes (1, 2, 3, 5, and 7) and the ODE for M includes four rate terms, R, and efflux, J, as shown in Equation 1 below:

where R_np is the reversible nucleation-polymerization rate, R_2n is the secondary nucleation rate catalyzed by plaque (P), R_Pg is the addition of monomers to oligomers and their conversion to plaque (P), RclIDE is the microglia enzymatic degradation of soluble Aβ (M), and J_{B − b} is the Aβ (M) efflux rate by various transporters and fluid clearance between brain interstitial fluids (ISF) and body fluids.

The reversible nucleation-polymerization rate for monomer M binding to higher aggregates (D, o, O, F, P), Box 1 in Figure 4B is:

Detailed rate kinetics and rate constants are provided in the Supplementary material. While nucleation of additional species is feasible, nucleation of monomers to multimers was selected in this work as the most energetically favorable option.

The mAD model simulation of Aβ biodistribution in the whole body was adapted from a whole body PBPK model topology originally developed for modeling antibodies targeting the central nervous system (CNS) (Bloomingdale et al., 2021). The Aβ transport module spans the CNS compartments (brain vascular, BBB, BCSFB, ISF, CSF, and PVS) and the systemic compartments (plasma, lymph, tissue vascular, tissue barrier and tissues), as shown in Figure 5A. Flow assumptions are based on biodistribution principles of small molecules.

Small molecules and Aβ-peptides distribute across body fluids (interstitial (ISF), cerebrospinal (CSF), perivascular spaces (PVS) and plasma) through convective and diffusive transport. While the blood-brain barrier (BBB) limits exchange between ISF and plasma, ISF and CSF are in direct fluid communication, enabling Aβ exchange, including various soluble Aβ-peptides (sAβs), which are in constant equilibrium between the ISF and CSF (Mroczko et al., 2018; Schreiner et al., 2023; Teunissen et al., 2018). Within the ISF, diffusion and convection are comparable; however, in the CSF and PVS, convection dominates with drainage velocity on the order of 8.3 × 10⁻⁶ m/s (Rey and Sarntinoranont, 2018; Thomas, 2019). Although the convective transport rate for soluble molecules does not depend on the molecule size, the diffusive flux in the “porous” extracellular space is a strong function of the sAβ molecule size, shape, charge, tortuosity of pathway (λ~1.6 in ISF) and on the sAβ concentration gradient. We have used these property data to derive the size-independent Péclet numbers (Table 2), defined as the ratio of bulk fluid motion to the rate of diffusive transport between the ISF, PVS, and the lymph.

A schematic of the whole body biodistribution assumptions for diffusive and active transport is shown in Figure 5A. The “reaction” mechanisms, shown in Figure 5B, are used by the CoBi ODE-Gen module to generate the corresponding ODEs. The model incorporates 11 compartments and therefore 11 ODEs are used to describe transport of each Aβ peptide (Aβ₄₀, Aβ₄₂). Detailed reaction kinetics and constants for Aβ monomer (M) transport in the CNS compartments (M_bv, M_cb, M_bb, M_i, M_c, M_pv,) and the systemic compartments (M_pl, M_L, M_tv, M_tvb, M_ti) are provided in the Supplementary material. For simplicity, the schematic and rate equations are presented for a generic Aβ peptide.

Outside of the CNS, Aβ monomers were assumed to degrade at a constant rate of 1.9 × 10⁻⁴/s. Within the CNS, Aβ was assumed to be degraded intracellularly in lysosomes of microglia and astrocytes and extracellularly by either secreted or membrane-bound proteases (Marr and Hafez, 2014). Of these, Neprilysin (NEP) and insulin-degrading enzyme (IDE) are the two major catabolic enzymes that degrade Aβ peptides. Both proteases decrease with age and show decreased expression in AD, especially in regions with high Aβ loads, such as the hippocampus (Loeffler, 2023). Therefore, in our model, the Aβ monomer protease degradation mechanism is represented by a Hill kinetics term with Aβ monomer as a ligand and the maximum reaction velocity was assumed to decrease as a function of the patient's age.

Microglia, the brain's resident innate immune cells, clear pathological proteins and prune excess neuronal synapses from the CNS. In AD, oligomeric Aβ bind to synapses which triggers microglial activation, contributing to excessive elimination of synapses and cognitive deficits. Normally, microglia exist in a quiescent state but can be activated by surrounding stimuli such as cellular debris and Aβ agglomerates. This activation process involves microglial proliferation, increased secretion of inflammatory factors, cell surface receptor expression, and morphological changes. The early activation of microglia into the M2 phenotype that attempts to clear Aβ is considered neuroprotective and anti-inflammatory. Compared to resting state, M2-polarized microglia show enhanced phagocytosis. However, with the development of the AD pathology, the M2 phenotype may become dysfunctional over time and be replaced by the microglia M1 phenotype. M1-polarized microglia are pro-inflammatory and lose their phagocytosis capabilities (Wang et al., 2021; Guo et al., 2022).

Microglia interact with soluble and insoluble/fibrillar Aβ forms. The present model accounts for these mechanisms by assuming that soluble Aβ monomers (M) are degraded enzymatically by various proteases, such as NEP and IDE (Box 5 of Figure 4B), defined using Hill kinetic equations and assumptions in the Supplementary material.

All higher-order insoluble Aβ agglomerate forms (o, O, F, P) were assumed to undergo microglial-dependent clearance in the ISF (Box 6 of Figure 4B). The clearance rate (kg,cli) of insoluble Aβ forms (o, O, F and P) is expressed in Equation 3.

Where μ(t) is the normalized microglia density, fr(t) is the microglia phenotype fraction (varies between 0 and 1). At steady state, μ(t) was assumed to be 1 and fr(t) was assumed to be 0.03 (close to zero). Vihigh for the healthy controls and Vilow for AD subjects are the high and low clearance rate for specific Aβ forms. We assumed that oligomers and protofibrils had the same clearance rate, but plaque clearance rate was 50% lower due to its insoluble more compact nature. These assumptions were adapted from Geerts et al. (2023b). Soluble and insoluble concentrations were modeled in the brain ISF and validated against experimental datasets reported in Karelina et al. (2017).

Family history and genetics are strong risk factors for AD. Late-onset AD (LOAD) is a polygenic disorder associated with at least 50 genes, of which the apolipoprotein E (APOE) ε4 allele is the strongest risk factor (Yu et al., 2021). In humans, APOE is expressed as ε2, ε3 and ε4 isoforms with frequency of 8%, 78% and 14%, respectively (Schipper, 2011). APOE lipoproteins bind to several cell-surface receptors and hydrophobic Aβ peptides. The exact mechanism by which APOE isoforms increase/decrease AD risk is not fully understood, but APOE isoforms differently affect brain homeostasis and neuroinflammation, BBB permeability, glial function, synaptogenesis, oral/gut microbiota, neural networks, Aβ clearance, and tau-mediated neurodegeneration. It has been generally accepted that APOE ε4 decreases Aβ clearance, increases aggregation and amyloid seeding without affecting Aβ production. On the other hand, the APOE ε2 allele is the strongest genetic protective factor (Hampel et al., 2020). Expression of various APOE alleles directly affects the risk of AD (Fernández-Calle et al., 2022).

In our model we account for APOE effects by multiplying the microglial clearance rate (kg,cli) in Equation 3 by a factor (1-α), controlling the kinetic rate constant of microglia clearance of individual Aβ isoforms and agglomerates. We established a baseline value α = 0 for APOE non-carriers (APOE-) and α > 0 for APOE carriers (APOE+). For APOE carriers, α was assumed to range from −0.02 to 1, and groups were stratified by APOE genotype and sex. These stratified APOE AD risk factors are aligned with recent clinical findings based on male/female population clinical data (Chai et al., 2021). Homozygous (ε4 and ε4) carriers had the greatest increase in risk [12 x (men), 15 x (women)], heterozygous (ε4 and ε3) carriers had a mild increase in risk [3 x (men), 3.5–4 x (women)], and APOE ε2 carriers have a slightly reduced risk [0.7 x (both sexes)].

Positron emission tomography (PET) imaging can be conducted to evaluate AD progression in patient populations. Cerebral amyloid loads are quantified by administration of radioligands, which bind to amyloid fibrils and plaques at brain synapses. The radioactivity concentrations throughout the brain are quantified in terms of the Standardized Uptake Value Ratio (SUVR) between the target and reference brain tissue regions, shown in Equation 4.

The cerebellum is commonly used as a reference region because it is notably free from fibrillar Aβ in sporadic AD and a majority of neurons are granule cells with only a handful of synapses, compared to cortical neurons which may host tens of thousands of synapses (Lyoo et al., 2015). Equation 5 was formulated to calculate the SUVR using computed Aβ load. The Aβ load (β_L) was calculated as a weighted sum of individual Aβ agglomerates (o, O, F, P) for Aβ₄₀, Aβ₄₂ in Equation 6.

where calibrated constants C₀ = 1.0 (fixed), C₁ = 4.65, C₂ = 3.3, C₃ = 630, 000, and C₄ =1.95. Note that C₄ > 1 indicates that the PET tracer has higher affinity for plaques compared to other agglomerates. Calculated SUVR was then validated against clinical data of aging healthy individuals and in amyloid positive subjects (Jack et al., 2013a).

APP processing and subsequent generation of Aβ peptides through the amyloidogenic pathway was implemented in the CoBi framework based on the model developed by Madrasi et al. (2021) and outputs were replicated. The 25-variable Aβ aggregation model defined in Geerts et al. (2023b) was then replicated in CoBi and reduced to a 6-variable reduced order model (ROM) of Aβ aggregation. Assumptions and model parameters for monomers and dimers were unchanged and resulting concentration profiles for Aβ₄₀ and Aβ₄₂ in the isolated brain ISF compartment were compared between the 6-variable mAD model and the 25-variable Geerts model (Figure 6). The average percent difference between models was 0.36% for Aβ₄₀ monomers and 0.45% for Aβ₄₀ dimers, demonstrating excellent agreement. The average percent difference between the mAD model and the Geerts model was 14.29% for Aβ₄₂ monomers and 17.91% for Aβ₄₂ dimers. Greater deviation in Aβ₄₂ predictions is due to greater effect of the higher order species on Aβ₄₂ agglomeration cascades. Direct comparison between outputs for higher-order agglomerates was not feasible as it was difficult to establish correlation between present “lumped” species (o,O,F,P) and individual components of the 25-species reference model. Nevertheless, monomer and dimer profile agreements provided sufficient confidence for integration of Aβ generation and aggregation terms with full body transport and further validation.

Aβ transport and distribution accuracy relies on accuracy of transport from the brain ISF, which is where Aβ generation and aggregation were assumed to occur. Simulations in the mAD model compared the effect of accumulated insoluble Aβ₄₂ in the brain ISF over time (Figure 7A) vs. soluble Aβ₄₂ (Figure 7B). Insoluble concentrations increased to orders of magnitude greater than soluble concentrations, which adequately simulates how soluble, toxic Aβ peptides aggregate into insoluble forms. Compared to the clinical data, reported by Karelina et al. (2017), the model effectively captures concentrations of soluble and insoluble concentrations of Aβ₄₂ in the ISF of the AD brain between the ages of 70–80 years old.

The mAD model was validated against clinical data of aging healthy individuals and in amyloid positive subjects. In Jack et al. (2013a), an SUVR profile of the temporal trajectory of β-amyloid accumulation was generated from 260 participants 70–92 years old. Because clinical data are typically collected from elderly populations with amyloid present, the current model can be used to computationally “extrapolate” the SUVR status not only into the future but also for the prodromal stage. As shown in Figure 8A, based on the fit of the initial clinical SUVR data collected, we extrapolated the SUVR back into a prodromal baseline state at age 60. The clinically observed SUVR was then correlated to Aβ₄₂ plaque profiles in the brain ISF and compared to the predicted Aβ₄₂ plaque concentrations from the mAD progression model (Figure 8B). This computational capability correlating the clinical SUVR and various brain Aβ agglomerates (o, O, F, P) could be a useful tool to correlate medical imaging and body fluid biomarkers data.

The full aggregation model described by Geerts et al. accounts for APOE carriers/non-carriers without distinction between various APOE alleles (ε4, ε3, ε2, and their combinations) (Geerts et al., 2023b). The mAD model incorporates the simulated the effect of APOE alleles on Aβ₄₂ plaque concentrations in the brain ISF, however, only the effects of ε3 and ε4 alleles were demonstrated in this report. Kinetic parameters controlling the effect of APOE on various Aβ profiles were identified during APOE model calibration. Simulation of the effect of APOE kinetic parameters on profiles of Aβ₄₂ plaque in the ISF demonstrated accelerated accumulation of Aβ₄₂ plaques in the ISF up to 5 years earlier compared to non-carriers (Figure 9). A limitation of the current model is that it does not directly account for risk factors associated with specific ε2, ε3, and ε4 APOE isoforms and only accounts for different microglial clearance rates. In the future, this capability could be adapted to account for risk factors for all APOE alleles (ε4, ε3, ε2, and their combinations) in the model.

Time profiles of Aβ₄₂ species (M, O, F, P) in the brain ISF was simulated in APOE carriers and non-carriers (Figure 10). As expected, APOE carriers with ε3 and/or ε4 alleles have accelerated agglomeration processes causing earlier development of AD. Once the insoluble species starts forming, such as oligomers and protofibrils, the enzymatic degradation by microglial cells is less effective with age. This is demonstrated by the lack of convergence of oligomer and protofibril concentrations between 80 to 100 years of age. On the other hand, once the plaque is formed, APOE has less of an effect on microglial clearance and the concentration of Aβ₄₂ plaque converges. This observation could be important for understanding toxicity of intermediate species where recent evidence shows that the heterogeneous nature of oligomers contributes substantially to neurotoxicity and resulting neurodegeneration (Tolar et al., 2024, 2021). The mAD model also demonstrates the effect of sex on Aβ dynamics in the presence or absence of APOE alleles. In general, females had slightly higher concentrations of Aβ compared to males and the discrepancies between male and female-predicted concentrations was greater in the non-carrier group (Figure 11).

Construction of the mAD model by adaptation and integration of previously developed models takes on the limitations inherent in the original models (Madrasi et al., 2021; Bloomingdale et al., 2021; Geerts et al., 2023b). A few suggestions for future refinement of the mAD model are provided below.

The APP processing model neglects the intra-neuronal paths of APP synthesis, transport and recycling. The mAD model only accounts for a singular rate of APP synthesis and peptide generation into the ISF. However, within the neuron, APP can be distributed throughout the axonal and somatodendritic domains and peptides are not always cleaved at the synapse (Wang et al., 2024). As more information about APP processing phenotypes of AD arise, the effect of AD on the spatiotemporal regulation of APP trafficking and location(s) of APP processing in human neurons should be accounted for in these models. Further, while the mAD model accounts for both the amyloidogenic and non-amyloidogenic pathways, only the former has been elaborated and partially validated. Future calibration of the non-amyloidogenic pathway could be performed through comparison of published concentrations of the p3 peptide (known to develop its own aggregates), which may be important for analyzing downstream effects of APP processing (Kuhn et al., 2020).

Aβ₄₀ and Aβ₄₂ agglomeration was assumed to occur independently and form homogeneous aggregates. This assumption was inherently defined by incorporation of the Geerts et al. (2023b) model. However, Aβ plaques can have different morphologies and compositions depending on the AD etiology (Koutarapu et al., 2025). Co-aggregation and off-pathway aggregation of the two isoforms can also occur (Li et al., 2023; Oren et al., 2021), further indicating that etiology-specific agglomeration cascades may be developed as population data arises to better support assumptions for plaque composition. Additionally, simplification of the agglomeration cascade to only six species limits the ability of the mAD model to investigate the effects of intermediate products (i.e. trimers → large oligomers) on AD progression without further validation.

A relatively simple model of neuroinflammation caused by accumulation of higher-level Aβ aggregates was postulated. A recent study showed that a majority of the published models of neuroinflammation were developed in the context of understanding AD, as opposed to other neurodegenerative diseases (Foster-Powell et al., 2025). Further, the complexity of these models continues to expand to include microglia, astrocyte, and t-cell interactions as well as pro-inflammatory cytokines. Receptor binding and transcription factor integration was also proposed as a future direction for AD modeling based on common cancer models (Foster-Powell et al., 2025). Development of more complex neuroinflammation/inflammasome models influencing amyloid aggregation could be important for investigation of mechanistic factors leading to AD and related dementias, such as traumatic brain injury-related dementia.

The current model assumes that all APP/Aβ pathways occur in a homogeneous brain space. There are two problems with that. First, this does not account for the role of peripheral amyloid peptide generation and aggregation. Over 90% of Aβ peptides found in the circulating blood are platelet-derived and AD is known to effect metabolism of platelet-derived Aβ (Fu et al., 2023) and aggregation outside of the CNS (Gamez and Morales, 2025; Shi et al., 2024). Second, the model represents the CNS volume by only six sub compartments (vascular, BBB, BCSFB, ISF, CSF and PVS), which does not account for spatial effects of Aβ pathology within the AD brain. Distinct patterns of Aβ deposition can occur depending on different clinical phenotypes, which may be important to consider when developing diagnostic and prognostic models (Lecy et al., 2024). As CoBi tools enable multiscale, multiphysics simulations (Przekwas et al., 2006), the single brain compartment can be split into anatomically distributed regions with variable disease progression rates observed in neuroimaging. Nevertheless, the AD progression model provides a good foundation for future refinement.

The rate of Aβ transport across the BBB was assumed to be constant. However, Aβ efflux is known to be affected by APOE protein isoforms (ε2, ε3, ε4), which bind to LRP1 with different affinities. LRP1 can bind not only Aβ but also APOE and Aβ:APOE complexes. The impaired binding of APOEε4 can lead to reduced clearance efficiency of Aβ, enhancing AD pathology. Moreover, APOEε2/Aβ and APOEε3/Aβ complexes are cleared at the BBB via LRP1 at a substantially faster rate than APOEε4/Aβ complexes (Kanekiyo et al., 2014; Belaidi et al., 2025). Such considerations should be implemented in future model iterations.

Development of AD pathology involves not only formation of Aβ plaques but also growth of intracellular neurofibrillary tangles containing hyper-phosphorylated Tau. Abnormal phosphorylation of Tau can lead to aggregation of Tau fibrils in a similar fashion to Aβ peptides, leading to neurofibrillary tangles (NFTs) where much of the developed framework reported here can be applied to modeling NFT formation. Implementation a of Tau pathology model coupled to the existing Aβ model could help improve accuracy of AD progression predictions. Further, prediction of Tau pathology in the context of AD can also enable estimation of the pathological burden of other tauopathies contributing to cognitive and behavioral deficits (Granholm and Hamlett, 2024).

Robust clinical validation is necessary to strengthen predictive capabilities of this tool. This study performs validation of Aβ₄₂ concentrations in the brain ISF. Improved access to larger datasets is required for validation of the mAD model predictions in the CSF, blood, and other tissues as well as validation of additional amyloidogenic and non-amyloidogenic species.