Abstract WMP85: Recovery Rate vs. Recovery Capacity: A Mathematical Model and its Implications for Rehabilitation

Stroke ◽  
2013 ◽  
Vol 44 (suppl_1) ◽  
Author(s):  
Adam B Schweber ◽  
Lauren E Dunn ◽  
Andrea R Lendaris ◽  
Brandon M Minzer ◽  
Ronald M Lazar ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Recovery Rate ◽  
Goodness Of Fit ◽  
Recovery Period ◽  
Stroke Onset ◽  
Motor Deficit ◽  
Model Parameters ◽  
Stroke Severity ◽  
Recovery Capacity ◽  
Rate Dynamic

INTRODUCTION: Recovery of most hemiparetic patients at 90 days can be well predicted as a fixed proportion (70%) of initial motor deficit. However, recent work has shown considerable variability in the rate of recovery among proportional recoverers, prompting consideration of whether rate of recovery and recovery capacity are independent and whether a single rate dynamic governs proportional recovery. HYPOTHESIS: Among proportional recoverers, recovery rate variability can be accounted for by a single mathematical model in which: 1) recovery rate is independent of recovery capacity and 2) recovery has a sigmoid trajectory parameterized only by initial stroke severity. METHODS: We studied 23 patients with first-ever unilateral hemiparetic stroke previously identified as proportional recoverers. Fugl-Meyer Upper Extremity Motor Exam (FM-UE) had been measured at <72h, 1 week, and 90 days. A non-linear model predicting patients’ FM-UE score at any time after stroke onset was posited and model parameters were estimated by regressing one-week FM-UE scores against initial scores. Statistical significance and goodness of fit were evaluated. RESULTS: The model accounted for 86% of variability in motor recovery achieved by patients at 1 week after stroke onset (pseudo-R 2 =0.863, F 23,21= 418.0, p <.0001) and predicted that more severely impaired patients will have a slower maximum recovery rate and a recovery period that is longer in duration and more delayed in onset. CONCLUSION: The model provides evidence that proportional recovery is governed by a single rate dynamic and that recovery rate is independent of recovery capacity. It provides a tool for predicting motor impairment at any time following stroke onset and suggests a framework for characterizing the biology of recovery and the role of therapeutic interventions as either capacity-enhancing or rate-enhancing.

scholarly journals A NUMERICAL EXPERIMENT ON MATHEMATICAL MODEL OF FORECASTING THE RESULTS OF KNOWLEDGE TESTING

2011 ◽  
Vol 17 (1) ◽  
pp. 42-61 ◽  
Author(s):  
Natalja Kosareva ◽  
Aleksandras Krylovas
Keyword(s):  
Mathematical Model ◽  
Characteristic Function ◽  
Goodness Of Fit ◽  
Characteristic Functions ◽  
Model Parameters ◽  
Information Function ◽  
Test Information ◽  
Parametric Functions ◽  
Office Rooms ◽  
Test Information Function

In this paper the new approach to the forecasting the results of knowledge testing, proposed earlier by authors, is extended with four classes of parametric functions, the best fitting one from which is selected to approximate item characteristic function. Mathematical model is visualized by two numerical experiments. The first experiment was performed with the purpose to show the procedure of selecting the most appropriate item characteristic function and adjusting the parameters of the model. Goodness-of-fit statistic for detecting misfit of the selected model is calculated. In the second experiment a test of 10 items is constructed for the population with latent ability having normal distribution. Probability distribution of total test result and test information function are calculated when item characteristic functions are selected from four classes of parametric functions. In the next step it is shown how test information function value could be increased by adjusting parameters of item characteristic functions to the observed population. This model could be used not only for knowledge testing but also when solving diagnostic tasks in various fields of human activities. Other advantage of this method is the reduction of resources of testing process by more precise adjustment of the model parameters and decreasing the standard error of measurement of the estimated examinee ability. In the presented example the methodology is applied for solving the problem of microclimate evaluation in office rooms.

scholarly journals Intrahost modeling of artemisinin resistance in Plasmodium falciparum

2010 ◽  
Vol 108 (1) ◽  
pp. 397-402 ◽  
Author(s):  
Sompob Saralamba ◽  
Wirichada Pan-Ngum ◽  
Richard J. Maude ◽  
Sue J. Lee ◽  
Joel Tarning ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Plasmodium Falciparum ◽  
Goodness Of Fit ◽  
Artemisinin Resistance ◽  
Parasite Clearance ◽  
Model Parameters ◽  
Asexual Parasite ◽  
Ring Stage ◽  
Reduced Ring

Artemisinin-resistant Plasmodium falciparum malaria has emerged in western Cambodia. Resistance is characterized by prolonged in vivo parasite clearance times (PCTs) following artesunate treatment. The biological basis is unclear. The hypothesis that delayed parasite clearance results from a stage-specific reduction in artemisinin sensitivity of the circulating young asexual parasite ring stages was examined. A mathematical model was developed, describing the intrahost parasite stage-specific pharmacokinetic–pharmacodynamic relationships. Model parameters were estimated using detailed pharmacokinetic and parasite clearance data from 39 patients with uncomplicated falciparum malaria treated with artesunate from Pailin (western Cambodia) where artemisinin resistance was evident and 40 patients from Wang Pha (northwestern Thailand) where efficacy was preserved. The mathematical model reproduced the observed parasite clearance for each patient with an accurate goodness of fit (rmsd: 0.03–0.67 in log10 scale). The parameter sets that provided the best fits with the observed in vivo data consist of a highly conserved concentration–effect relationship for the trophozoite and schizont parasite stages, but a variable relationship for the ring stages. The model-derived assessment suggests that the efficacy of artesunate on ring stage parasites is reduced significantly in Pailin. This result supports the hypothesis that artemisinin resistance mainly reflects reduced ring-stage susceptibility and predicts that doubling the frequency of dosing will accelerate clearance of artemisinin-resistant parasites.

scholarly journals Timing of stroke onset determines discharge-functional status but not stroke severity: A hospital-based study

2013 ◽  
Vol 29 (1) ◽  
pp. 32-36 ◽  
Author(s):  
Li-Min Liou ◽  
Hsiu-Fen Lin ◽  
Chin-Ling Tsai ◽  
Ruey-Tay Lin ◽  
Chiou-Lian Lai
Keyword(s):  
Functional Status ◽  
Stroke Onset ◽  
Stroke Severity

Abstract WP385: Seasonal, Circaseptan and Diurnal Variations in Stroke Onset, Severity and Costs: Findings from the Royal Melbourne Hospital Stroke Registry 2004-2011

Stroke ◽  
2013 ◽  
Vol 44 (suppl_1) ◽  
Author(s):  
Lucy Busija ◽  
Danny Liew ◽  
Bernard Yan ◽  
Louise Weir ◽  
Peter Hand ◽  
...  
Keyword(s):  
Resource Allocation ◽  
Emergency Services ◽  
Diurnal Variations ◽  
Stroke Onset ◽  
Stroke Severity ◽  
Royal Melbourne Hospital ◽  
Stroke Frequency ◽  
Stroke Incidence ◽  
Early Afternoon ◽  
Generalized Linear Modelling

Introduction: Information on regular variations in the volume and severity of strokes has important implications for planning of emergency services and resource allocation. A number of studies have investigated seasonal, circaseptan and diurnal variations in stroke incidence but little is known about corresponding variations in stroke severity and costs. Hypotheses: Following results of previous studies, we hypothesized an increase in strokes in winter months, on Mondays, and between 09:00 and 12:00 hours. We also explored associations between stroke onset and stroke severity and in-patient costs. Methods: Data were analyzed for 4484 consecutive admissions to the Stroke Care Unit at the Royal Melbourne Hospital (Australia) from January 2005 to September 2011. Temporal variations in stroke frequency, severity and costs were assessed using generalized linear modelling. Stroke severity was measured using NIH Stroke Severity (NIHSS) scores. Results: The mean (SD) age of patients was 70.6 (14.3) years and 56% were males. Ischemic strokes accounted for 62% of admissions, 19% were haemorrhages, and 19% were TIAs. Stroke frequency varied significantly during the day (p<0.001). Contrary to expectation, strokes peaked between 06:00 and 21:00. The daily incidence of strokes differed significantly during the year (p<0.001), being highest in August (2.8/day, 95%CI 2.6,3.1) and lowest in January (2.1/day, 95% CI 1.8,2.3). Weekday was not associated with variations in stroke frequency (p=0.130). NIHSS scores were not associated with weekday (p=0.465) but varied significantly during the year (p=0.012) and day (p=0.011). Most severe strokes occurred in July and at 12:00-15:00, and least severe strokes occurred in December and at 09:00-12:00. Admission costs differed significantly during the year (p=0.039) but not during the week (p=0.469) or day (p=0.099). The highest admission costs were in August ($16053, 95%CI $12586,$19521) and lowest in October ($11256, 95% $9131,$13380). Conclusions: The frequency of stroke peaks between late morning and early afternoon and is highest in winter. The severity and costs of stroke admissions are also highest during winter. This information can be used in the planning of emergency services and resource allocation.

scholarly journals Evaluating performances of simplified physically based models for landslide susceptibility

2015 ◽  
Vol 12 (12) ◽  
pp. 13217-13256 ◽  
Author(s):  
G. Formetta ◽  
G. Capparelli ◽  
P. Versace
Keyword(s):  
Landslide Susceptibility ◽  
Goodness Of Fit ◽  
Shallow Landslides ◽  
Model Parameters ◽  
Test Case ◽  
Susceptibility Analysis ◽  
Physically Based ◽  
Private And Public ◽  
Physically Based Models

Abstract. Rainfall induced shallow landslides cause loss of life and significant damages involving private and public properties, transportation system, etc. Prediction of shallow landslides susceptible locations is a complex task that involves many disciplines: hydrology, geotechnical science, geomorphology, and statistics. Usually to accomplish this task two main approaches are used: statistical or physically based model. Reliable models' applications involve: automatic parameters calibration, objective quantification of the quality of susceptibility maps, model sensitivity analysis. This paper presents a methodology to systemically and objectively calibrate, verify and compare different models and different models performances indicators in order to individuate and eventually select the models whose behaviors are more reliable for a certain case study. The procedure was implemented in package of models for landslide susceptibility analysis and integrated in the NewAge-JGrass hydrological model. The package includes three simplified physically based models for landslides susceptibility analysis (M1, M2, and M3) and a component for models verifications. It computes eight goodness of fit indices by comparing pixel-by-pixel model results and measurements data. Moreover, the package integration in NewAge-JGrass allows the use of other components such as geographic information system tools to manage inputs-output processes, and automatic calibration algorithms to estimate model parameters. The system was applied for a case study in Calabria (Italy) along the Salerno-Reggio Calabria highway, between Cosenza and Altilia municipality. The analysis provided that among all the optimized indices and all the three models, the optimization of the index distance to perfect classification in the receiver operating characteristic plane (D2PC) coupled with model M3 is the best modeling solution for our test case.

scholarly journals Estimation of baseflow parameters of variable infiltration capacity model with soil and topography properties for predictions in ungauged basins

2011 ◽  
Vol 8 (4) ◽  
pp. 7017-7053 ◽  
Author(s):  
Z. Bao ◽  
J. Liu ◽  
J. Zhang ◽  
G. Fu ◽  
G. Wang ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Model Simulation ◽  
Parameters Estimation ◽  
Model Parameters ◽  
Ungauged Basins ◽  
Variable Infiltration Capacity ◽  
Infiltration Capacity ◽  
Ungauged Catchments ◽  
Vic Model ◽  
Predictions In Ungauged Basins

Abstract. Equifinality is unavoidable when transferring model parameters from gauged catchments to ungauged catchments for predictions in ungauged basins (PUB). A framework for estimating the three baseflow parameters of variable infiltration capacity (VIC) model, directly with soil and topography properties is presented. When the new parameters setting methodology is used, the number of parameters needing to be calibrated is reduced from six to three, that leads to a decrease of equifinality and uncertainty. This is validated by Monte Carlo simulations in 24 hydro-climatic catchments in China. Using the new parameters estimation approach, model parameters become more sensitive and the extent of parameters space will be smaller when a threshold of goodness-of-fit is given. That means the parameters uncertainty is reduced with the new parameters setting methodology. In addition, the uncertainty of model simulation is estimated by the generalised likelihood uncertainty estimation (GLUE) methodology. The results indicate that the uncertainty of streamflow simulations, i.e., confidence interval, is lower with the new parameters estimation methodology compared to that used by original calibration methodology. The new baseflow parameters estimation framework could be applied in VIC model and other appropriate models for PUB.

scholarly journals Analytical and Numerical Connections between Fractional Fickian and Intravoxel Incoherent Motion Models of Diffusion MRI

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1963
Author(s):  
Jingting Yao ◽  
Muhammad Ali Raza Anjum ◽  
Anshuman Swain ◽  
David A. Reiter
Keyword(s):  
Skeletal Muscle ◽  
Goodness Of Fit ◽  
Numerical Models ◽  
Tissue Perfusion ◽  
Parametric Models ◽  
Intravoxel Incoherent Motion ◽  
Fickian Diffusion ◽  
Model Parameters ◽  
Mathematical Framework ◽  
Stretched Exponential

Impaired tissue perfusion underlies many chronic disease states and aging. Diffusion-weighted imaging (DWI) is a noninvasive MRI technique that has been widely used to characterize tissue perfusion. Parametric models based on DWI measurements can characterize microvascular perfusion modulated by functional and microstructural alterations in the skeletal muscle. The intravoxel incoherent motion (IVIM) model uses a biexponential form to quantify the incoherent motion of water molecules in the microvasculature at low b-values of DWI measurements. The fractional Fickian diffusion (FFD) model is a parsimonious representation of anomalous superdiffusion that uses the stretched exponential form and can be used to quantify the microvascular volume of skeletal muscle. Both models are established measures of perfusion based on DWI, and the prognostic value of model parameters for identifying pathophysiological processes has been studied. Although the mathematical properties of individual models have been previously reported, quantitative connections between IVIM and FFD models have not been examined. This work provides a mathematical framework for obtaining a direct, one-way transformation of the parameters of the stretched exponential model to those of the biexponential model. Numerical simulations are implemented, and the results corroborate analytical results. Additionally, analysis of in vivo DWI measurements in skeletal muscle using both biexponential and stretched exponential models is shown and compared with analytical and numerical models. These results demonstrate the difficulty of model selection based on goodness of fit to experimental data. This analysis provides a framework for better interpreting and harmonizing perfusion parameters from experimental results using these two different models.

scholarly journals Eligibility for intravenous thrombolysis in acute stroke: A multicenter prospective study

Stroke ◽  
2001 ◽  
Vol 32 (suppl_1) ◽  
pp. 372-372
Author(s):  
Enrique Mostacero ◽  
Sonia Santos ◽  
Antonio Davalos ◽  
Alberto Gil-Peralta ◽  
Jose Castillo ◽  
...  
Keyword(s):  
Risk Factors ◽  
Prospective Study ◽  
Acute Stroke ◽  
Life Support ◽  
Advanced Life Support ◽  
Stroke Onset ◽  
Stroke Severity ◽  
Street Hospital ◽  
Modifiable Factors ◽  
Dispatch System

P182 Objective: To elucidate the proportion of patients who would have been eligible for alteplase treatment following the ECASS II criteria in a prospective study conducted in 20 Spanish general or university hospitals. Methods: The first 100 consecutive patients with an acute stroke admitted between 9/98 and 4/99 in each participating hospital were evaluated. Data concerning exclusion criteria for tPA, demographic variables, distance to hospital (<5km,5–20km,>20km), time (0–6am,6–12,12–6pm,6–12pm) and place (home, work/street, hospital) of symptoms onset, subject detecting the event (victim, family member, bystander), dispatch system (own initiative, EMS, primary physician, community hospital), delay and type of transport (own transport, basic, or advanced life support ambulance), cardiovascular risk factors, stroke severity (Canadian scale) and type of stroke were recorded. Results: Out of 1599 screened patients, 166 (10.4%) fulfilled all criteria for tPA treatment. Multiple reasons for exclusion were time from onset >6h in 23%, or unknown in 23%, delay in neurological attention >6h in 39%, TC not available within 6h from onset in 34%, hemorrhage in 14%, early signs of infarction involving >33% MCA in 8%, TIA or rapidly improving symptoms in 24%, coma or hemiplegia plus forced eye deviation in 5%, hypertension >185/110 in 2%, coagulation abnormalities in 1%, and other reasons in 6%. Univariate analyses showed that high eligibility for tPA was associated with type of the first medical intervention (emergency medical system)(p=0.006), type of transport (basic or advanced life support ambulance)(p<0.0001), stroke severity (p<0.001), and type of stroke (cardioembolic) (p=0.0027). Age, distance to hospital, time and place of stroke onset, subject detecting the event, and risk factors were not significantly related to eligibility. Conclusions: Candidates for intravenous tPA treatment within 6 hours from stroke onset are 10% of patients admitted in general hospitals of an EU country. Delay in neurologic attention and CT examination were the main reasons for exclusion. Dispatch system, and type of transport were modifiable factors related to eligibility.

scholarly journals Simple MSEIR Model for Measles Transmission

2019 ◽  
pp. 1-11
Author(s):  
Mojeeb Al-Rahman EL-Nor Osman ◽  
Appiagyei Ebenezer ◽  
Isaac Kwasi Adu
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Recovery Rate ◽  
Birth Rate ◽  
Reproduction Number ◽  
Progression Rate ◽  
Asymptotically Stable ◽  
The Stability ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, an Immunity-Susceptible-Exposed-Infectious-Recovery (MSEIR) mathematical model was used to study the dynamics of measles transmission. We discussed that there exist a disease-free and an endemic equilibria. We also discussed the stability of both disease-free and endemic equilibria.  The basic reproduction number  is obtained. If , then the measles will spread and persist in the population. If , then the disease will die out.  The disease was locally asymptotically stable if  and unstable if  . ALSO, WE PROVED THE GLOBAL STABILITY FOR THE DISEASE-FREE EQUILIBRIUM USING LASSALLE'S INVARIANCE PRINCIPLE OF Lyaponuv function. Furthermore, the endemic equilibrium was locally asymptotically stable if , under certain conditions. Numerical simulations were conducted to confirm our analytic results. Our findings were that, increasing the birth rate of humans, decreasing the progression rate, increasing the recovery rate and reducing the infectious rate can be useful in controlling and combating the measles.

scholarly journals The identification of a device based on a Peltier element by the least squares method

2020 ◽  
pp. 17-27
Author(s):  
Vladimir Grinkevich ◽  
Keyword(s):  
Mathematical Model ◽  
Least Squares ◽  
Least Squares Method ◽  
Control Object ◽  
Object Identification ◽  
Model Parameters ◽  
Peltier Element ◽  
Transport Delay ◽  
Non Linear ◽  
The Mathematical Model

The evaluation of the mathematical model parameters of a non-linear object with a transport delay is considered in this paper. A temperature controlled stage based on a Peltier element is an identification object in the paper. Several input signal implementations are applied to the input of the identification object. The least squares method is applied for the calculation of the non-linear differential equitation parameters which describe the identification object. The least squares method is used due to its simplicity and the possibility of identification non-linear objects. The parameters values obtained in the process of identification are provided. The plots of temperature changes in the temperature control system with a controller designed based on the mathematical model of the control object obtained as a result of identification are shown. It is found that the mathematical model obtained in the process of identification may be applied to design controllers for non-linear systems, in particular for a temperature stage based on a Peltier element, and for self-tuning controllers. However, the least square method proposed in the paper cannot estimate the transport delay time. Therefore it is required to evaluate the time delay by temperature transient processes. Dynamic object identification is applied when it is required to obtain a mathematical model structure and evaluate the parameters by an input and output control object signal. Also, identification is applied for auto tuning of controllers. A mathematical model of a control object is required to design the controller which is used to provide the required accuracy and stability of control systems. Peltier elements are applied to design low-power and small- size temperature stage . Hot benches based on a Peltier element can provide the desired temperature above and below ambient temperature.

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