Solutions to Some Real-Life Problems Based on Mathematical Modeling and Functional Minimization

Building mathematical models that can describe, predict, and explain real-life phenomena is useful. This paper features the functional dependency model and the square of this functional dependency which hold significant information. A mathematical model that relates these functional dependencies with the average value of the function was developed to show that for an arbitrary well-behaved function, the definite integral of the square of the function over a finite interval is minimal when the function is constant over the interval. Finally, the model’s validity and accuracy in representing real-world problems for different situations in physics like mechanics, quantum mechanics, and electricity in economics were evaluated.

Current Incidence and Risk Factors of Fecal Incontinence After Acute Stroke Affecting Functionally Independent People

Background: Previously published retrospective series show a high prevalence of fecal incontinence (FI) in stroke patients. We aimed to analyze in a prospective series the current incidence of FI in acute stroke in functionally independent patients and its evolution over time and the patient characteristics associated with the appearance of FI in acute stroke.Methods: We included consecutive patients with acute stroke admitted in our stroke unit who fulfilled the following inclusion criteria: a first episode of stroke, aged >18 years, with no previous functional dependency [modified Rankin Scale (mRS) ≤ 2] and without previous known FI. FI was assessed by a multidisciplinary trained team using dedicated questionnaires at 72 ± 24 h (acute phase) and at 90 ± 15 days (chronic phase). Demographic, medical history, clinical and stroke features, mortality, and mRS at 7 days were collected.Results: Three hundred fifty-nine (48.3%) of 749 patients (mean age 65.9 ± 10, 64% male, 84.1% ischemic) fulfilled the inclusion criteria and were prospectively included during a 20-month period. FI was identified in 23 patients (6.4%) at 72 ± 24 h and in 7 (1.9%) at 90 days ± 15 days after stroke onset. FI was more frequent in hemorrhagic strokes (18 vs. 5%, p 0.007) and in more severe strokes [median National Institute of Health Stroke Scale (NIHSS) 18 (14–22) vs. 5 (3–13), p < 0.0001]. No differences were found regarding age, sex, vascular risk factors, or other comorbidities, or affected hemisphere. Patients with NIHSS ≥12 (AUC 0.81, 95% CI 0.71 to 0.89) had a 17-fold increase for the risk of FI (OR 16.9, IC 95% 4.7–60.1) adjusted for covariates.Conclusions: At present, the incidence of FI in acute stroke patients without previous functional dependency is lower than expected, with an association of a more severe and hemorrhagic stroke. Due to its impact on the quality of life, it is necessary to deepen the knowledge of the underlying mechanisms to address therapeutic strategies.

The Elderly Nutritional Index for Geriatric Malnutrition Assessment (ENIGMA): concurrent, construct and predictive validity in an external evaluation cohort of community-dwelling older persons

We previously developed a malnutrition risk index, the Elderly Nutritional Index for Geriatric Malnutrition Assessment (ENIGMA) with good predictive accuracy for mortality risk in an original population cohort (SLAS1). Herein, we further evaluate the concurrent and predictive validity of the ENIGMA construct in an external validation cohort (SLAS-2) of 2824 community-dwelling older adults aged 55+. They were assessed on the ENIGMA index, Mini Nutritional Assessment-Short Form (MNA-SF) and the Geriatric Nutritional Risk Index (GNRI), known correlates of malnutrition, and baseline and follow-up functional dependency and 10-year mortality risk. Higher ENIGMA risk categories were significantly associated (p<0.001) with lower education, living alone, smoking, low physical activity, BMI <18.5kg/m2, poorer muscle strength and functional mobility, exhaustion, physical frailty, homocysteine, eGFR, haemoglobin, red and white blood cell counts, platelets, systemic inflammation indexes, metabolic syndrome, cardiovascular disease, cognitive impairment and depressive symptoms (GDS≥5). ENIGMA scores showed statistically significant (p<0.001) correlations but low-to-moderate concordance with MNA-SF (r=0.148, agreement=45.9%, kappa=0.085) and GNRI scores (r=0.156, agreement=45.8%, kappa=0.096). Controlling for known correlates of malnutrition, only high-risk ENIGMA among the indexes significantly predicted baseline functional dependency (OR=1.64, 95%CI 1.01-2.65) and mortality (HR=1.65 (95%CI 1.04, 2.62). ENIGMA marginally out-performed MNA-SF and GNRI in predicting baseline functional dependency (AUC: 0.625 vs 0.584 vs 0.526), follow up functional dependency (AUC: 0.594 vs 0.525 vs 0.479) and 10-year mortality risk (AUC: 0.641 vs 0.596 vs 0.595). The concurrent and predictive validity of the ENIGMA construct is replicated in an external evaluation study of community-dwelling older persons.

Dynamic reciprocal relationships between cognitive and functional declines along the Alzheimer’s disease continuum in the prospective COGICARE study

Background Thoroughly understanding the temporal associations between cognitive and functional dimensions along the dementia process is fundamental to define preventive measures likely to delay the disease’s onset. This work aimed to finely describe the trajectories of cognitive and functional declines, and assess their dynamic bidirectional relationships among subjects at different stages of the dementia process. Methods We leveraged extensive repeated data of cognition and functional dependency from the French prospective COGICARE study, designed to better characterize the natural history of cognitive and functional declines around dementia diagnosis. Cognition was measured by the Mini-Mental State Examination, the Isaacs Set Test for verbal fluency, the Benton Visual Retention Test for visuo-spatial memory, and Trail Making Test Part B for executive functioning. Functional dependency was measured by basic and instrumental activities of daily living. The study included 102 cognitively normal, 123 mildly cognitively impaired, and 72 dementia cases with a median of 5 repeated visits over up to 57 months. We used a dynamic causal model which addresses the two essential issues in temporal associations assessment: focusing on intra-individual change and accounting for time. Results Better cognitive abilities were associated with lower subsequent decline of the functional level among the three clinical stages with an intensification over time but no reciprocity of the association whatever the clinical status. Conclusion This work confirms that the progressive functional dependency could be induced by cognitive impairment. Subjects identified as early as possible with clinically significant cognitive impairments could benefit from preventive measures before the deterioration of activities of daily living and the appearance of dementia clinical signs.

Can functional walk tests add value to the prediction of cardiorespiratory fitness after stroke? A prospective cohort study

Background Cardiorespiratory fitness is often impaired following stroke, and peak oxygen consumption (VO2peak) is an important prognostic value of all-cause mortality. The primary objective was to investigate whether functional walk tests assessed in the subacute phase after stroke added value in predicting VO2peak in chronic stroke, in addition to age, sex and functional dependency. Secondary objectives were to investigate associations between daily physical activity and functional walk tests, and with VO2peak in chronic stroke. Methods This prospective cohort study included eligible participants originally included in the randomized controlled trial Life After Stroke. Functional walk tests, i.e., six-minute walk test (6MWT) and maximal gait speed, were assessed at inclusion and 18 months later. VO2peak [ml/kg/min] was assessed by a cardiopulmonary exercise test on a treadmill 20 months after inclusion. Daily physical activity was measured by a uniaxial accelerometer (activPAL) at 18-month follow-up. Results Ninety-two community-dwelling individuals, with a mean (SD) age of 69.2 (10.6) years and 33 (35.9%) women, were included 3 months after stroke onset. Eighty-three (90.2%) participants had a modified Rankin Scale (mRS) score of 1 or 2, indicating functional independence. An overall assessment of four prediction models indicated the combination of age, sex, mRS and 6MWT as predictors to be the best fitted model in predicting VO2peak (adjusted R2 = 0.612). Secondary results showed statistically significant, but not clinically significant, associations between daily physical activity and functional walk tests, and with VO2peak. Conclusions 6MWT add significant value to the prediction of mean VO2peak in the chronic phase in mild strokes, in combination with age, sex and functional dependency. This prediction model may facilitate clinical decisions and rehabilitation strategies for mildly affected stroke survivors in risk of low levels of VO2peak. Future studies should validate the model in various stages after stroke and in patients moderately and severely affected.

Neuropsychological Predictors of Severe Functional Dependency in a Multiethnic Community Cohort of Individuals with Alzheimer’s Disease

To assess the predictive value of neuropsychological tests for severe dependency in Alzheimer’s disease as defined by the Equivalent Institutional Care Rating Scale, in a multiethnic, community cohort. The sample included 146 elders from the Predictors 3 cohort. Cox proportional hazard models tested the predictive value of each neuropsychological test at baseline on relative risk of meeting severe dependency. Higher semantic Processing and Memory test scores at baseline were associated with lower risk of meeting severe dependency in the adjusted Cox models. The integrity of semantic processing and memory abilities in dementia appears to predict time to severe functional dependency.

Sociodemographic characteristics and probabilities for the labor inclusion of people with disabilities in Chile. Implications for critical social policies

In Chile, labor inclusion for people in the situation of disability is low. By using the Second National Survey of Disability in Chile and running a logistic regression model (N=2,618), this study explores how sex, education, age, and level of functional dependency are associated with the probability of people in the situation of disability of having work. Findings suggest that being a woman with a disability or being older reduces the probability of having work. Besides, having more years of education increases the probability of it. Implications for critical social policies are also discussed.