An Algorithm for Activity Recognition and Assessment of Adults Poststroke.

IMPORTANCE: Stroke is the leading cause of long-term disability in the United States. Providers have no robust tools to objectively and accurately measure the activity of people with stroke living at home. OBJECTIVE: To explore the integration of validated upper extremity assessments poststroke within an activity recognition system. DESIGN: Exploratory descriptive study using data previously collected over 3 mo to report on algorithm testing and assessment integration. SETTING: Data were collected in the homes of community-dwelling participants. PARTICIPANTS: Participants were at least 6 mo poststroke, were able to ambulate with or without an assistive device, and self-reported some difficulty using their arm in everyday activities. OUTCOMES AND MEASURES: The activity detection algorithm's accuracy was determined by comparing its activity labels with manual labels. The algorithm integrated assessment by describing the quality of upper extremity movement, which was determined by reporting extent of reach, mean and maximum speed during movement, and smoothness of movement. RESULTS: Sixteen participants (9 women, 7 men) took part in this study, with an average age of 63.38 yr (SD = 12.84). The algorithm was highly accurate in correctly identifying activities, with 87% to 95% accuracy depending on the movement. The algorithm was also able to detect the quality of movement for upper extremity movements. CONCLUSIONS AND RELEVANCE: The algorithm was able to accurately identify in-kitchen activities performed by adults poststroke. Information about the quality of these movements was also successfully calculated. This algorithm has the potential to supplement clinical assessments in treatment planning and outcomes reporting. Plain-Language Summary: This study shows that clinical algorithms have the potential to inform occupational therapy practice by providing clinically relevant data about the in-home activities of adults poststroke. The algorithm accurately identified activities that were performed in the kitchen by adults poststroke. The algorithm also identified the quality of upper extremity movements of people poststroke who were living at home.

Smart Technology for Aging and Reducing Disability (STAReD): Study protocol for a randomized pragmatic clinical trial.

BACKGROUND: There is a critical need to improve quality of life for community-dwelling older adults with disabilities. Prior research has demonstrated that a smart, in-home sensor system can facilitate aging in place for older adults living in independent living apartments with care coordination support by identifying early illness and injury detection. Self-management approaches have shown positive outcomes for many client populations. Pairing the smart, in-home sensor system with a self-management intervention for community-dwelling older adults with disabilities may lead to positive outcomes. METHODS: This study is a prospective, two-arm, randomized, pragmatic clinical trial to compare the effect of a technology-supported self-management intervention on disability and health-related quality of life to that of a health education control, for rural, community-dwelling older adults. Individuals randomized to the self-management study arm will receive a multidisciplinary (nursing, occupational therapist, and social work) self-management approach coupled with the smart-home sensor system. Individuals randomized to the health education study arm will receive standard health education coupled with the smart-home sensor system. The primary outcomes of disability and health-related quality of life will be assessed at baseline and post-intervention. Generalizable guidance to scale the technology-supported self-management intervention will be developed from qualitatively developed exemplar cases. CONCLUSION: This study has the potential to impact the health and well-being of rural, community-dwelling older adults with disabilities. We have overcome barriers including recruitment in a rural population and supply chain issues for the sensor system. Our team remains on track to meet our study aims.

Fall Risk Prediction in Older Adults Using Free-Text Nursing Notes and Medications in Electronic Health Records.

Nursing notes in Electronic Health Records (EHR) contain critical health information, including fall risk factors. However, an exploration of fall risk prediction using nursing notes is not well examined. In this study, we explored deep learning architectures to predict fall risk in older adults using text in nursing notes and medications in the EHR. EHR predictor data and fall events outcome data were obtained from 162 older adults living at TigerPlace, a senior living facility located in Columbia, MO. We used pre-trained BioWordVec embeddings to represent the words in the clinical notes and medications and trained multiple recurrent neural network-based natural language processing models to predict future fall events. Our final model predicted falls with an accuracy of 0.81, a sensitivity of 0.75, a specificity of 0.83, and an F1 score of 0.82. This preliminary exploratory analysis provides supporting evidence that fall risk can be predicted from clinical notes and medications. Future studies will utilize additional data modalities available in the EHR to potentially improve fall risk prediction from EHR data.

A semi-supervised approach to unobtrusively predict abnormality in breathing patterns using hydraulic bed sensor data in older adults aging in place.

Shortness of breath is often considered a repercussion of aging in older adults, as respiratory illnesses like COPD1 or respiratory illnesses due to heart-related issues are often misdiagnosed, under-diagnosed or ignored at early stages. Continuous health monitoring using ambient sensors has the potential to ameliorate this problem for older adults at aging-in-place facilities. In this paper, we leverage continuous respiratory health data collected by using ambient hydraulic bed sensors installed in the apartments of older adults in aging-in-place Americare facilities to find data-adaptive indicators related to shortness of breath. We used unlabeled data collected unobtrusively over the span of three years from a COPD-diagnosed individual and used data mining to label the data. These labeled data are then used to train a predictive model to make future predictions in older adults related to shortness of breath abnormality. To pick the continuous changes in respiratory health we make predictions for shorter time windows (60-s). Hence, to summarize each day's predictions we propose an abnormal breathing index (ABI) in this paper. To showcase the trajectory of the shortness of breath abnormality over time (in terms of days), we also propose trend analysis on the ABI quarterly and incrementally. We have evaluated six individual cases retrospectively to highlight the potential and use cases of our approach.

Cardiovascular sex-differences: insights via physiology-based modeling and potential for noninvasive sensing via ballistocardiography.

In this study, anatomical and functional differences between men and women in their cardiovascular systems and how these differences manifest in blood circulation are theoretically and experimentally investigated. A validated mathematical model of the cardiovascular system is used as a virtual laboratory to simulate and compare multiple scenarios where parameters associated with sex differences are varied. Cardiovascular model parameters related with women's faster heart rate, stronger ventricular contractility, and smaller blood vessels are used as inputs to quantify the impact (i) on the distribution of blood volume through the cardiovascular system, (ii) on the cardiovascular indexes describing the coupling between ventricles and arteries, and (iii) on the ballistocardiogram (BCG) signal. The model-predicted outputs are found to be consistent with published clinical data. Model simulations suggest that the balance between the contractile function of the left ventricle and the load opposed by the arterial circulation attains similar levels in females and males, but is achieved through different combinations of factors. Additionally, we examine the potential of using the BCG waveform, which is directly related to cardiovascular volumes, as a noninvasive method for monitoring cardiovascular function. Our findings provide valuable insights into the underlying mechanisms of cardiovascular sex differences and may help facilitate the development of effective noninvasive cardiovascular monitoring methods for early diagnosis and prevention of cardiovascular disease in both women and men.

Development and Testing of a Daily Activity Recognition System for Post-Stroke Rehabilitation.

Those who survive the initial incidence of a stroke experience impacts on daily function. As a part of the rehabilitation process, it is essential for clinicians to monitor patients' health status and recovery progress accurately and consistently; however, little is known about how patients function in their own homes. Therefore, the goal of this study was to develop, train, and test an algorithm within an ambient, in-home depth sensor system that can classify and quantify home activities of individuals post-stroke. We developed the Daily Activity Recognition and Assessment System (DARAS). A daily action logger was implemented with a Foresite Healthcare depth sensor. Daily activity data were collected from seventeen post-stroke participants' homes over three months. Given the extensive amount of data, only a portion of the participants' data was used for this specific analysis. An ensemble network for activity recognition and temporal localization was developed to detect and segment the clinically relevant actions from the recorded data. The ensemble network, which learns rich spatial-temporal features from both depth and skeletal joint data, fuses the prediction outputs from a customized 3D convolutional-de-convolutional network, customized region convolutional 3D network, and a proposed region hierarchical co-occurrence network. The per-frame precision and per-action precision were 0.819 and 0.838, respectively, on the test set. The outcomes from the DARAS can help clinicians to provide more personalized rehabilitation plans that benefit patients.

Novel clinically-relevant assessment of upper extremity movement using depth sensors.

BACKGROUND: For individuals post-stroke, home-based programs are necessary to deliver additional hours of therapy outside of the limited time in the clinic. Virtual reality (VR)-based approaches show modest outcomes in improving client function when delivered in the home. The movement sensors used in these VR-based approaches, such as the Microsoft Kinect® have been validated against gold standards tools but have not been used as an assessment of upper extremity movement quality in the stroke population. OBJECTIVES: The purpose of this study was to explore the use of a movement sensor paired with a VR-based intervention to assess upper extremity movement for individuals post-stroke. METHODS: Movement data captured with the Microsoft Kinect® from four separate studies were aggregated for analysis (n = 8 individuals post-stroke, n = 30 individuals without disabilities). For all participants, the skeletal data (x, y, z coordinates for 15 tracked joints) for each game play session were processed in MatLab and movement variables (normalized jerk, movement path ratio, average path sway) were calculated using an OPTICS density-based cluster algorithm. RESULTS: Data from the 30 healthy individuals created a normative baseline for the three kinematic variables. Individuals post-stroke were less efficient and had more jerky movements in both upper extremities as compared to healthy individuals. CONCLUSION: It is feasible to use a movement sensor paired with a VR-based intervention to quantify and qualify upper extremity movement for individuals post-stroke. Further research with a larger cohort is necessary to establish clinical sensitivity and specificity.

Stepping Beyond Assessment: Fall Risk Prediction Models Among Older Adults from Cumulative Change in Gait Parameter Estimates.

Falls significantly affect the health of older adults. Injuries sustained through falls have long-term consequences on the ability to live independently and age in place, and are the leading cause of injury death in the United States for seniors. Early fall risk detection provides an important opportunity for prospective intervention by healthcare providers and home caregivers. In-home depth sensor technologies have been developed for real-time fall detection and gait parameter estimation including walking speed, the sixth vital sign, which has been shown to correlate with the risk of falling. This study evaluates the use of supervised classification for estimating fall risk from cumulative changes in gait parameter estimates as captured by 3D depth sensors placed within the homes of older adult participants. Using recall as the primary metric for model success rate due to the severity of fall injuries sustained by false negatives, we demonstrate an enhancement of assessing fall risk with univariate logistic regression using multivariate logistic regression, support vector, and hierarchical tree-based modeling techniques by an improvement of 18.80%, 31.78%, and 33.94%, respectively, in the 14 days preceding a fall event. Random forest and XGBoost models resulted in recall and precision scores of 0.805 compared to the best univariate regression model of Y-Entropy with a recall of 0.639 and precision of 0.527 for the 14-day window leading to a predicted fall event.

HTIDB: Hierarchical Time-Indexed Database for Efficient Storage and Access to Irregular Time-series Health Sensor Data.

With the enormous amount of data collected by unobtrusive sensors, the potential of utilizing these data and applying various multi-modal advanced analytics on them is numerous and promising. However, taking advantage of the ever-growing data requires high-performance data-handling systems to enable high data scalability and easy data accessibility. This paper demonstrates robust design, developments, and techniques of a hierarchical time-indexed database for decision support systems leveraging irregular and sporadic time series data from sensor systems, e.g., wearables or environmental. We propose a technique that leverages the flexibility of general purpose, high-scalability database systems, while integrating data analytics focused column stores that leverage hierarchical time indexing, compression, and dense raw numeric data storage. We have evaluated the performance characteristics and tradeoffs of each to understand the data access latencies and storage requirements, which are key elements for capacity planning for scalable systems.

Explainable Fall Risk Prediction in Older Adults Using Gait and Geriatric Assessments.

Older adults aged 65 and above are at higher risk of falls. Predicting fall risk early can provide caregivers time to provide interventions, which could reduce the risk, potentially avoiding a possible fall. In this paper, we present an analysis of 6-month fall risk prediction in older adults using geriatric assessments, GAITRite measurements, and fall history. The geriatric assessments included were Activities of Daily Living (ADL), Instrumental Activities of Daily Living (IADL), Mini-Mental State Examination (MMSE), Geriatric Depression Scale (GDS), and Short Form 12 (SF12). These geriatric assessments are collected by staff nurses regularly in senior care facilities. From the GAITRite assessments on the residents, we included the Functional Ambulatory Profile (FAP) scores and gait speed to predict fall risk. We used the SHAP (SHapley Additive exPlanations) approach to explain our model predictions to understand which predictor variables contributed to increase or decrease the fall risk for an individual prediction. In case of a high fall risk prediction, predictor variables that contributed the most to elevate the risk could be further examined by the health providers for more personalized health interventions. We used the geriatric assessments, GAITRite measurements, and fall history data collected from 92 older adult residents (age = 86.2 ± 6.4, female = 57) to train machine learning models to predict 6-month fall risk. Our models predicted a 6-month fall with an AUC of 0.80 (95% CI of 0.76-0.85), sensitivity of 0.82 (95% CI of 0.74-0.89), specificity of 0.72 (95% CI of 0.67-0.76), F1 score of 0.76 (95% CI of 0.72-0.79), and accuracy of 0.75 (95% CI of 0.72-0.79). These results show that our early fall risk prediction method performs well in identifying residents who are at higher fall risk, which offers care providers and family members valuable time to perform preventive actions.

Mechanism-Driven Modeling to Aid Non-invasive Monitoring of Cardiac Function via Ballistocardiography.

Left ventricular (LV) catheterization provides LV pressure-volume (P-V) loops and it represents the gold standard for cardiac function monitoring. This technique, however, is invasive and this limits its applicability in clinical and in-home settings. Ballistocardiography (BCG) is a good candidate for non-invasive cardiac monitoring, as it is based on capturing non-invasively the body motion that results from the blood flowing through the cardiovascular system. This work aims at building a mechanistic connection between changes in the BCG signal, changes in the P-V loops and changes in cardiac function. A mechanism-driven model based on cardiovascular physiology has been used as a virtual laboratory to predict how changes in cardiac function will manifest in the BCG waveform. Specifically, model simulations indicate that a decline in LV contractility results in an increase of the relative timing between the ECG and BCG signal and a decrease in BCG amplitude. The predicted changes have subsequently been observed in measurements on three swine serving as pre-clinical models for pre- and post-myocardial infarction conditions. The reproducibility of BCG measurements has been assessed on repeated, consecutive sessions of data acquisitions on three additional swine. Overall, this study provides experimental evidence supporting the utilization of mechanism-driven mathematical modeling as a guide to interpret changes in the BCG signal on the basis of cardiovascular physiology, thereby advancing the BCG technique as an effective method for non-invasive monitoring of cardiac function.

A system for automated acquisition of digital flexion using a 3-D camera and custom gantry.

Introduction: Automated measurement of digital range of motion (ROM) may improve the accuracy of reporting and increase clinical efficiency. We hypothesize that a 3-D camera on a custom gantry will produce ROM measurements similar to those obtained with a manual goniometer. Methods: A 3-D camera mounted on a custom gantry, was mechanized to rotate 200° around a platform. The video was processed to segment each digit and calculate joint angles in people with no history of any hand conditions or surgery to validate the system. A second-generation prototype was then assessed in people with different hand conditions. Metacarpophalangeal (MCP) and proximal interphalangeal (PIP) joint flexion were measured repeatedly with a goniometer and the automated system. The average difference between manual and automatic measurements was calculated along with intraclass correlation coefficients (ICC). Results: In the initial validation, 1,488 manual and 1,488 automated joint measurements were obtained and the measurement algorithm was refined. In people with hand conditions, 688 manual and 688 automated joint measurements were compared. Average acquisition time was 7 s per hand, with an additional 2-3 s required for data processing. ICC between manual and automated data in the clinical study ranged from 0.65 to 0.85 for the MCP joints, and 0.22 to 0.66 for PIP joints. Discussion: The automated system resulted in rapid data acquisition, with reliability varying by type of joint and location. It has the potential to improve efficiency in the collection of physical exam findings. Further developments of the system are needed to measure thumb and distal phalangeal motions.

Noninvasive cardiovascular monitoring based on electrocardiography and ballistocardiography: a feasibility study on patients in the surgical intensive care unit.

The time interval between the peaks in the electroccardiogram (ECG) and ballistocardiogram (BCG) waveforms, TEB, has been associated with the pre-ejection period (PEP), which is an important marker of ventricular contractility. However, the applicability of BCG-related markers in clinical practice is limited by the difficulty to obtain a replicable and consistent signal on patients. In this study, we test the feasibility of BCG measurements within a complex clinical setting, by means of an accelerometer under the head pillow of patients admitted to the Surgical Intensive Care Unit (SICU). The proposed technique proved capable of capturing TEB based on the R peaks in the ECG and the BCG in its head-to-toe and dorso- ventral directions. TEB detection was found to be consistent and repeatable both in healthy individuals and SICU patients over multiple data acquisition sessions. This work provides a promising starting point to investigate how TEB changes may relate to the patients' complex health conditions and give additional clinical insight into their care needs.

Leveraging Unsupervised Machine Learning to Discover Patterns in Linguistic Health Summaries for Eldercare.

The Center for Eldercare and Rehabilitation Technology, at University of Missouri, has researched the use of smart, unobtrusive sensors for older adult residents' health monitoring and alerting in aging-in-place communities for many years. Sensors placed in the apartments of older adult residents generate a deluge of daily data that is automatically aggregated, analyzed, and summarized to aid in health awareness, clinical care, and research for healthy aging. When anomalies or concerning trends are detected within the data, the sensor information is converted into linguistic health messages using fuzzy computational techniques, so as to make it understandable to the clinicians. Sensor data are analyzed at the individual level, therefore, through this study we aim to discover various combinations of patterns of anomalies happening together and recurrently in the older adult's population using these text summaries. Leveraging various computational text data processing techniques, we are able to extract relevant analytical features from the health messages. These features are transformed into a transactional encoding, then processed with frequent pattern mining techniques for association rule discovery. At individual level analysis, resident ID 3027 was considered as an exemplar to describe the analysis. Seven combinations of anomalies/rules/associations were discovered in this resident, out of which rule group three showed an increased recurrence during the COVID lockdown of facility. At the population level, a total of 38 associations were discovered that highlight the health patterns, and we continue to explore the health conditions associated with them. Ultimately, our goal is to correlate the combinations of anomalies with certain health conditions, which can then be leveraged for predictive analytics and preventative care. This will improve the current clinical care systems for older adult residents in smart sensor, aging-in-place communities.

Social practices of nurse care coordination using sensor technologies - Challenges with an alert system adoption in assisted living communities for older adults.

OBJECTIVES: From the view of everyday practices and the socio-technical coordination lens, this study aimed to analyz the gap between creators' intention and the users' implementation (mainly nursing staff and social workers) of an alert system in assisted living communities. METHODS: Qualitative methods were employed by way of five user interviews and focus groups with six system developers. Modeling instruments were applied for data collection to analyze the different clinical workflows versus the expectations of the system development team. RESULTS: Results indicate that the clinical workflow changed over time, which led to a mismatch of nurse care coordination, social practices, and technology use. The results show different mental models of the socio-technical practice. Applying the coordination theory, the following recommendations could be developed to overcome the mismatch. First, it is recommended that nursing staff set goals together. Second, a communication rhythm with the nursing staff and developer teams should be established, with guided questions to facilitate the conversation, to shed light on the different workflows and the difference in social practices when using sensor technologies or alert systems. Third, a checklist for new employees should be created so they know how and on which devices to use the alert system. Fourth, the user experience with the alert system should be improved (e.g., an improved user interface). CONCLUSIONS: This work indicates recommendations to close the mental model gap to overcome the mismatch between optimal use of the alert system and how the nursing staff is actually using it.

Non-Invasive Heart Rate Estimation From Ballistocardiograms Using Bidirectional LSTM Regression.

Non-invasive heart rate estimation is of great importance in daily monitoring of cardiovascular diseases. In this paper, a bidirectional long short term memory (bi-LSTM) regression network is developed for non-invasive heart rate estimation from the ballistocardiograms (BCG) signals. The proposed deep regression model provides an effective solution to the existing challenges in BCG heart rate estimation, such as the mismatch between the BCG signals and ground-truth reference, multi-sensor fusion and effective time series feature learning. Allowing label uncertainty in the estimation can reduce the manual cost of data annotation while further improving the heart rate estimation performance. Compared with the state-of-the-art BCG heart rate estimation methods, the strong fitting and generalization ability of the proposed deep regression model maintains better robustness to noise (e.g., sensor noise) and perturbations (e.g., body movements) in the BCG signals and provides a more reliable solution for long term heart rate monitoring.

Combining Physiology-Based Modeling and Evolutionary Algorithms for Personalized, Noninvasive Cardiovascular Assessment Based on Electrocardiography and Ballistocardiography.

Purpose: This study proposes a novel approach to obtain personalized estimates of cardiovascular parameters by combining (i) electrocardiography and ballistocardiography for noninvasive cardiovascular monitoring, (ii) a physiology-based mathematical model for predicting personalized cardiovascular variables, and (iii) an evolutionary algorithm (EA) for searching optimal model parameters. Methods: Electrocardiogram (ECG), ballistocardiogram (BCG), and a total of six blood pressure measurements are recorded on three healthy subjects. The R peaks in the ECG are used to segment the BCG signal into single BCG curves for each heart beat. The time distance between R peaks is used as an input for a validated physiology-based mathematical model that predicts distributions of pressures and volumes in the cardiovascular system, along with the associated BCG curve. An EA is designed to search the generation of parameter values of the cardiovascular model that optimizes the match between model-predicted and experimentally-measured BCG curves. The physiological relevance of the optimal EA solution is evaluated a posteriori by comparing the model-predicted blood pressure with a cuff placed on the arm of the subjects to measure the blood pressure. Results: The proposed approach successfully captures amplitudes and timings of the most prominent peak and valley in the BCG curve, also known as the J peak and K valley. The values of cardiovascular parameters pertaining to ventricular function can be estimated by the EA in a consistent manner when the search is performed over five different BCG curves corresponding to five different heart-beats of the same subject. Notably, the blood pressure predicted by the physiology-based model with the personalized parameter values provided by the EA search exhibits a very good agreement with the cuff-based blood pressure measurement. Conclusion: The combination of EA with physiology-based modeling proved capable of providing personalized estimates of cardiovascular parameters and physiological variables of great interest, such as blood pressure. This novel approach opens the possibility for developing quantitative devices for noninvasive cardiovascular monitoring based on BCG sensing.

Heartbeat Detection and Rate Estimation from Ballistocardiograms using the Gated Recurrent Unit Network.

Inspired by the application of recurrent neural networks (RNNs) to image recognition, in this paper, we propose a heartbeat detection framework based on the Gated Recurrent Unit (GRU) network. In this contribution, the heartbeat detection task from ballistocardiogram (BCG) signals was modeled as a classification problem where the segments of BCG signals were formulated as images fed into the GRU network for feature extraction. The proposed framework has advantages in fusion of multi-channel BCG signals and effective extraction of the temporal and waveform characteristics of the heartbeat signal, thereby enhancing heart rate estimation accuracy. In laboratory collected BCG data, the proposed method achieved the best heart rate estimation results compared to previous algorithms.

Tracking personalized functional health in older adults using geriatric assessments.

BACKGROUND: Higher levels of functional health in older adults leads to higher quality of life and improves the ability to age-in-place. Tracking functional health objectively could help clinicians to make decisions for interventions in case of health deterioration. Even though several geriatric assessments capture several aspects of functional health, there is limited research in longitudinally tracking personalized functional health of older adults using a combination of these assessments. METHODS: We used geriatric assessment data collected from 150 older adults to develop and validate a functional health prediction model based on risks associated with falls, hospitalizations, emergency visits, and death. We used mixed effects logistic regression to construct the model. The geriatric assessments included were Activities of Daily Living (ADL), Instrumental Activities of Daily Living (IADL), Mini-Mental State Examination (MMSE), Geriatric Depression Scale (GDS), and Short Form 12 (SF12). Construct validators such as fall risks associated with model predictions, and case studies with functional health trajectories were used to validate the model. RESULTS: The model is shown to separate samples with and without adverse health event outcomes with an area under the receiver operating characteristic curve (AUC) of > 0.85. The model could predict emergency visit or hospitalization with an AUC of 0.72 (95% CI 0.65-0.79), fall with an AUC of 0.86 (95% CI 0.83-0.89), fall with hospitalization with an AUC of 0.89 (95% CI 0.85-0.92), and mortality with an AUC of 0.93 (95% CI 0.88-0.97). Multiple comparisons of means using Turkey HSD test show that model prediction means for samples with no adverse health events versus samples with fall, hospitalization, and death were statistically significant (p < 0.001). Case studies for individual residents using predicted functional health trajectories show that changes in model predictions over time correspond to critical health changes in older adults. CONCLUSIONS: The personalized functional health tracking may provide clinicians with a longitudinal view of overall functional health in older adults to help address the early detection of deterioration trends and decide appropriate interventions. It can also help older adults and family members take proactive steps to improve functional health.

Corrections to "Cardiovascular Function and Ballistocardiogram: A Relationship Interpreted via Mathematical Modeling" [Oct 19 2906-2917].

Presents a missing funding acknowledgment for Dr. Mihail Popescu in the above named paper.