Predictive analytics and tailored interventions improve clinical outcomes in older adults: a randomized controlled trial.

This study explored the potential to improve clinical outcomes in patients at risk of moving to the top segment of the cost acuity pyramid. This randomized controlled trial evaluated the impact of a Stepped-Care approach (predictive analytics + tailored nurse-driven interventions) on healthcare utilization among 370 older adult patients enrolled in a homecare management program and using a Personal Emergency Response System. The Control group (CG) received care as usual, while the Intervention group (IG) received Stepped-Care during a 180-day intervention period. The primary outcome, decrease in emergency encounters, was not statistically significant (15%, p = 0.291). However, compared to the CG, the IG had significant reductions in total 90-day readmissions (68%, p = 0.007), patients with 90-day readmissions (76%, p = 0.011), total 180-day readmissions (53%, p = 0.020), and EMS encounters (49%, p = 0.006). Predictive analytics combined with tailored interventions could potentially improve clinical outcomes in older adults, supporting population health management in home or community settings.

Predictive Modeling of 30-Day Emergency Hospital Transport of German Patients Using a Personal Emergency Response: Retrospective Study and Comparison with the United States.

BACKGROUND: Predictive analytics based on data from remote monitoring of elderly via a personal emergency response system (PERS) in the United States can identify subscribers at high risk for emergency hospital transport. These risk predictions can subsequently be used to proactively target interventions and prevent avoidable, costly health care use. It is, however, unknown if PERS-based risk prediction with targeted interventions could also be applied in the German health care setting. OBJECTIVE: The objectives were to develop and validate a predictive model of 30-day emergency hospital transport based on data from a German PERS provider and compare the model with our previously published predictive model developed on data from a US PERS provider. METHODS: Retrospective data of 5805 subscribers to a German PERS service were used to develop and validate an extreme gradient boosting predictive model of 30-day hospital transport, including predictors derived from subscriber demographics, self-reported medical conditions, and a 2-year history of case data. Models were trained on 80% (4644/5805) of the data, and performance was evaluated on an independent test set of 20% (1161/5805). Results were compared with our previously published prediction model developed on a data set of PERS users in the United States. RESULTS: German PERS subscribers were on average aged 83.6 years, with 64.0% (743/1161) females, with 65.4% (759/1161) reported 3 or more chronic conditions. A total of 1.4% (350/24,847) of subscribers had one or more emergency transports in 30 days in the test set, which was significantly lower compared with the US data set (2455/109,966, 2.2%). Performance of the predictive model of emergency hospital transport, as evaluated by area under the receiver operator characteristic curve (AUC), was 0.749 (95% CI 0.721-0.777), which was similar to the US prediction model (AUC=0.778 [95% CI 0.769-0.788]). The top 1% (12/1161) of predicted high-risk patients were 10.7 times more likely to experience an emergency hospital transport in 30 days than the overall German PERS population. This lift was comparable to a model lift of 11.9 obtained by the US predictive model. CONCLUSIONS: Despite differences in emergency care use, PERS-based collected subscriber data can be used to predict use outcomes in different international settings. These predictive analytic tools can be used by health care organizations to extend population health management into the home by identifying and delivering timelier targeted interventions to high-risk patients. This could lead to overall improved patient experience, higher quality of care, and more efficient resource use.

Evaluating the Impact of a Risk Assessment System With Tailored Interventions in Germany: Protocol for a Prospective Study With Matched Controls.

BACKGROUND: With a worldwide increase in the elderly population, and an associated increase in health care utilization and costs, preventing avoidable emergency department visits and hospitalizations is becoming a global priority. A personal emergency response system (PERS), consisting of an alarm button and a means to establish a live connection to a response center, can help the elderly live at home longer independently. Individual risk assessment through predictive modeling can help indicate what PERS subscribers are at elevated risk of hospital transport so that early intervention becomes possible. OBJECTIVE: The aim is to evaluate whether the combination of risk scores determined through predictive modeling and targeted interventions offered by a case manager can result in a reduction of hospital admissions and health care costs for a population of German PERS subscribers. The primary outcome of the study is the difference between the number of hospitalizations in the intervention and matched control groups. METHODS: As part of the Sicher Zuhause program, an intervention group of 500 PERS subscribers will be tracked for 8 months. During this period, risk scores will be determined daily by a predictive model of hospital transport, and at-risk participants may receive phone calls from a case manager who assesses the health status of the participant and recommends interventions. The health care utilization of the intervention group will be compared to a group of matched controls, retrospectively drawn from a population of PERS subscribers who receive no interventions. RESULTS: Differences in health care utilization and costs between the intervention group and the matched controls will be determined based on reimbursement records. In addition, qualitative data will be collected on the participants' satisfaction with the Sicher Zuhause program and utilization of the interventions offered as part of the program. CONCLUSIONS: The study evaluation will offer insight into whether a combination of predictive analytics and case manager-driven interventions can help in avoiding hospital admissions and health care costs for PERS subscribers in Germany living at home independently. In the future, this may lead to improved quality of life and reduced medical costs for the population of the study. TRIAL REGISTRATION: Deutsches Register Klinischer Studien (DRKS), DRKS00017328; https://www.drks.de/drks_web/navigate.do?navigationId=trial.HTML&TRIAL_ID=DRKS00017328. INTERNATIONAL REGISTERED REPORT IDENTIFIER (IRRID): DERR1-10.2196/17584.

Predictive Modeling of 30-Day Emergency Hospital Transport of Patients Using a Personal Emergency Response System: Prognostic Retrospective Study.

BACKGROUND: Telehealth programs have been successful in reducing 30-day readmissions and emergency department visits. However, such programs often focus on the costliest patients with multiple morbidities and last for only 30 to 60 days postdischarge. Inexpensive monitoring of elderly patients via a personal emergency response system (PERS) to identify those at high risk for emergency hospital transport could be used to target interventions and prevent avoidable use of costly readmissions and emergency department visits after 30 to 60 days of telehealth use. OBJECTIVE: The objectives of this study were to (1) develop and validate a predictive model of 30-day emergency hospital transport based on PERS data; and (2) compare the model's predictions with clinical outcomes derived from the electronic health record (EHR). METHODS: We used deidentified medical alert pattern data from 290,434 subscribers to a PERS service to build a gradient tree boosting-based predictive model of 30-day hospital transport, which included predictors derived from subscriber demographics, self-reported medical conditions, caregiver network information, and up to 2 years of retrospective PERS medical alert data. We evaluated the model's performance on an independent validation cohort (n=289,426). We linked EHR and PERS records for 1815 patients from a home health care program to compare PERS-based risk scores with rates of emergency encounters as recorded in the EHR. RESULTS: In the validation cohort, 2.22% (6411/289,426) of patients had 1 or more emergency transports in 30 days. The performance of the predictive model of emergency hospital transport, as evaluated by the area under the receiver operating characteristic curve, was 0.779 (95% CI 0.774-0.785). Among the top 1% of predicted high-risk patients, 25.5% had 1 or more emergency hospital transports in the next 30 days. Comparison with clinical outcomes from the EHR showed 3.9 times more emergency encounters among predicted high-risk patients than low-risk patients in the year following the prediction date. CONCLUSIONS: Patient data collected remotely via PERS can be used to reliably predict 30-day emergency hospital transport. Clinical observations from the EHR showed that predicted high-risk patients had nearly four times higher rates of emergency encounters than did low-risk patients. Health care providers could benefit from our validated predictive model by targeting timely preventive interventions to high-risk patients. This could lead to overall improved patient experience, higher quality of care, and more efficient resource utilization.

Evaluating the Impact of a Web-Based Risk Assessment System (CareSage) and Tailored Interventions on Health Care Utilization: Protocol for a Randomized Controlled Trial.

BACKGROUND: Soaring health care costs and a rapidly aging population, with multiple comorbidities, necessitates the development of innovative strategies to deliver high-quality, value-based care. OBJECTIVE: The goal of this study is to evaluate the impact of a risk assessment system (CareSage) and targeted interventions on health care utilization. METHODS: This is a two-arm randomized controlled trial recruiting 370 participants from a pool of high-risk patients receiving care at a home health agency. CareSage is a risk assessment system that utilizes both real-time data collected via a Personal Emergency Response Service and historical patient data collected from the electronic medical records. All patients will first be observed for 3 months (observation period) to allow the CareSage algorithm to calibrate based on patient data. During the next 6 months (intervention period), CareSage will use a predictive algorithm to classify patients in the intervention group as "high" or "low" risk for emergency transport every 30 days. All patients flagged as "high risk" by CareSage will receive nurse triage calls to assess their needs and personalized interventions including patient education, home visits, and tele-monitoring. The primary outcome is the number of 180-day emergency department visits. Secondary outcomes include the number of 90-day emergency department visits, total medical expenses, 180-day mortality rates, time to first readmission, total number of readmissions and avoidable readmissions, 30-, 90-, and 180-day readmission rates, as well as cost of intervention per patient. The two study groups will be compared using the Student t test (two-tailed) for normally distributed and Mann Whitney U test for skewed continuous variables, respectively. The chi-square test will be used for categorical variables. Time to event (readmission) and 180-day mortality between the two study groups will be compared by using the Kaplan-Meier survival plots and the log-rank test. Cox proportional hazard regression will be used to compute hazard ratio and compare outcomes between the two groups. RESULTS: We are actively enrolling participants and the study is expected to be completed by end of 2018; results are expected to be published in early 2019. CONCLUSIONS: Innovative solutions for identifying high-risk patients and personalizing interventions based on individual risk and needs may help facilitate the delivery of value-based care, improve long-term patient health outcomes and decrease health care costs. TRIAL REGISTRATION: ClinicalTrials.gov NCT03126565; https://clinicaltrials.gov/ct2/show/NCT03126565 (Archived by WebCite at http://www.webcitation.org/6ymDuAwQA).

Health Care Cost Analyses for Exploring Cost Savings Opportunities in Older Patients: Longitudinal Retrospective Study.

BACKGROUND: Half of Medicare reimbursement goes toward caring for the top 5% of the most expensive patients. However, little is known about these patients prior to reaching the top or how their costs change annually. To address these gaps, we analyzed patient flow and associated health care cost trends over 5 years. OBJECTIVE: To evaluate the cost of health care utilization in older patients by analyzing changes in their long-term expenditures. METHODS: This was a retrospective, longitudinal, multicenter study to evaluate health care costs of 2643 older patients from 2011 to 2015. All patients had at least one episode of home health care during the study period and used a personal emergency response service (PERS) at home for any length of time during the observation period. We segmented all patients into top (5%), middle (6%-50%), and bottom (51%-100%) segments by their annual expenditures and built cost pyramids based thereon. The longitudinal health care expenditure trends of the complete study population and each segment were assessed by linear regression models. Patient flows throughout the segments of the cost acuity pyramids from year to year were modeled by Markov chains. RESULTS: Total health care costs of the study population nearly doubled from US $17.7M in 2011 to US $33.0M in 2015 with an expected annual cost increase of US $3.6M (P=.003). This growth was primarily driven by a significantly higher cost increases in the middle segment (US $2.3M, P=.003). The expected annual cost increases in the top and bottom segments were US $1.2M (P=.008) and US $0.1M (P=.004), respectively. Patient and cost flow analyses showed that 18% of patients moved up the cost acuity pyramid yearly, and their costs increased by 672%. This was in contrast to 22% of patients that moved down with a cost decrease of 86%. The remaining 60% of patients stayed in the same segment from year to year, though their costs also increased by 18%. CONCLUSIONS: Although many health care organizations target intensive and costly interventions to their most expensive patients, this analysis unveiled potential cost savings opportunities by managing the patients in the lower cost segments that are at risk of moving up the cost acuity pyramid. To achieve this, data analytics integrating longitudinal data from electronic health records and home monitoring devices may help health care organizations optimize resources by enabling clinicians to proactively manage patients in their home or community environments beyond institutional settings and 30- and 60-day telehealth services.

Healthcare utilization in older patients using personal emergency response systems: an analysis of electronic health records and medical alert data : Brief Description: A Longitudinal Retrospective Analyses of healthcare utilization rates in older patients using Personal Emergency Response Systems from 2011 to 2015.

BACKGROUND: Personal Emergency Response Systems (PERS) are traditionally used as fall alert systems for older adults, a population that contributes an overwhelming proportion of healthcare costs in the United States. Previous studies focused mainly on qualitative evaluations of PERS without a longitudinal quantitative evaluation of healthcare utilization in users. To address this gap and better understand the needs of older patients on PERS, we analyzed longitudinal healthcare utilization trends in patients using PERS through the home care management service of a large healthcare organization. METHODS: Retrospective, longitudinal analyses of healthcare and PERS utilization records of older patients over a 5-years period from 2011-2015. The primary outcome was to characterize the healthcare utilization of PERS patients. This outcome was assessed by 30-, 90-, and 180-day readmission rates, frequency of principal admitting diagnoses, and prevalence of conditions leading to potentially avoidable admissions based on Centers for Medicare and Medicaid Services classification criteria. RESULTS: The overall 30-day readmission rate was 14.2%, 90-days readmission rate was 34.4%, and 180-days readmission rate was 42.2%. While 30-day readmission rates did not increase significantly (p = 0.16) over the study period, 90-days (p = 0.03) and 180-days (p = 0.04) readmission rates did increase significantly. The top 5 most frequent principal diagnoses for inpatient admissions included congestive heart failure (5.7%), chronic obstructive pulmonary disease (4.6%), dysrhythmias (4.3%), septicemia (4.1%), and pneumonia (4.1%). Additionally, 21% of all admissions were due to conditions leading to potentially avoidable admissions in either institutional or non-institutional settings (16% in institutional settings only). CONCLUSIONS: Chronic medical conditions account for the majority of healthcare utilization in older patients using PERS. Results suggest that PERS data combined with electronic medical records data can provide useful insights that can be used to improve health outcomes in older patients.

Predicting target displacements using ultrasound elastography and finite element modeling.

Soft tissue displacements during minimally invasive surgical procedures may cause target motion and subsequent misplacement of the surgical tool. A technique is presented to predict target displacements using a combination of ultrasound elastography and finite element (FE) modeling. A cubic gelatin/agar phantom with stiff targets was manufactured to obtain pre- and post-loading ultrasound radio frequency (RF) data from a linear array transducer. The RF data were used to compute displacement and strain images, from which the distribution of elasticity was reconstructed using an inverse FE-based approach. The FE model was subsequently used to predict target displacements upon application of different boundary and loading conditions to the phantom. The influence of geometry was investigated by application of the technique to a breast-shaped phantom. The distribution of elasticity in the phantoms as determined from the strain distribution agreed well with results from mechanical testing. Upon application of different boundary and loading conditions to the cubic phantom, the FE model-predicted target motion were consistent with ultrasound measurements. The FE-based approach could also accurately predict the displacement of the target upon compression and indentation of the breast-shaped phantom. This study provides experimental evidence that organ geometry and boundary conditions surrounding the organ are important factors influencing target motion. In future work, the technique presented in this paper could be used for preoperative planning of minimally invasive surgical interventions.

Validated finite element models of the proximal femur using two-dimensional projected geometry and bone density.

Two-dimensional finite element models of cadaveric femoral stiffness were developed to study their suitability as surrogates of bone stiffness and strength, using two-dimensional representations of femoral geometry and bone mineral density distributions. If successfully validated, such methods could be clinically applied to estimate patient bone stiffness and strength using simpler and less costly radiographs. Two-dimensional femur images were derived by projection of quantitative computed tomography scans of 22 human cadaveric femurs. The same femurs were fractured in a fall on the hip configuration. Femoral stiffness and fracture load were measured, and high speed video was recorded. Digital image correlation analysis was used to calculate the strain distribution from the high speed video recordings. Two-dimensional projection images were segmented and meshed with second-order triangular elements for finite element analysis. Elastic moduli of the finite elements were calculated based on the projected mineral density values inside the elements. The mapping of projection density values to elastic modulus was obtained using optimal parameter identification in a set of nine of the 22 specimens, and validated on the remaining 13 specimens. Finite element calculated proximal stiffness and strength correlated much better with experimental data than areal bone mineral density alone. In addition, finite element calculated strain distributions compared very well with strains obtained from digital image processing of the high speed video recordings, further validating the two-dimensional projected subject-specific finite element models.

Robust QCT/FEA models of proximal femur stiffness and fracture load during a sideways fall on the hip.

Clinical implementation of quantitative computed tomography-based finite element analysis (QCT/FEA) of proximal femur stiffness and strength to assess the likelihood of proximal femur (hip) fractures requires a unified modeling procedure, consistency in predicting bone mechanical properties, and validation with realistic test data that represent typical hip fractures, specifically, a sideways fall on the hip. We, therefore, used two sets (n = 9, each) of cadaveric femora with bone densities varying from normal to osteoporotic to build, refine, and validate a new class of QCT/FEA models for hip fracture under loading conditions that simulate a sideways fall on the hip. Convergence requirements of finite element models of the first set of femora led to the creation of a new meshing strategy and a robust process to model proximal femur geometry and material properties from QCT images. We used a second set of femora to cross-validate the model parameters derived from the first set. Refined models were validated experimentally by fracturing femora using specially designed fixtures, load cells, and high speed video capture. CT image reconstructions of fractured femora were created to classify the fractures. The predicted stiffness (cross-validation R (2) = 0.87), fracture load (cross-validation R (2) = 0.85), and fracture patterns (83% agreement) correlated well with experimental data.

Target motion predictions for pre-operative planning during needle-based interventions.

During biopsies, breast tissue is subjected to displacement upon needle indentation, puncture, and penetration. Thus, accurate needle placement requires pre-operative predictions of the target motions. In this paper, we used ultrasound elastography measurements to non-invasively predict elastic properties of breast tissue phantoms. These properties were used in finite element (FE) models of indentation of breast soft tissue phantoms. To validate the model predictions of target motion, experimental measurements were carried out. Breast tissue phantoms with cubic and hemispherical geometries were manufactured and included materials with different elastic properties to represent skin, adipose tissue, and lesions. Ultrasound was used to track the displacement of the target (i.e., the simulated lesion) during indentation. The FE model predictions were compared with ultrasound measurements for cases with different boundary conditions and phantom geometry. Maximum errors between measured and predicted target motions were 12% and 3% for the fully supported and partially supported cubic phantoms at 6.0 mm indentation, respectively. Further, FE-based parameter sensitivity analysis indicated that increasing skin elastic modulus and reducing the target depth location increased the target motion. Our results indicate that with a priori knowledge about the geometry, boundary conditions, and linear elastic properties, indentation of breast tissue phantoms can be accurately predicted with FE models. FE models for pre-operative planning in combination with robotic needle insertions, could play a key role in improving lesion targeting for breast biopsies.

Branching morphology of the rat hepatic portal vein tree: a micro-CT study.

In contrast to the lung and the myocardium, the liver is a relatively homogeneous organ with fewer anatomic constraints on vascular branching. Hence, we hypothesize that the hepatic vasculature could more closely follow optimization of branching geometry than is the case in other organs. The geometrical and fractal properties of the rat hepatic portal vein tree were investigated, with the aid of three-dimensional micro-computed tomography data. Frequency distributions of vessel radii were obtained at three different voxel resolutions and fitted to a theoretical model of dichotomous branching. The model predicted an average junction exponent of 3.09. Hemodynamic model calculations showed that with generation, relative shear stress decreases. Branching angles were found to oscillate between those predicted by two optimality principles of minimum power loss and volume, and of minimum shear stress and surface. The liver shows a variation in branching morphology similar to that of other organs. Therefore, we conclude that anatomic constraints do not have a major perturbing impact.

Altered calcium handling is an early sign of streptozotocin-induced diabetic cardiomyopathy.

The main objective of the present study was to determine alterations of calcium handling in the diabetic rat heart during the transition from adaptive to maladaptive phase of cardiomyopathy. By inhibiting the nuclear enzyme poly(ADP-ribose) polymerase (PARP), we also investigated the possible role of this enzyme in the sequence of pathological events. Six weeks after induction of type I diabetes by injection of streptozotocin in rats, the hearts were perfused according to Langendorff. Intracellular-free calcium (Ca(2+)(i)) levels were measured by surface fluorometry using Indo-1 AM. Cyclic changes in Ca(2+)(i) concentrations and hemodynamic parameters were measured simultaneously. The hearts were challenged by infusion of isoproterenol. Six weeks of diabetes resulted in reduced inotropy and lusitropy. The diabetic hearts (DM) expressed a significantly elevated end-diastolic Ca(2+)(i) level (control, 111-/+20 vs DM, 221-/+35 nM). The maximal transport capacity of SERCA2a and conductance of RyR2 were reduced. These changes were not accompanied by major alterations in the tissue content of SERCA2a, RyR2, phospholamban and Na(+)/Ca(2+) exchanger. In response to beta-adrenergic activation, SERCA2a transport capacity and RyR2 conductance were stunted in the DM hearts. Inhibition of PARP induced minor changes in the mechanical function and calcium handling of the DM hearts. In conclusion, the observed changes in contractility and in Ca(2+)(i) handling are most likely attributable to functional disturbances of SERCA2a and RyR2 in this transitional phase of diabetes. At this stage of diabetes, PARP does not appear to play a significant pathogenetic role in the alterations in contractile function and calcium handling.

In vivo heat shock preconditioning mitigates calcium overload during ischaemia/reperfusion in the isolated, perfused rat heart.

Heat shock (HS) pretreatment of the heart is effective in mitigating the deleterious effects of ischaemia/reperfusion. The main objective of this study was to determine whether the beneficial effect of HS is associated with the preservation of intracellular Ca2+ handling in the ischaemic/reperfused, isolated rat heart. Twenty-four hours after raising body core temperature to 42 degrees C for 15 min, rat hearts were perfused according to Langendorff and subjected to 30 min ischaemia followed by 20 min reperfusion. Cyclic changes of cytoplasmic calcium ion [Ca2+i] levels were measured by surface fluorometry using Indo-1 AM. Reperfused HS hearts showed improved recovery of contractile function compared with control hearts: end-diastolic pressure: 45+/-11 vs. 64+/-22 mmHg; developed pressure: 72+/-12 vs. 41+/-20 mmHg; maximum rate of pressure increase (+dP/dtmax): 1,513+/-305 vs. 938+/-500 mmHg/s; maximum rate of pressure decrease (-dP/dtmax): -1,354+/-304 vs. -806+/-403 mmHg/s. HS hearts displayed a significantly lower end-diastolic cytosolic [Ca2+] ([Ca2+]i) after reinstallation of flow. The dynamic parameters of the Ca2+i transients, i.e. the maximum rate of increase/decrease (+/-dCa2+i/dtmax) and amplitude, did not differ between reperfused control and HS hearts. The novel finding of this study is that improved performance of the HS-preconditioned heart after an ischaemic insult is associated with a reduced end-diastolic Ca2+i load, and most likely, preserved Ca2+ sensitivity of the myocardial contractile machinery.

beta-Adrenergic activation reveals impaired cardiac calcium handling at early stage of diabetes.

Cardiac function is known to be impaired in diabetes. Alterations in intracellular calcium handling have been suggested to play a pivotal role. This study aimed to test the hypothesis that beta-adrenergic activation can reveal the functional derangements of intracellular calcium handling of the 4-week diabetic heart. Langendorff perfused hearts of 4-week streptozotocin-induced diabetic rats were subjected to the beta-adrenoceptor agonist isoproterenol. Cyclic changes in [Ca(2+)](i) levels were measured throughout the cardiac cycle using Indo-1 fluorescent dye. Based on the computational analysis of the [Ca(2+)](i) transient the kinetic parameters of the sarcoplasmic reticulum Ca(2+)-ATPase and the ryanodine receptor were determined by minimizing the squared error between the simulated and the experimentally obtained [Ca(2+)](i) transient. Under unchallenged conditions, hemodynamic parameters were comparable between control and diabetic hearts. Isoproterenol administration stimulated hemodynamic function to a greater extent in control than in diabetic hearts, which was exemplified by more pronounced increases in rate of pressure development and decline. Under unchallenged conditions, [Ca(2+)](i) amplitude and rate of rise and decline of [Ca(2+)](i) as measured throughout the cardiac cycle were comparable between diabetic and control hearts. Differences became apparent under beta-adrenoceptor stimulation. Upon beta-activation the rate-pressure product showed a blunted response, which was accompanied by a diminished rise in [Ca(2+)](i) amplitude in diabetic hearts. Computational analysis revealed a reduced function of the sarcoplasmic reticulum Ca(2+)-ATPase and Ca(2+)-release channel in response to beta-adrenoceptor challenge. Alterations in Ca(2+)(i) handling may play a causative role in depressed hemodynamic performance of the challenged heart at an early stage of diabetes.

Mathematical modeling of vascular endothelial layer maintenance: the role of endothelial cell division, progenitor cell homing, and telomere shortening.

Maintenance of the endothelial cell (EC) layer of the vessel wall is essential for proper functioning of the vessel and prevention of vascular disorders. Replacement of damaged ECs could occur through division of surrounding ECs. Furthermore, EC progenitor cells (EPCs), derived from the bone marrow and circulating in the bloodstream, can differentiate into ECs. Therefore, these cells might also play a role in maintenance of the endothelial layer in the vascular system. The proliferative potential of both cell types is limited by shortening of telomeric DNA. Accelerated telomere shortening might lead to senescent vascular wall cells and eventually to the inability of the endothelium to maintain a continuous monolayer. The aim of this study was to describe the dynamics of EC damage and repair and telomere shortening by a mathematical model. In the model, ECs were integrated in a two-dimensional structure resembling the endothelium in a large artery. Telomere shortening was described as a stochastic process with oxidative damage as the main cause of attrition. Simulating the model illustrated that increased cellular turnover or elevated levels of oxidative stress could lead to critical telomere shortening and senescence at an age of 65 yr. The model predicted that under those conditions the EC layer could display defects, which could initiate severe vascular wall damage in reality. Furthermore, simulations showed that 5% progenitor cell homing/yr can significantly delay the EC layer defects. This stresses the potential importance of EPC number and function to the maintenance of vascular wall integrity during the human life span.

Mathematical modeling confirms the length-dependency of telomere shortening.

Telomeres, the ends of chromosomes, shorten with each cell division in human somatic cells, because of the end-replication problem, C-strand processing and oxidative damage. On the other hand, the reverse transcriptase telomerase can add back telomeric repeats at the telomere ends. It has been suggested that once telomeres have reached a critical length, cells cease proliferation, also known as senescence. Evidence is accumulating that telomere shortening and subsequent senescence might play a crucial role in life-threatening diseases. So far, mathematical models described telomere shortening as an autonomous process, where the loss per cell division does not depend on the telomere length itself. In this study, published measurements of telomere distributions in human fibroblasts and human endothelial cells were used to show that telomeres shorten in a length-dependent fashion. Thereafter, a mathematical model of telomere attrition was composed, in which a shortening factor and an autonomous loss were incorporated. It was assumed that the percentage of senescence was related to the percentage of telomeres below a critical length. The model was compared with published data of telomere length and senescence of human endothelial cells using the maximum likelihood method. This enabled the estimation of physiologically important parameters and confirmed the length-dependency of telomere shortening.