Introduction: The Importance of Neuroimaging-Based Progression Models

Disease modeling in Parkinson’s disease (PD) plays a crucial role in understanding pathophysiology, predicting clinical outcomes, and optimizing clinical trial design1,2,3. Models serve multiple functions: they facilitate patient stratification, enable estimation of disease onset, disease state (staging), and progression rates, and provide a framework for assessing potential disease-modifying treatments. Hitherto, models have often assumed fixed and linear progression trajectories to reduce complexity, yet PD shows substantial variability across individuals and disease stages. In the field of neuroimaging, this modeling typically involves tracking changes in biomarkers such as dopamine transporter (DAT) binding or [18F]fluoro-L-dopa (FDOPA) uptake over time using PET or SPECT.

Yet a fundamental conceptual distinction is often blurred: what exactly are we modeling when we speak of “progression”? In PD, progression may refer to the advancement of the underlying pathological processes (e.g., dopaminergic neurodegeneration or alpha-synuclein spread), or to the evolution of clinical symptomatology (motor or non-motor). While these two types of progression are related, they are not necessarily tightly coupled. Biomarker changes may precede clinical symptoms by years, and compensatory mechanisms, such as motor reserve, may delay symptom onset or mask deterioration.

This misalignment is further compounded by two key issues. First, “de novo” PD patients can look strikingly different at diagnosis depending on when they first present to clinical attention, making any fixed staging assumptions problematic. Second, the clinical severity scores used in trials and observational cohorts, such as the MDS-UPDRS part III, are inherently noisy, with day-to-day variability and susceptibility to medication effects, rater variability, and fluctuations unrelated to underlying pathology.

Thus, while PET and SPECT imaging offer valuable objective indices of disease biology, interpreting their temporal trajectories as proxies for clinical progression remains challenging. A linear decline in dopaminergic signal, for example, does not necessarily imply a linear trajectory in motor symptoms. Recognizing and addressing this complexity is crucial for the next generation of progression models.

In this Comment, we revisit the use of linear, exponential, and sigmoidal frameworks in interpreting longitudinal neuroimaging studies in PD, in the context of recent propositions for biomarker-based definitions and staging of PD4,5. We argue for more flexible, individualized models that account for variability in progression patterns, clinical-biomarker misalignment, and the limitation of current measures.

Linear Progression Model: A Simplified but Practical Framework

The linear model assumes that neurodegeneration occurs at a relatively constant rate over time, a concept rooted in the idea that physiological decline in aging may follow approximately linear trajectories (Fig. 1A, the constant-rate model)6,7. While this assumption is a simplification, some support comes from studies in non-human primates showing cellular mechanisms that overlap between aging and PD8. One variant of this concept is the event-driven linear model (Fig. 1B), in which the onset of degeneration is triggered by a specific external or internal insult, such as an environmental exposure, after which neurodegeneration progresses at a steady rate. This contrasts with the long-latency model (Fig. 1A), where the disease reflects a lifelong predisposition or gradual deviation from normal aging without a clear trigger. Nonetheless, true clinical PD progression is unlikely to follow a strict linear path in most cases over the disease course.

Fig. 1: Prototypical Models of Neuronal Loss Patterns in PD.
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Illustrative models of dopaminergic neuron loss in the substantia nigra pars compacta, representing possible progression patterns in PD. For modeling, an initial count of 500,000 dopaminergic neurons at birth was assumed, decreasing to approximately 300,000–400,000 neurons by the seventh decade due to normal aging44. Motor symptoms in PD were set to emerge when dopaminergic neuron loss reaches 50% relative to age-matched healthy individuals13. The shaded region in each panel represents the premotor phase, the interval between the onset of neuronal pathology and the onset of motor symptoms. Green dotted line denotes age-related neuronal loss. A Linear Long Latency Model: This model assumes a congenital predisposition, with neuronal loss following a pattern of accelerated aging over a prolonged premotor phase. B Linear Model with Event: This model suggests an event at age 50 disrupts normal aging, leading to a linear decline in neuron count. The premotor period is estimated at 15 years. C Exponential Decay Model: Here, an acute event causes a sudden 10% reduction in neurons, followed by a rapid, exponential annual loss of 10%. The premotor period is approximately 5 years. D Sigmoidal Model: This model proposes a gradual initiation of pathology starting at age 40, with an accelerating decline that later decelerates, approaching a non-zero asymptote. The premotor phase spans roughly 25 years.

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Despite this, a subset of PET and SPECT studies focusing on presynaptic dopaminergic function, such as striatal DAT and aromatic amino acid decarboxylase (AADC, e.g. FDOPA) binding, have reported relatively steady, near-linear reductions over time (Table 1), particularly during the early stages of disease. Similarly, longitudinal studies in Alzheimer’s disease (AD) have shown that some biomarkers, including CSF Aβ, FDG-PET and hippocampal volume, may follow approximately linear trajectories across the disease course9. These findings suggest that for certain biological systems or disease phases, a linear progression model may provide a reasonable approximation.

Table 1 Longitudinal PET or SPECT studies (n ≥ 10) investigating the progression pattern of dopamine transporter (DAT) or aromatic amino acid decarboxylase (AADC) binding loss in PD
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Clinically, the linear model continues to be widely used due to its simplicity and interpretability. It remains a standard framework for therapeutic planning and clinical trial simulations, especially in early PD, where symptom progression may appear gradual and relatively uniform. For instance, a recent study by Dzialas et al. demonstrated a significant interaction between time and DAT loss, showing that the rate of DAT decline was indicative of increasing motor symptom severity10, supporting the model’s practical utility in correlating biomarker dynamics with clinical outcomes.

However, the linear model has certain limitations. It may obscure the biological and clinical heterogeneity of PD, particularly in later stages where compensatory mechanisms begin to fail. External modifiers such as co-morbidities, medication changes, or acute stressors can further influence the dynamics of biological and clinical progression. Moreover, the relative sparsity of longitudinal neuroimaging data, limited by cost, participant burden, and radiation exposure, constrains the development and validation of more complex models. Biomarkers, particularly those derived from PET and SPECT neuroimaging studies conducted in early to mid-stage PD patients, may not fully cover the final plateau phase, potentially creating the impression of linearity11. Furthermore, it is possible that the aggregate of individual exponential or sigmoidal decline patterns within a heterogeneous population could collectively appear as a linear trajectory. This effect may arise from variability in disease dynamics, including differences in onset timing, progression rates, and underlying pathological mechanisms across the observed cohort. Thus, while useful, the linear model should be applied cautiously, particularly when forecasting long-term clinical outcomes and modeling advanced disease.

Exponential Progression Model: The Concept of Accelerated Degeneration

Exponential decay is a well-characterized principle in the natural sciences, observed across diverse processes, such as radioactive decay and the physiological clearance of substances. It can be understood within a risk-based stochastic framework, where neurodegeneration occurs probabilistically, with each neuron facing a time-invariant risk of death. In such cases, the number of surviving neurons decreases exponentially over time, forming the basis of a constant-risk model7.

Applied to neurodegeneration, an exponential model suggests an early rapid loss of neurons following a short-term trigger, after which the rate of degeneration slows most likely due to reaching a biological “floor” (Fig. 1C). The landmark neuropathological study by Fearnley and Lees supported the non-linear model, proposing that the bulk loss of dopaminergic cells in PD happens within a relatively brief time period12. By fitting an exponential decay curve to the observed nigral neuronal loss, the authors estimated the presymptomatic phase to be around 5 years—considerably shorter than previous estimates. More recent findings, including evidence of a rapid decline in dopaminergic function within the putamen during the first 1-4 years post-diagnosis, followed by a plateau, further support a negative exponential non-linear trajectory13.

Much like the linear model, there is PET and SPECT dopaminergic neuroimaging evidence supporting an exponential model of PD progression (Table 1). One notable observation comes from hemispheric asymmetry: the ipsilateral hemisphere (relative to the initial side of motor symptom onset) often shows a delayed but steep decline in dopaminergic function compared to the contralateral side14. While this asymmetric pattern may reflect a non-linear trajectory of neuronal degeneration, it could also be influenced by compensatory mechanisms. For instance, early upregulation of DAT expression in the less affected hemisphere might temporarily mask underlying neurodegeneration. Once these compensatory processes are exhausted, a marked drop in DAT signal becomes detectable. Thus, the observed asymmetry may not solely reflect differences in neurodegeneration timing or rate, but also in the failure dynamics of compensatory responses, adding another layer of complexity to the interpretation of progression patterns captured by imaging.

Sigmoidal Progression Model: A Framework for Pathological and Clinical Complexity

Compared to the exponential decay model, sigmoidal biomarker progression may better reflect the heterogeneous and non-linear nature of PD. This model accounts for an initial resilience, followed by acceleration of degeneration and eventual plateauing (Fig. 1D). The sigmoidal model aligns with a prion-like spread of alpha-synuclein pathology, which follows non-linear propagation dynamics across brain regions1. This model also reflects the long premotor phase of PD, during which pathology may spread silently before the relatively rapid progression of motor symptoms. The pattern is mirrored in clinical observations where patients experience a rapid loss of motor function after a stable period15, and sigmoidal models may align more accurately with longitudinal UPDRS data, potentially capturing the initial slow progression, rapid middle-phase worsening, and later plateau3.

Sigmoidal patterns have been documented in AD, where repeated PET imaging suggests that PiB-PET binding follows a sigmoidal trajectory16, with similar patterns observed for tau and p-tau biomarkers9. In PD, the exponential decline observed in PET and SPECT studies could represent the tail-end of a longer sigmoidal trajectory, where initial progression is slow, followed by acceleration and then stabilization. However, limited sensitivity of neuroimaging at extreme stages of neurodegeneration can introduce both floor (detection limit) and ceiling (saturation) effects, potentially creating a sigmoid appearance, as observed in amyloid imaging studies17. While a sigmoidal trajectory is one possible interpretation of PD progression patterns, no published longitudinal dopaminergic neuroimaging studies to date have explicitly modelled progression using a sigmoidal function.

Although sigmoidal models are conceptually well-aligned with the prion-like spread of alpha-synuclein, a major limitation in current biomarker research is the absence of validated α-synuclein PET tracers for routine human use. As such, no longitudinal neuroimaging studies in PD have yet applied α-synuclein imaging to assess disease progression. The eventual availability of specific and reliable α-synuclein PET tracers could provide crucial data to directly test sigmoidal propagation hypotheses in vivo and help bridge the gap between pathology-based models and longitudinal biomarker trajectories.

Beyond Traditional Models: A Case for Multi-Dimensional Approaches

Given the variability in PD progression across patients and symptom domains, a single rigid model is unlikely to fully capture clinical disease complexity (Table 2). This complexity in PD parallels the inter- and intraindividual variability of disease progression in amyotrophic lateral sclerosis (ALS), which presents a wide range of decline patterns. ALS patients exhibit diverse clinical trajectories, including sigmoidal, convex, concave, and linear forms of progression18. Moreover, sudden and dramatic declines, or “functional cliffs,” can be triggered, possibly by external factors such as infections, vascular events, or medication changes18. In PD, similar “last straw” events may act as tipping points19, where a relatively stable disease state transitions into rapid deterioration due to minor external or internal perturbations. This concept mirrors models from other fields, such as climate science, where systems can remain in equilibrium until a threshold is crossed, leading to significant and dynamic changes. For example, cognitive function in PD patients appears to remain stable for years before reaching a certain inflection point, commonly around 13 years post-diagnosis, at which deterioration accelerates20. Data from the Parkinson’s Progression Markers Initiative (PPMI) further support this complexity18,21. Machine learning analyses of PPMI and Parkinson’s Disease Biomarkers Program (PDBP) data have identified eight unique PD states with overlapping trajectories of motor and non-motor impairments, highlighting the non-linear and non-sequential nature of clinical progression22.

Table 2 Conceptual and practical comparison of linear, exponential and sigmoidal progression models in PD
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Recent developments in data-driven disease progression modeling have introduced powerful statistical frameworks that complement and extend traditional biomarker trajectory models. Several approaches now estimate individualized disease time and stage while flexibly modeling non-linear biomarker change across the disease course. These include latent time joint mixed-effects models23, as well as disease course mapping that summarizes the range of possible PD trajectories by positioning the progression of each patient relative to a reference population in several dimensions24,25. Event-based generative statistical models offer an alternative formulation by ordering biomarker abnormality without assuming a fixed scale, with recent PD applications incorporating MRI data and subtyping strategies26,27,28. These methods collectively demonstrate the feasibility of reconstructing latent progression time, subtype, and inter-individual variation from cross-sectional and sparse longitudinal data. While many of these approaches are still in the research stage, their incorporation into future imaging studies could enhance the field’s capacity to capture the full complexity of PD progression.

Conclusions and Future Directions

Models assuming fixed progression rates for dopaminergic imaging in PD have thus far offered limited utility, largely due to their inability to account for individual variability, stage-dependent dynamics, and clinical-biomarker misalignment. Considering these insights, we advocate for the development and clinical implementation of adaptable, multimodal progression models that reflect the non-linear and heterogeneous nature of PD. Integrating neuroimaging with clinical, genetic, and digital health data into individualized modeling frameworks—validated across diverse longitudinal cohorts—should be a central aim of future research.

Although the assumption of an underlying sigmoidal model aligns with the dynamics of initially localized polynomial spreading of alpha-synuclein pathology, significant disconnects can exist between this pathological trajectory and clinical symptoms. Even the basic assumption of monotonicity (markers progressing consistently from normal to diseases levels) may not be true for all biomarkers11. The heterogeneity in PD progression calls for a flexible approach that goes beyond a uniform, rigid model, considering the influence of cerebral co-pathologies29, recognizing the limitations of relying on any single proteinopathic mechanism or neuroimaging method.

In the clinic, predicting individual disease progression based on a short-term clinical ‘snapshot’ remains challenging due to the unpredictable nature of PD and the wide range of possible trajectories. For neuroimaging research, developing integrative computational models11 that incorporate variability in progression rates, PD subtypes, and the impact of co-pathologies and co-morbidities is essential. These models should be validated with diverse longitudinal datasets and used to inform both clinical practice and trial designs.