Dynamical network model for age-related health deficits and mortality

Network topologies for maximal organismal health span and lifespan

The population dynamics of human health and mortality can be jointly captured by complex network models using scale-free network topology. To validate and understand the choice of scale-free networks, we investigate which network topologies maximize either lifespan or health span. Using the Generic Network Model (GNM) of organismal aging, we find that both health span and lifespan are maximized with a "star" motif. Furthermore, these optimized topologies exhibit maximal lifespans that are not far above the maximal observed human lifespan. To approximate the complexity requirements of the underlying physiological function, we then constrain network entropies. Using non-parametric stochastic optimization of network structure, we find that disassortative scale-free networks exhibit the best of both lifespan and health span. Parametric optimization of scale-free networks behaves similarly. We further find that higher maximum connectivity and lower minimum connectivity networks enhance both maximal lifespans and health spans by allowing for more disassortative networks. Our results validate the scale-free network assumption of the GNM and indicate the importance of disassortativity in preserving health and longevity in the face of damage propagation during aging. Our results highlight the advantages provided by disassortative scale-free networks in biological organisms and subsystems.

Measurements of damage and repair of binary health attributes in aging mice and humans reveal that robustness and resilience decrease with age, operate over broad timescales, and are affected differently by interventions

As an organism ages, its health-state is determined by a balance between the processes of damage and repair. Measuring these processes requires longitudinal data. We extract damage and repair transition rates from repeated observations of binary health attributes in mice and humans to explore robustness and resilience, which respectively represent resisting or recovering from damage. We assess differences in robustness and resilience using changes in damage rates and repair rates of binary health attributes. We find a conserved decline with age in robustness and resilience in mice and humans, implying that both contribute to worsening aging health - as assessed by the frailty index (FI). A decline in robustness, however, has a greater effect than a decline in resilience on the accelerated increase of the FI with age, and a greater association with reduced survival. We also find that deficits are damaged and repaired over a wide range of timescales ranging from the shortest measurement scales toward organismal lifetime timescales. We explore the effect of systemic interventions that have been shown to improve health, including the angiotensin-converting enzyme inhibitor enalapril and voluntary exercise for mice. We have also explored the correlations with household wealth for humans. We find that these interventions and factors affect both damage and repair rates, and hence robustness and resilience, in age and sex-dependent manners.

Allostatic load in the context of disasters

Environmental disasters, pandemics, and other major traumatic events such as the Covid-19 pandemic or war contribute to psychosocial stress which manifests in a wide range of mental and physical consequences. The increasing frequency and severity of such events suggest that the adverse effects of toxic stress are likely to become more widespread and pervasive in the future. The allostatic load (AL) model has important elements that lend themselves well for identifying adverse health effects of disasters. Here we examine several articulations of AL from the standpoint of using AL to gauge short- and long-term health effects of disasters and to provide predictive capacity that would enable mitigation or prevention of some disaster-related health consequences. We developed a transdisciplinary framework combining indices of psychosocial AL and physiological AL to produce a robust estimate of overall AL in people affected by disasters and other traumatic events. In conclusion, we urge researchers to consider the potential of using AL as a component in a proposed disaster-oriented human health observing system.

Recovery coupling in multilayer networks

The increased complexity of infrastructure systems has resulted in critical interdependencies between multiple networks—communication systems require electricity, while the normal functioning of the power grid relies on communication systems. These interdependencies have inspired an extensive literature on coupled multilayer networks, assuming a hard interdependence, where a component failure in one network causes failures in the other network, resulting in a cascade of failures across multiple systems. While empirical evidence of such hard failures is limited, the repair and recovery of a network requires resources typically supplied by other networks, resulting in documented interdependencies induced by the recovery process. In this work, we explore recovery coupling, capturing the dependence of the recovery of one system on the instantaneous functional state of another system. If the support networks are not functional, recovery will be slowed. Here we collected data on the recovery time of millions of power grid failures, finding evidence of universal nonlinear behavior in recovery following large perturbations. We develop a theoretical framework to address recovery coupling, predicting quantitative signatures different from the multilayer cascading failures. We then rely on controlled natural experiments to separate the role of recovery coupling from other effects like resource limitations, offering direct evidence of how recovery coupling affects a system’s functionality.

Infrastructure and power systems are often represented as multilayer structures of interdependent networks. Danziger and Barabási demonstrate the presence of recovery coupling in such systems, where the recovery of an element in one network requires resources from nodes and links in another network.

Modeling aging and its impact on cellular function and organismal behavior

Aging is a complex phenomenon of functional decay in a biological organism. Although the effects of aging are readily recognizable in a wide range of organisms, the cause(s) of aging are ill defined and poorly understood. Experimental methods on model organisms have driven significant insight into aging as a process, but have not provided a complete model of aging. Computational biology offers a unique opportunity to resolve this gap in our knowledge by generating extensive and testable models that can help us understand the fundamental nature of aging, identify the presence and characteristics of unaccounted aging factor(s), demonstrate the mechanics of particular factor(s) in driving aging, and understand the secondary effects of aging on biological function. In this review, we will address each of the above roles for computational biology in aging research. Concurrently, we will explore the different applications of computational biology to aging in single-celled versus multicellular organisms. Given the long history of computational biogerontological research on lower eukaryotes, we emphasize the key future goals of gradually integrating prior models into a holistic map of aging and translating successful models to higher-complexity organisms.

The degree of frailty as a translational measure of health in aging

Frailty is a multiply determined, age-related state of increased risk for adverse health outcomes. We review how the degree of frailty conditions the development of late-life diseases and modifies their expression. The risks for frailty range from subcellular damage to social determinants. These risks are often synergistic-circumstances that favor damage also make repair less likely. We explore how age-related damage and decline in repair result in cellular and molecular deficits that scale up to tissue, organ and system levels, where they are jointly expressed as frailty. The degree of frailty can help to explain the distinction between carrying damage and expressing its usual clinical manifestations. Studying people-and animals-who live with frailty, including them in clinical trials and measuring the impact of the degree of frailty are ways to better understand the diseases of old age and to establish best practices for the care of older adults.

The potential for complex computational models of aging

The gradual accumulation of damage and dysregulation during the aging of living organisms can be quantified. Even so, the aging process is complex and has multiple interacting physiological scales - from the molecular to cellular to whole tissues. In the face of this complexity, we can significantly advance our understanding of aging with the use of computational models that simulate realistic individual trajectories of health as well as mortality. To do so, they must be systems-level models that incorporate interactions between measurable aspects of age-associated changes. To incorporate individual variability in the aging process, models must be stochastic. To be useful they should also be predictive, and so must be fit or parameterized by data from large populations of aging individuals. In this perspective, we outline where we have been, where we are, and where we hope to go with such computational models of aging. Our focus is on data-driven systems-level models, and on their great potential in aging research.

Generating synthetic aging trajectories with a weighted network model using cross-sectional data

We develop a computational model of human aging that generates individual health trajectories with a set of observed health attributes. Our model consists of a network of interacting health attributes that stochastically damage with age to form health deficits, leading to eventual mortality. We train and test the model for two different cross-sectional observational aging studies that include simple binarized clinical indicators of health. In both studies, we find that cohorts of simulated individuals generated from the model resemble the observed cross-sectional data in both health characteristics and mortality. We can generate large numbers of synthetic individual aging trajectories with our weighted network model. Predicted average health trajectories and survival probabilities agree well with the observed data.

Brain aging and garbage cleaning : Modelling the role of sleep, glymphatic system, and microglia senescence in the propagation of inflammaging

Brain aging is a complex process involving many functions of our body and described by the interplay of a sleep pattern and changes in the metabolic waste concentration regulated by the microglial function and the glymphatic system. We review the existing modelling approaches to this topic and derive a novel mathematical model to describe the crosstalk between these components within the conceptual framework of inflammaging. Analysis of the model gives insight into the dynamics of garbage concentration and linked microglial senescence process resulting from a normal or disrupted sleep pattern, hence, explaining an underlying mechanism behind healthy or unhealthy brain aging. The model incorporates accumulation and elimination of garbage, induction of glial activation by garbage, and glial senescence by over-activation, as well as the production of pro-inflammatory molecules by their senescence-associated secretory phenotype (SASP). Assuming that insufficient sleep leads to the increase of garbage concentration and promotes senescence, the model predicts that if the accumulation of senescent glia overcomes an inflammaging threshold, further progression of senescence becomes unstoppable even if a normal sleep pattern is restored. Inverting this process by "rejuvenating the brain" is only possible via a reset of concentration of senescent glia below this threshold. Our model approach enables analysis of space-time dynamics of senescence, and in this way, we show that heterogeneous patterns of inflammation will accelerate the propagation of senescence profile through a network, confirming a negative effect of heterogeneity.

Optimal control of aging in complex networks

Many complex systems experience damage accumulation, which leads to aging, manifest as an increasing probability of system collapse with time. This naturally raises the question of how to maximize health and longevity in an aging system at minimal cost of maintenance and intervention. Here, we pose this question in the context of a simple interdependent network model of aging in complex systems and show that it exhibits cascading failures. We then use both optimal control theory and reinforcement learning alongside a combination of analysis and simulation to determine optimal maintenance protocols. These protocols may motivate the rational design of strategies for promoting longevity in aging complex systems with potential applications in therapeutic schedules and engineered system maintenance.

Network analysis of frailty and aging: Empirical data from the Mexican Health and Aging Study

BACKGROUND

Frailty remains a challenge in the aging research area with a number of gaps in knowledge still to be filled. Frailty seems to behave as a network, and in silico evidence is available on this matter. Having in vivo evidence that frailty behaves as a complex network was the main purpose of our study.

METHODS

Data from the Mexican Health and Aging Study (main data 2012, mortality 2015) was used. Frailty was operationalized with a 35-deficit frailty index (FI). Analyzed nodes were the deficits plus death. The edges, linking those nodes were obtained through structural learning, and an undirected graph associated with a discrete probabilistic graphical model (Markov network) was derived. Two algorithms, hill-climbing (hc) and Peter and Clark (PC), were used to derive the graph structure. Analyses were performed for the whole population and tertiles of the total FI score.

RESULTS

From the total sample of 10,983 adults aged 50 or older, 43.8% were women, and the mean age was 64.6 years (SD = 9.3). The number of connections increased according to the tertile level of the FI score. As the FI score raised, groups of interconnected deficits increased and how the nodes are connected changed.

CONCLUSIONS

Frailty phenomenon can be modeled using a Bayesian network. Using the full sample, the most central nodes were self-report of health (most connected node) and difficulty walking a block, and all deficits related to mobility were very interconnected. When frailty levels are considered, the most connected nodes differ, but are related with vitality, mainly at lower frailty levels. We derived that not all deficits are equally related since clusters of very related deficits and non-connected deficits were obtained, which might be considered in the construction of the FI score. Further research should aim to identify the nature of all observed interactions, which might allow the development of specific interventions to mitigate the consequences of frailty in older adults.

Aging in transport processes on networks with stochastic cumulative damage

In this paper we explore the evolution of transport capacity on networks with stochastic incidence of damage and accumulation of faults in their connections. For each damaged configuration of the network, we analyze a Markovian random walker that hops over weighted links that quantify the capacity of transport of each connection. The weights of the links in the network evolve due to randomly occurring damage effects that reduce gradually the transport capacity of the structure. We introduce a global measure to determine the functionality of each configuration and how the system ages due to the accumulation of damage that cannot be repaired completely. Then, by assuming a minimum value of the functionality required for the system to be "alive," we explore the statistics of the lifetimes for several realizations of this process in different types of networks. Finally, we analyze the characteristic longevity of such a system and its relation with the "complexity" of the network structure. One finding is that systems with greater complexity live longer. Our approach introduces a model of aging processes relating the reduction of functionality with the accumulation of "misrepairs" and the lifetime of a complex system.

Heterogeneity of Human Aging and Its Assessment

Understanding the heterogeneity in health of older adults is a compelling question in the biology of aging. We analyzed the performance of five measures of health heterogeneity, judging them by their ability to predict mortality. Using clinical and biomarker data on 1,013 participants of the Canadian Study of Health and Aging who were followed for up to 6 years, we calculated two indices of biological age using the Klemera and Doubal method, which controversially includes using chronological age as a "biomarker," and three frailty indices (FIs) that do not include chronological age: a standard clinical FI, an FI from standard laboratory blood tests and blood pressure, and their combination (FI-combined). Predictive validity was tested using Cox proportional hazards analysis and discriminative ability by the area under the receiver-operating characteristic curves. All five measures showed moderate performance that was improved by combining measures to evaluate larger numbers of items. The greatest addition in explanatory power came from the FI-combined that showed the best mortality prediction in an age-adjusted model. More extensive comparisons across different databases are required, but these results do not support including chronological age as a biomarker.

Changes in the Lethality of Frailty Over 30 Years: Evidence From Two Cohorts of 70-Year-Olds in Gothenburg Sweden

Background

With aging, health deficits accumulate: people with few deficits for their age are fit, and those with more are frail. Despite recent reports of improved health in old age, how deficit accumulation is changing is not clear. Our objectives were to evaluate changes over 30 years in the degree of deficit accumulation and in the relationship between frailty and mortality in older adults.

Methods

We analyzed data from two population based, prospective longitudinal cohorts, assembled in 1971-1972 and 2000-2001, respectively. Residents of Gothenburg Sweden, systematically drawn from the Swedish population registry. The 1901-1902 cohort (N = 973) had a response rate of 84.8%; the 1930 cohort (N = 500) had a response rate of 65.1%. A frailty index using 36 deficits was calculated using data from physical examinations, assessments of physical activity, daily, sensory and social function, and laboratory tests. We evaluated mortality over 12.5 years in relation to the frailty index.

Results

Mean frailty levels were the same (x¯ = 0.20, p = .37) in the 1901-1902 cohort as in the 1930 cohort. Although the frailty index was linked to the risk of death in both cohorts, the hazards ratio decreased from 1.67 per 0.1 increment in the frailty index for the first cohort to 1.32 for the second cohort (interaction term p = .005).

Discussion

Although frailty was as common at age 70 as before, its lethality appears to be less. Just why this is so should be explored further.

Outcomes of octogenarians discharged from the hospital after prolonged intensive care unit length of stay after cardiac surgery

OBJECTIVE

Octogenarians offered complex cardiac surgery frequently experience a prolonged intensive care unit length of stay; however, minimal data exist on the outcomes of these patients. We sought to determine the rates and predictors of 1-year noninstitutionalized survival ("functional survival") and rehospitalization for octogenarian patients with prolonged intensive care unit length of stay after cardiac surgery and who were discharged from hospital.

METHODS

The outcomes of discharged patients aged 80 years or more who underwent cardiac surgery with prolonged intensive care unit length of stay (≥5 consecutive days) from January 1, 2000, to December 31, 2011, were examined retrospectively from linked clinical and administrative provincial databases. Regression analysis was used to determine predictors of 1-year functional survival and rehospitalization after discharge from the hospital.

RESULTS

A total of 80 of 683 (11.7%) discharged octogenarian patients had prolonged intensive care unit length of stay. Functional survival at 1 year was 92% and 81% for those with nonprolonged and prolonged intensive care unit lengths of stay, respectively (P < .01). Lack of outpatient physician visits within 30 days of discharge (hazard ratio, 5.18; P < .01) was a significant predictor of poor 1-year functional survival. The 1-year rehospitalization rates were 38% and 48% for those with nonprolonged and prolonged intensive care unit lengths of stay, respectively, with 41% of all rehospitalizations occurring within 30 days of initial discharge. A rural residence (hazard ratio, 1.82; P < .01) and nosocomial pneumonia during patients' operative admissions (hazard ratio, 2.74; P < .01) were associated with rehospitalization within 30 days of discharge.

CONCLUSIONS

Octogenarians with prolonged intensive care unit length of stay have acceptable functional survival at 1 year but have high rates of early rehospitalization. Access to health services may influence functional survival and early rehospitalizations. These data suggest that close follow-up of these vulnerable patients after hospital discharge is warranted.

The impact of frailty on intensive care unit outcomes: a systematic review and meta-analysis

Purpose

Functional status and chronic health status are important baseline characteristics of critically ill patients. The assessment of frailty on admission to the intensive care unit (ICU) may provide objective, prognostic information on baseline health. To determine the impact of frailty on the outcome of critically ill patients, we performed a systematic review and meta-analysis comparing clinical outcomes in frail and non-frail patients admitted to ICU.

Methods

We searched the Cochrane Central Register of Controlled Trials, MEDLINE, EMBASE, PubMed, CINAHL, and Clinicaltrials.gov. All study designs with the exception of narrative reviews, case reports, and editorials were included. Included studies assessed frailty in patients greater than 18 years of age admitted to an ICU and compared outcomes between fit and frail patients. Two reviewers independently applied eligibility criteria, assessed quality, and extracted data. The primary outcomes were hospital and long-term mortality. We also determined the prevalence of frailty, the impact on other patient-centered outcomes such as discharge disposition, and health service utilization such as length of stay.

Results

Ten observational studies enrolling a total of 3030 patients (927 frail and 2103 fit patients) were included. The overall quality of studies was moderate. Frailty was associated with higher hospital mortality [relative risk (RR) 1.71; 95% CI 1.43, 2.05; p < 0.00001; I² = 32%] and long-term mortality (RR 1.53; 95% CI 1.40, 1.68; p < 0.00001; I² = 0%). The pooled prevalence of frailty was 30% (95% CI 29–32%). Frail patients were less likely to be discharged home than fit patients (RR 0.59; 95% CI 0.49, 0.71; p < 0.00001; I² = 12%).

Conclusions

Frailty is common in patients admitted to ICU and is associated with worsened outcomes. Identification of this previously unrecognized and vulnerable ICU population should act as the impetus for investigating and implementing appropriate care plans for critically ill frail patients. Registration: PROSPERO (ID: CRD42016053910).

Electronic supplementary material

The online version of this article (doi:10.1007/s00134-017-4867-0) contains supplementary material, which is available to authorized users.

Aging, frailty and complex networks

When people age their mortality rate increases exponentially, following Gompertz's law. Even so, individuals do not die from old age. Instead, they accumulate age-related illnesses and conditions and so become increasingly vulnerable to death from various external and internal stressors. As a measure of such vulnerability, frailty can be quantified using the frailty index (FI). Larger values of the FI are strongly associated with mortality and other adverse health outcomes. This association, and the insensitivity of the FI to the particular health variables that are included in its construction, makes it a powerful, convenient, and increasingly popular integrative health measure. Still, little is known about why the FI works so well. Our group has recently developed a theoretical network model of health deficits to better understand how changes in health are captured by the FI. In our model, health-related variables are represented by the nodes of a complex network. The network has a scale-free shape or "topology": a few nodes have many connections with other nodes, whereas most nodes have few connections. These nodes can be in two states, either damaged or undamaged. Transitions between damaged and non-damaged states are governed by the stochastic environment of individual nodes. Changes in the degree of damage of connected nodes change the local environment and make further damage more likely. Our model shows how age-dependent acceleration of the FI and of mortality emerges, even without specifying an age-damage relationship or any other time-dependent parameter. We have also used our model to assess how informative individual deficits are with respect to mortality. We find that the information is larger for nodes that are well connected than for nodes that are not. The model supports the idea that aging occurs as an emergent phenomenon, and not as a result of age-specific programming. Instead, aging reflects how damage propagates through a complex network of interconnected elements.

A Frailty Index Based On Deficit Accumulation Quantifies Mortality Risk in Humans and in Mice

Although many common diseases occur mostly in old age, the impact of ageing itself on disease risk and expression often goes unevaluated. To consider the impact of ageing requires some useful means of measuring variability in health in animals of the same age. In humans, this variability has been quantified by counting age-related health deficits in a frailty index. Here we show the results of extending that approach to mice. Across the life course, many important features of deficit accumulation are present in both species. These include gradual rates of deficit accumulation (slope = 0.029 in humans; 0.036 in mice), a submaximal limit (0.54 in humans; 0.44 in mice), and a strong relationship to mortality (1.05 [1.04–1.05] in humans; 1.15 [1.12–1.18] in mice). Quantifying deficit accumulation in individual mice provides a powerful new tool that can facilitate translation of research on ageing, including in relation to disease.

Network model of human aging: Frailty limits and information measures

Aging is associated with the accumulation of damage throughout a persons life. Individual health can be assessed by the Frailty Index (FI). The FI is calculated simply as the proportion f of accumulated age-related deficits relative to the total, leading to a theoretical maximum of f≤1. Observational studies have generally reported a much more stringent bound, with f≤f_{max}<1. The value of f_{max} in observational studies appears to be nonuniversal, but f_{max}≈0.7 is often reported. A previously developed network model of individual aging was unable to recover f_{max}<1 while retaining the other observed phenomenology of increasing f and mortality rates with age. We have developed a computationally accelerated network model that also allows us to tune the scale-free network exponent α. The network exponent α significantly affects the growth of mortality rates with age. However, we are only able to recover f_{max} by also introducing a deficit sensitivity parameter 1-q, which is equivalent to a false-negative rate q. Our value of q=0.3 is comparable to finite sensitivities of age-related deficits with respect to mortality that are often reported in the literature. In light of nonzero q, we use mutual information I to provide a nonparametric measure of the predictive value of the FI with respect to individual mortality. We find that I is only modestly degraded by q<1, and this degradation is mitigated when increasing number of deficits are included in the FI. We also find that the information spectrum, i.e., the mutual information of individual deficits versus connectivity, has an approximately power-law dependence that depends on the network exponent α. Mutual information I is therefore a useful tool for characterizing the network topology of aging populations.

Changes in Frailty Predict Changes in Cognition in Older Men: The Honolulu-Asia Aging Study

BACKGROUND

As cognitive decline mostly occurs in late life, where typically it co-exists with many other ailments, it is important to consider frailty in understanding cognitive change.

OBJECTIVE

Here, we examined the association of change in frailty status with cognitive trajectories in a well-studied cohort of older Japanese-American men.

METHODS

Using the prospective Honolulu-Asia Aging Study (HAAS), 2,817 men of Japanese descent were followed (aged 71-93 at baseline). Starting in 1991 with follow-up health assessments every two to three years, cognition was measured using the Cognitive Abilities Screening Instrument (CASI). For this study, health data was used to construct an accumulation of deficits frailty index (FI). Using six waves of data, multilevel growth curve analyses were constructed to examine simultaneous changes in cognition in relation to changes in FI, controlling for baseline frailty, age, education, and APOE-ɛ4 status.

RESULTS

On average, CASI scores declined by 2.0 points per year (95% confidence interval 1.9-2.1). Across six waves, each 10% within-person increase in frailty from baseline was associated with a 5.0 point reduction in CASI scores (95% confidence interval 4.7-5.2). Baseline frailty and age were associated both with lower initial CASI scores and with greater decline across the five follow-up assessments (p < 0.01).

DISCUSSION

Cognition is adversely affected by impaired health status in old age. Using a multidimensional measure of frailty, both baseline status and within-person changes in frailty were predictive of cognitive trajectories.

Conceptual Models of Frailty: Accumulation of Deficits

Frailty was introduced to explain why people of the same age have varying degrees of risk. The deficit accumulation approach shows that as people age, they accumulate health deficits, and that more deficits confer greater risk. Frailty results because not everyone of the same age has the same number of deficits. This is readily quantified using a frailty index, which has been translated to preclinical models. The frailty index grades risk without requiring special instrumentation. It allows a central clinical challenge to be addressed, which is that with age, diseases rarely travel alone.