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ABSTRACT: Functional electrical stimulation (FES) has been used to improve function in individuals with hemiparesis following stroke. An ideal functional electrical stimulation (FES) system needs an accurate mathematical model capable of designing subject and task-specific stimulation patterns. Such a model was previously developed in our laboratory and shown to predict the isometric forces produced by the quadriceps femoris muscles of able-bodied individuals and individuals with spinal cord injury in response to a wide range of clinically relevant stimulation frequencies and patterns. The aim of this study was to test our isometric muscle force model on the quadriceps femoris, ankle dorsiflexor, and ankle plantar-flexor muscles of individuals with post-stroke hemiparesis.
Subjects were seated on a force dynamometer and isometric forces were measured in response to a range of stimulation frequencies (10 to 80-Hz) and 3 different patterns. Subject-specific model parameter values were obtained by fitting the measured force responses from 2 stimulation trains. The model parameters thus obtained were then used to obtain predicted forces for a range of frequencies and patterns. Predicted and measured forces were compared using intra-class correlation coefficients, r2 values, and model error relative to the physiological error (variability of measured forces).
Results showed excellent agreement between measured and predicted force-time responses (r2 >0.80), peak forces (ICCs>0.84), and force-time integrals (ICCs>0.82) for the quadriceps, dorsiflexor, and plantar-fexor muscles. The model error was within or below the +95% confidence interval of the physiological error for >88% comparisons between measured and predicted forces.
Our results show that the model has potential to be incorporated as a feed-forward controller for predicting subject-specific stimulation patterns during FES.
Journal of NeuroEngineering and Rehabilitation 01/2008; 5:7. · 3.26 Impact Factor
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ABSTRACT: 1] A suite of particulate, gaseous and meteorological measurements during the Pittsburgh Supersite experiment were used to characterize the impact of the 2002 Quebec wildfires on pollutant concentrations and physical and chemical processes dominant in the region. Temporal trends in the number distribution of wildfire particles (isolated using Rapid Single-ultrafine-particle Mass Spectrometry data) combined with CO, NO x and O 3 mixing ratios identified two separate periods (Periods I and II) when the measurement site was directly impacted by plumes of relatively unprocessed wildfire emissions; i.e., increases in primary ultrafine wildfire particles, CO and NO x concomitant with a decrease in O 3 from intraplume NO x titration. Carbonaceous particle number distributions predominantly associated with vehicular emissions, PM 2.5 sulfate mass concentration and SO 2 mixing ratio resolved individual components of local and regional sources. Single particle signatures indicated a period of intense atmospheric processing following Period II that caused rapid growth of the ultrafine mode due to simultaneous sulfate and secondary organic mass accumulation, resulting in significant changes to particle physical and chemical properties. Particle growth was concurrent with large increases in O 3 and maxima in incoming solar radiation and ambient temperature and is posited to have occurred in situ as the air mass, containing a mixture of urban and wildfire emissions, was advected past the site. In total, the current work demonstrates significant added severity for pollution episodes in an area already burdened by large anthropogenic emission rates due to the impact of the 2002 Quebec wildfires. High levels of atmospheric processing increased sulfate accumulation and SOA formation and brought PM 2.5 mass concentrations close to, and O 3 mixing ratios in excess of, the National Ambient Air Quality Standards. Projections of increasing wildfire activity under a warming climate may increase the frequency and severity of such events.
J. Geophys. Res. 01/2008; 113.
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ABSTRACT: Sulfuric acid-water nucleation is thought to be a key atmospheric mechanism for forming new condensation nuclei. In earlier literature, measurements of sulfuric acid activity were interpreted as the total (monomer plus hydrate) concentration above solution. Due to recent reinterpretations, most literature values for H(2)SO(4) activity are thought to represent the number density of monomers. Based on this reinterpretation, the current work uses the most recent models of H(2)O-H(2)SO(4) binary nucleation along with perturbation analyses to predict a decrease in critical cluster mole fraction, increase in critical cluster diameter, and orders of magnitude decrease in nucleation rate. Nucleation rate parameterizations available in the literature, however, give opposite trends. To resolve these discrepancies, nucleation rates were calculated for both interpretations of H(2)SO(4) activity and directly compared to the available parameterizations as well as the perturbation analysis. Results were in excellent agreement with older parameterizations that assumed H(2)SO(4) activity represents the total concentration and duplicated the predicted trends from the perturbation analysis, but differed by orders of magnitude from more recent parameterizations that assume H(2)SO(4) activity represents only the monomer. Comparison with experimental measurements available in the literature revealed that the calculations of the current work assuming a(a) represents the total concentration are most frequently in agreement with observations.
The Journal of Chemical Physics 10/2007; 127(12):124316. · 3.33 Impact Factor
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ABSTRACT: Sulfuric acid–water nucleation is thought to be a key atmospheric mechanism for forming new condensation nuclei. In earlier literature, measurements of sulfuric acid activity were interpreted as the total (monomer plus hydrate) concentration above solution. Due to recent reinterpretations, most literature values for H2SO4 activity are thought to represent the number density of monomers. Based on this reinterpretation, the current work uses the most recent models of H2O–H2SO4 binary nucleation along with perturbation analyses to predict a decrease in critical cluster mole fraction, increase in critical cluster diameter, and orders of magnitude decrease in nucleation rate. Nucleation rate parameterizations available in the literature, however, give opposite trends. To resolve these discrepancies, nucleation rates were calculated for both interpretations of H2SO4 activity and directly compared to the available parameterizations as well as the perturbation analysis. Results were in excellent agreement with older parameterizations that assumed H2SO4 activity represents the total concentration and duplicated the predicted trends from the perturbation analysis, but differed by orders of magnitude from more recent parameterizations that assume H2SO4 activity represents only the monomer. Comparison with experimental measurements available in the literature revealed that the calculations of the current work assuming aa represents the total concentration are most frequently in agreement with observations.
The Journal of Chemical Physics 09/2007; 127(12):124316-124316-11. · 3.33 Impact Factor
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ABSTRACT: We have previously developed and tested a muscle model that predicts the effect of stimulation frequency on muscle force responses. The aim of this study was to enhance our isometric mathematical model to predict muscle forces in response to stimulation trains with a wide range of frequencies and intensities for the quadriceps femoris muscles of individuals with spinal cord injuries. Isometric forces were obtained experimentally from 10 individuals with spinal cord injuries (time after injury, 1.5-8 years) and then compared to forces predicted by the model. Our model predicted accurately the force-time integrals (FTI) and peak forces (PF) for stimulation trains of a wide range of frequencies (12.5-80 HZ) and intensities (150-600-mus pulse duration), and two different stimulation patterns (constant-frequency trains and doublet-frequency trains). The accurate predictions of our model indicate that our model, which now incorporates the effects of stimulation frequency, intensity, and pattern on muscle forces, can be used to design optimal customized stimulation strategies for spinal cord-injured patients.
Muscle & Nerve 09/2007; 36(2):214-22. · 2.37 Impact Factor
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ABSTRACT: During volitional muscle activation, motor units often fire with varying discharge patterns that include brief, high-frequency bursts of activity. These variations in the activation rate allow the central nervous system to precisely control the forces produced by the muscle. The present study explores how varying the instantaneous frequency of stimulation pulses within a train affects nonisometric muscle performance. The peak excursion produced in response to each stimulation train was considered as the primary measure of muscle performance. The results showed that at each frequency tested between 10 and 50 Hz, variable-frequency trains that took advantage of the catchlike property of skeletal muscle produced greater excursions than constant-frequency trains. In addition, variable-frequency trains that could achieve targeted trajectories with fewer pulses than constant-frequency trains were identified. These findings suggest that similar to voluntary muscle activation patterns, varying the instantaneous frequency within a train of pulses can be used to improve muscle performance during functional electrical stimulation.
Journal of Applied Physiology 06/2007; 102(5):1985-91. · 3.75 Impact Factor
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ABSTRACT: Lung airway morphogenesis is simulated in a simplified diffusing environment that simulates the mesenchyme to explore the role of morphogens in airway architecture development. Simple rules govern local branching morphogenesis. Morphogen gradients are modeled by four pairs of sources and their diffusion through the mesenchyme. Sensitivity to lobar architecture and mesenchymal morphogen are explored. Even if the model accurately represents observed patterns of local development, it could not produce realistic global patterns of lung architecture if interaction with its environment was not taken into account, implying that reciprocal interaction between airway growth and morphogens in the mesenchyme plays a critical role in producing realistic global features of lung architecture.
Journal of Applied Physiology 02/2007; 102(1):294-305. · 3.75 Impact Factor
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Aerosol Science and Technology 10/2006; 40(10):873-882. · 2.67 Impact Factor
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ABSTRACT: Electrical stimulation of skeletal muscles of patients with upper motor neuron lesions can be used to restore functional movements such as standing or walking. Mathematical muscle models can assist in designing stimulation patterns that will enable patients to perform particular tasks more efficiently. In this study we extend our previous model to allow us to predict changes in knee joint angle in response to electrical stimulation of the human quadriceps femoris muscle. The model was tested both with and without inertial loads placed around the ankle joints of healthy subjects. Results showed that the model predicted the knee extensions with a RMS angle error that was generally <or=8 degrees. The coefficients of determination between the measured and predicted data showed the model accounted for approximately 71%, approximately 94%, approximately 73%, and approximately 89% of the variances in the experimental maximum excursion, time to maximum excursion, maximum shortening velocity, and time to maximum shortening velocity, respectively. This study showed that our general non-isometric model predicted the lower limb motion in response to a range of stimulation frequencies and patterns, and external loads. This model can be implemented in an algorithm for controlling the position of the lower leg during the swing phase of gait during functional electrical stimulation.
Journal of Biomechanics 01/2006; 39(15):2826-36. · 2.43 Impact Factor
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ABSTRACT: The ideal functional electrical stimulation (FES) system requires a mathematical model to provide feedforward control of the stimulation parameters such that they are optimal for different individuals across a range of physiological conditions, muscles, and tasks. Recently we tested and validated such a model using able-bodied subjects. The purpose of this study was to determine whether this model applied to persons with spinal cord injuries (SCI). To this end, the isometric force responses of the paralyzed quadriceps femoris muscles of 14 adolescents and young adults were tested. For each subject, the force responses to two six-pulse stimulation trains were used to identify the parameter values of the model and then the model was used to predict the force responses to three train patterns across a range of frequencies in both a nonfatigued and fatigued condition. The intraclass correlation coefficients (ICCs) between the experimental and predicted force-time integrals and peak forces were above 0.90 for 12 of the 13 stimulation trains tested in the nonfatigued condition and all 13 trains tested in the fatigued condition. The success of our model with SCI subjects leads us to believe that our model may be useful for designing optimal stimulation parameters for standing and ambulation in patients who use FES.
Muscle & Nerve 07/2005; 31(6):702-12. · 2.37 Impact Factor
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ABSTRACT: Functional electrical stimulation is the use of electrical currents to activate paralyzed muscles to produce functional movements. Muscle force output must meet or exceed the external load to maintain a posture or produce movements. A mathematical force-fatigue modeling system that predicts muscle force responses during repetitive electrical stimulation has been developed in our laboratory to help identify stimulation patterns that optimize force output for individual subjects. This study tests how well this model predicts the number of contractions that can be maintained above a required force level (successful contractions) during repetitive activation of a muscle. Healthy human quadriceps muscles were tested isometrically on 12 subjects. Data were first collected and used to parameterize the model. Next, the model was used to predict the number of successful contractions that were produced by trains with frequencies ranging from 5 to 100 Hz while the pulse durations and amplitudes were held constant. Finally, three clinically relevant stimulation frequencies were selected and tested to verify the model's predictions. Under these conditions, the model accurately predicted the number of successful contractions for clinically relevant stimulation frequencies. Furthermore, the model appears to have the potential to identify the stimulation frequency that maximizes muscle force output and minimizes fatigue for each subject.
Journal of Electromyography and Kinesiology 07/2005; 15(3):300-9. · 1.97 Impact Factor
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ABSTRACT: We previously reported the development of a force- and fatigue-model system that predicted accurately forces during repetitive fatiguing activation of human skeletal muscles using brief duration (six-pulse) stimulation trains. The model system was tested in the present study using force responses produced by longer duration stimulation trains, containing up to 50 pulses. Our results showed that our model successfully predicted the peak forces produced when the muscle was repetitively activated with stimulation trains of frequencies ranging from 20 to 40 Hz, train durations ranging from 0.5 to 1 s, and varied pulse patterns. The predicted peak forces throughout each protocol matched the experimental peak forces with r2 values above 0.9 and predicted successfully the forces at the end of each protocol with <15% error for all protocols tested. The success of our model system further supports its potential use for the design of optimal stimulation patterns for individual users during functional electrical stimulation.
Journal of Electromyography and Kinesiology 12/2003; 13(6):575-88. · 1.97 Impact Factor
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ABSTRACT: The performance of the real-time single-particle mass spectrometer RSMS III is evaluated for ambient fine and ultrafine particle number concentration measurements. The RSMS III couples aerodynamic size selection with laser ablation time-of-flight mass spectrometry for single-particle analysis. It was deployed at the Baltimore particulate matter Supersite for semi-continuous operation over an 8-month period. The sampling protocol adopted for this study permitted the analysis of on average 2000 particles per day. The number of particles analyzed is a tradeoff between generating a statistically significant data set and maintaining instrument operation over a long period of time. The optimum particle size range of analysis was found to be ca. 50-770 nm in diameter, although particles as small as 45 nm and as large as 1250 nm were also analyzed. While nitrate, sulfate, and carbon (elemental and organic) were found to dominate the ambient aerosol, over 10% of the detected particles contained transition and/or heavy metals. The (size-dependent) detection efficiency, defined as the fraction of particles entering the inlet that are analyzed, was determined by comparison with scanning mobility particle sizing data. Using the experimentally determined detection efficiencies, particle number concentrations of specific chemical components were estimated. While the sampling protocol allowed the particle concentrations of major chemical components to be followed as a function of both time and particle size, minor components required averaging over time and/or size to achieve adequate precision.
Environmental Science and Technology 09/2003; 37(15):3268-74. · 5.23 Impact Factor
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ABSTRACT: In previous work we developed and validated a mathematical model that predicted force output from skeletal muscles subjected to six-pulse stimulation trains under isometric condition. The current study investigated the model's ability to predict force responses to longer stimulation trains under both nonfatigued and fatigued conditions. Using the six-pulse train model to predict the force produced by longer stimulation trains showed that the model was successful, but a modified parameter identification scheme was required. For most of the trains tested the model accounted for 95% of the variance in the experimental forces produced by stimulation trains, with mean frequencies from 12.5 to 100 HZ, train durations from 485 to 1000 ms, and number of pulses from 14 to 50 for both nonfatigued and fatigued muscles. The success of our mathematical model in predicting forces produced by stimulations with a wide range of frequencies, durations, and number of pulses implies great potential of the model for the identification of optimal activation patterns that should be used during functional electrical stimulation.
Muscle & Nerve 11/2002; 26(4):477-85. · 2.37 Impact Factor
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ABSTRACT: Functional electrical stimulation is used to restore movement and function of paralyzed muscles by activating skeletal muscle artificially. An accurate and predictive mathematical model can facilitate the design of stimulation patterns that produce the desired force. The present study is a first step in developing a mathematical model for non-isometric muscle contractions. The goals of this study were to: (1) identify how our isometric force model's parameters vary with changes in knee joint angle, (2) identify the best knee flexion angle to parameterize this model, and (3) validate the model by comparing experimental data to predictions in response to a wide range of stimulation frequencies and muscle lengths. Results showed that by parabolically varying one of the free parameters with knee joint angle and fixing the other parameters at the values identified at 40 degrees of knee flexion, the model could predict the force responses to a wide range of stimulation frequencies and patterns at different muscle lengths. This work showed that the current isometric force model is capable of predicting the changes in skeletal muscle force at different muscle lengths.
Journal of Biomechanics 08/2002; 35(7):919-30. · 2.43 Impact Factor
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04/2002;
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ABSTRACT: Previously we developed a mathematical force- and fatigue-model system that could predict fatigue produced by a wide range of frequencies and pulse patterns. However, the models tended to overestimate the forces produced by higher frequency trains. This paper presents modifications to our previously developed force- and fatigue-model system to improve the accuracy in predicting forces during repetitive activation of human skeletal muscle. By comparing the predictions produced by the modified force and fatigue models to those by our previous models, the modification appears to be successful. The current force- and fatigue-model system accounts for about 93% variance in experimental data produced by fatigue protocols consisting of trains with a wide range of frequencies and pulse patterns. In addition, the present models successfully predict the effect of stimulation frequency and pulse pattern on muscle fatigue. The success of our current force- and fatigue-model system suggests its potential use in helping to identify the optimal activation pattern to use during the clinical application of functional electrical stimulation.
IEEE Transactions on Neural Systems and Rehabilitation Engineering 04/2002; 10(1):48-58. · 3.44 Impact Factor
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ABSTRACT: We have recently developed a force- and fatigue-model system that accurately predicted the effect of stimulation frequency on muscle fatigue. The data used to test the model were produced by stimulation trains with resting times of 500 ms. Because the resting times between stimulation trains affect muscle fatigue, this study tested the model's ability to predict the effect of resting times on fatigue. In addition, because this study included different subjects than those used to develop the model, the validity of the model could be tested. Data were collected from human quadriceps femoris muscles using fatigue protocols that included resting times of 500, 750, or 1000 ms. Our results showed that the model predicted fatigue as being a decreasing function of resting time, which was consistent with experimental data. Reliability tests between the experimental data and predictions showed interclass correlation coefficients of 0.97, 0.95, and 0.81 for the initial, final, and percentage decline in peak forces, respectively, suggesting strong agreement between the experimental data and the predictions by the model. The success of our current force- and fatigue-model system helps to validate the model and suggests its potential use in identifying the optimal activation pattern during clinical application of functional electrical stimulation.
IEEE Transactions on Neural Systems and Rehabilitation Engineering 04/2002; 10(1):59-67. · 3.44 Impact Factor
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ABSTRACT: A single particle mass spectrometer, RSMS-3, and a MOUDI were deployed during the Pittsburgh Air Quality Study (PAQS), July 2001–September 2002, to obtain size resolved measurements of elemental composition for particulate matter (PM) within the Pittsburgh area. Elemental mass distributions from analysis of the MOUDI stages were directly compared to those constructed using the single particle data, in conjunction with coincident SMPS measurements, for specific days within the PAQS.Results from one episode on 27 October 2001 showed that approximately 80% of the metal containing particles detected on this day belonged to the Na/Si/K/Ca/Fe/Ga/Pb particle class. The density and shape factor of these particles were estimated to be 3.9±0.8 g/cc and 1.5±0.2, respectively, and the relative sensitivity factors for individual metals showed little variation with respect to particle diameter over the size range of 70–800 nm.Compared to the 27 October 2001 episode, there was a larger degree of variability in the metal containing particles detected during another episode on 14 March 2002. The Ca and Pb mass distributions from this day represent an ensemble of externally mixed particles. Estimates of particle density were provided for the dominant particle types, including EC/OC/Ca, Al/Si/Ca/Fe, EC/OC/Pb and Na/K/Zn/Pb, and estimates of particle shape factor were provided for the EC/OC/Ca and Na/K/Zn/Pb classes. Comparison with the 27 October 2001 Ca and Pb mass distributions revealed that the RSMS data reconstructed the MOUDI mass much better from the Ca/Pb containing particles detected on 14 March 2002 than those observed on 27 October 2001, suggesting that the single particle instrument sensitivity to both Ca and Pb depends on the particle matrix.
Atmospheric Environment.
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ABSTRACT: Typical classification schemes for large data sets of single-particle mass spectra involve statistical or neural network analysis. In this work, a new approach is evaluated in which particle spectra are pre-selected on the basis of an above threshold signal intensity at a specified m/z (mass to charge ratio). This provides a simple way to identify candidate particles that may contain the specific chemical component associated with that m/z. Once selected, the candidate particle spectra are then classified by the fast adaptive resonance algorithm, ART 2-a, to confirm the presence of the targeted component in the particle and to study the intra-particle associations with other chemical components. This approach is used to characterize metals in a 75,000 particle data set obtained in Baltimore, Maryland. Particles containing a specific metal are identified and then used to determine the size distribution, number concentration, time/wind dependencies and intra-particle correlations with other metals. Four representative elements are considered in this study: vanadium, iron, arsenic and lead. Number concentrations of ambient particles containing these elements can exceed 10,000 particles cm−3 at the measurement site. Vanadium, a primary marker for fuel oil combustion, is observed from all wind directions during this time period. Iron and lead are observed from the east–northeast. Most particles from this direction that contain iron also contain lead and most particles that contain lead also contain iron, suggesting a common emission source for the two. Arsenic and lead are observed from the south–southeast. Particles from this direction contain either arsenic or lead but rarely both, suggesting different sources for each element.
Atmospheric Environment.
