One-hit stochastic decline in a mechanochemical model of cytoskeleton-induced neuron death III: diffusion pulse death zones

The Impact of Mathematical Modeling in Understanding the Mechanisms Underlying Neurodegeneration: Evolving Dimensions and Future Directions

Neurodegenerative diseases are a heterogeneous group of disorders that are characterized by the progressive dysfunction and loss of neurons. Here, we distil and discuss the current state of modeling in the area of neurodegeneration, and objectively compare the gaps between existing clinical knowledge and the mechanistic understanding of the major pathological processes implicated in neurodegenerative disorders. We also discuss new directions in the field of neurodegeneration that hold potential for furthering therapeutic interventions and strategies.

Mathematical and computational models of the retina in health, development and disease

The retina confers upon us the gift of vision, enabling us to perceive the world in a manner unparalleled by any other tissue. Experimental and clinical studies have provided great insight into the physiology and biochemistry of the retina; however, there are questions which cannot be answered using these methods alone. Mathematical and computational techniques can provide complementary insight into this inherently complex and nonlinear system. They allow us to characterise and predict the behaviour of the retina, as well as to test hypotheses which are experimentally intractable. In this review, we survey some of the key theoretical models of the retina in the healthy, developmental and diseased states. The main insights derived from each of these modelling studies are highlighted, as are model predictions which have yet to be tested, and data which need to be gathered to inform future modelling work. Possible directions for future research are also discussed. Whilst the present modelling studies have achieved great success in unravelling the workings of the retina, they have yet to achieve their full potential. For this to happen, greater involvement with the modelling community is required, and stronger collaborations forged between experimentalists, clinicians and theoreticians. It is hoped that, in addition to bringing the fruits of current modelling studies to the attention of the ophthalmological community, this review will encourage many such future collaborations.

Shapes of the trajectories of 5 major biomarkers of Alzheimer disease

OBJECTIVE

To characterize the shape of the trajectories of Alzheimer disease biomarkers as a function of Mini-Mental State Examination (MMSE) score.

DESIGN AND SETTING

Longitudinal registries from the Mayo Clinic and the Alzheimer's Disease Neuroimaging Initiative.

PATIENTS

Two different samples (n = 343 and n = 598) were created that spanned the cognitive spectrum from normal to Alzheimer disease dementia. Subgroup analyses were performed in members of both cohorts (n = 243 and n = 328) who were amyloid positive at baseline.

MAIN OUTCOME MEASURES

The shape of biomarker trajectories as a function of MMSE score, adjusted for age, was modeled and described as baseline (cross-sectional) and within-subject longitudinal effects. Biomarkers evaluated were cerebrospinal fluid (CSF) Aβ42 and tau levels, amyloid and fluorodeoxyglucose positron emission tomography imaging, and structural magnetic resonance imaging.

RESULTS

Baseline biomarker values generally worsened (ie, nonzero slope) with lower baseline MMSE score. Baseline hippocampal volume, amyloid positron emission tomography, and fluorodeoxyglucose positron emission tomography values plateaued (ie, nonlinear slope) with lower MMSE score in 1 or more analyses. Longitudinally, within-subject rates of biomarker change were associated with worsening MMSE score. Nonconstant within-subject rates (deceleration) of biomarker change were found in only 1 model.

CONCLUSIONS

Biomarker trajectory shapes by MMSE score were complex and were affected by interactions with age and APOE status. Nonlinearity was found in several baseline effects models. Nonconstant within-subject rates of biomarker change were found in only 1 model, likely owing to limited within-subject longitudinal follow-up. Creating reliable models that describe the full trajectories of Alzheimer disease biomarkers will require significant additional longitudinal data in individual participants.

Rates of decline in Alzheimer disease decrease with age

Age is the strongest risk factor for sporadic Alzheimer disease (AD), yet the effects of age on rates of clinical decline and brain atrophy in AD have been largely unexplored. Here, we examined longitudinal rates of change as a function of baseline age for measures of clinical decline and structural MRI-based regional brain atrophy, in cohorts of AD, mild cognitive impairment (MCI), and cognitively healthy (HC) individuals aged 65 to 90 years (total n = 723). The effect of age was modeled using mixed effects linear regression. There was pronounced reduction in rates of clinical decline and atrophy with age for AD and MCI individuals, whereas HCs showed increased rates of clinical decline and atrophy with age. This resulted in convergence in rates of change for HCs and patients with advancing age for several measures. Baseline cerebrospinal fluid densities of AD-relevant proteins, Aβ_1–42, tau, and phospho-tau_181p (ptau), showed a similar pattern of convergence with advanced age across cohorts, particularly for ptau. In contrast, baseline clinical measures did not differ by age, indicating uniformity of clinical severity at baseline. These results imply that the phenotypic expression of AD is relatively mild in individuals older than approximately 85 years, and this may affect the ability to distinguish AD from normal aging in the very old. Our findings show that inclusion of older individuals in clinical trials will substantially reduce the power to detect disease-modifying therapeutic effects, leading to dramatic increases in required clinical trial sample sizes with age of study sample.

Alzheimer disease: new concepts on its neurobiology and the clinical role imaging will play

Alzheimer disease (AD) is one of, if not the most, feared diseases associated with aging. The prevalence of AD increases exponentially with age after 60 years. Increasing life expectancy coupled with the absence of any approved disease-modifying therapies at present position AD as a dominant public health problem. Major advances have occurred in the development of disease biomarkers for AD in the past 2 decades. At present, the most well-developed AD biomarkers are the cerebrospinal fluid analytes amyloid-β 42 and tau and the brain imaging measures amyloid positron emission tomography (PET), fluorodeoxyglucose PET, and magnetic resonance imaging. CSF and imaging biomarkers are incorporated into revised diagnostic guidelines for AD, which have recently been updated for the first time since their original formulation in 1984. Results of recent studies suggest the possibility of an ordered evolution of AD biomarker abnormalities that can be used to stage the typical 20-30-year course of the disease. When compared with biomarkers in other areas of medicine, however, the absence of standardized quantitative metrics for AD imaging biomarkers constitutes a major deficiency. Failure to move toward a standardized system of quantitative metrics has substantially limited potential diagnostic usefulness of imaging in AD. This presents an important opportunity that, if widely embraced, could greatly expand the application of imaging to improve clinical diagnosis and the quality and efficiency of clinical trials.

A network diffusion model of disease progression in dementia

Patterns of dementia are known to fall into dissociated but dispersed brain networks, suggesting that the disease is transmitted along neuronal pathways rather than by proximity. This view is supported by neuropathological evidence for "prion-like" transsynaptic transmission of disease agents like misfolded tau and beta amyloid. We mathematically model this transmission by a diffusive mechanism mediated by the brain's connectivity network obtained from tractography of 14 healthy-brain MRIs. Subsequent graph theoretic analysis provides a fully quantitative, testable, predictive model of dementia. Specifically, we predict spatially distinct "persistent modes," which, we found, recapitulate known patterns of dementia and match recent reports of selectively vulnerable dissociated brain networks. Model predictions also closely match T1-weighted MRI volumetrics of 18 Alzheimer's and 18 frontotemporal dementia subjects. Prevalence rates predicted by the model strongly agree with published data. This work has many important implications, including dimensionality reduction, differential diagnosis, and especially prediction of future atrophy using baseline MRI morphometrics.