Exponential modelling of heart rate recovery after a maximal exercise

Objectives: Heart rate recovery (HRR) after exercise is clinically important as a predictor of mortality. In addition, HRR is an indicator of cardiac autonomic activity, since increased vagal activity and diminished sympathetic activity return the heart rate to resting conditions after exercise. The previous attempts to model HRR using polynomial, first-order and second-order modelling have produced mixed results. In this study, we hypothesised that the double-exponential fit would model the HRR more accurately than the single-exponential fit as it would capture the activity of both autonomic arms responsible for heart rate decay and investigated the outcome of these two models on the HRR data following a maximal exercise. Materials and Methods: Exponential curve fitting was done on a set of previously published data from our laboratory. The HRR data were acquired from 40 male participants (19–38 years) after a maximal treadmill exercise. The normalised HRR data from a 5-min time window from maximal heart rate were fitted using single and double-exponential curves, to obtain, respectively, the time constants Tau and, Tau 1 and Tau 2. The goodness-of-fit of the model was assessed with Chi-square values computed for each participant data set with both models. Considering that Chi-square of zero is a perfect fit, and therefore, smaller Chi-square values indicate a better fit than larger values, we computed the difference in the Chi-square values (??2 ) between the models by subtracting the Chi-square value of the double-exponential fit from the Chi-square value of the singleexponential fit. This was based on the premise that if the calculated ??2 is positive, it would indicate a better fit with double-exponential than single-exponential decay model. The data are presented as mean ± standard deviation. Comparisons were made with Student’s t-test. Results: Data from four participants were excluded for technical reasons. The Tau of the single-exponential fit was 65.50 ± 12.13 s, while Tau 1 and Tau 2 of the double-exponential fit were 43.75 ± 18.96 s and 120.30 ± 91.32 s, respectively, the Tau 1 value being significantly lower than the Tau 2 value (P < 0.0001). Remarkably among the 36 participants, the difference in the Chi-square value was positive (127.2 ± 171.04) in 22 subjects and zero or marginally negative (?0.17 ± 0.31) in 14 subjects. Conclusion: Our results indicate that the double-exponential model fitted the HRR data better than the single-exponential model in almost two-thirds (61%) of our study population. In the remaining participants, the goodness-of-fit was nearly equivalent for both fits with no evidence of superior modelling with the singleexponential fit. Our data show that while the single-exponential fit is sufficient for modelling the HRR of 14 subjects, it was less efficient for fitting the data of most participants. In comparison, the double-exponential curve fit effectively modelled 100% of our study population. Given our findings, we conclude that the doubleexponential model is more inclusive and better represented the HRR data of our study population than the singleexponential model.

Rational design of a 500 m3 fermenter for erythromycin production by Saccharopolyspora erythraea / 生物工程学报

Erythromycin is a macrolide antibiotic produced by Saccharopolyspora erythraea. Its yield is greatly affected by the fermentation conditions and the bioreactor configurations. In this study, a novel scale-up method for erythromycin fermentation was developed based on computational fluid dynamics (CFD) and time constant analysis. Firstly, the dissolved oxygen (DO) was determined as a key parameter according to the physiological properties of S. erythraea cultivated in a 50 L bioreactor. It was found that the time constant of oxygen supply (tmt) in a 500 m3 bioreactor should be less than 6.25 s in order to satisfy the organism's oxygen uptake rate (OUR). Subsequently, a 500 m3 bioreactor was designed using the time constant method combined with empirical correlations. The impeller combination with one BDT8 impeller at bottom and two MSX4 impellers at upper part was determined, and then validated by numerical simulation. The results indicated that the tmt of the bioreactor (< 6.25 s) and the fluid properties, including gas hold-up, shear stress and fluid vector, met the requirements of erythromycin fermentation. Finally, the industrial production of erythromycin in the 500 m3 showed the design method was applicable in large scale fermentation.

Measurement and discussion of circuit time constants for radiation detectors / 中华放射医学与防护杂志

Objective To measure the circuit time constants of 4 kinds of radiation survey meters (451P ionization chamber dosimeter,6150AD6 + 6150AD-b dose meter,FH40G + FHZ672E-10 dose meter and AT1123 dose meter) and,to discuss the formula of time response correction and its application.Methods In the condition of continuous exposure of X-ray machine,the ambient dose equivalent rates shown by survey meters were recorded.In order to get the circuits time constant,the least squares fittingmethod was used to fit the data using the time response formula of circuit having a capacitance C and a resistance R in series.Results The relative uncertainty of fitted circuit time constants was higher than 20％ except for 6150AD6 + 6150AD-b dose meter.The relative uncertainty of fitted r was 8％ for 6150AD6 + 6150AD-b dose meter.Conclusions The time required to stabilize the dosimeter readings was 8,5,3 and 2 s,respectively,for the 451P ionization chamber dosimeter,6150AD6 +6150AD-b dose meter,FH40G + FHZ672E-10 dose meter and AT1123 dose meter.The rising trend of their measured values was not fully accordance with the RC circuit time response correction formula.

Calculation of left ventricular relaxation time constant Tau in dogs with aortic regurgitation by continuous wave Doppler / 中华医学超声杂志（电子版）

Objective To find a new method for evaluating the left ventricular relaxation time constant Tau with aortic regurgitation by continuous wave Doppler.Methods Twelve Beagle dogs were included in the study.The dog aortic regurgitation model was produced under ultrasound guiding by carotid artery puncture.Aortic pressure was measured by pressure catheter and left ventricular pressure was measured by Millar catheter which was introduced into the left ventricular through cardiac apex.Then microspheres were injected into the left coronary artery under the guidance of ultrasound to induce acute ischemic left ventricular dysfunction,when left ventricular end-diastolic pressure increased more than 5 mmHg (1 mmHg=0.133 kPa).Dobutamine or esmolol was infused to alter left ventricular function.Aortic regurgitation velocity spectrum was recorded by the continuous-wave Doppler echocardiography in different hemodynamic status.At the same time,left ventricular pressure,dp/dt,aortic pressure and continuous ECG tracing were displayed on the multi-channel physiological recorder.Measurement was recorded of-dp/dtmax in the dp/dt tracings and the pressure at the time of-dp/dtmax in the left ventricular pressure tracings.Tau =-P/(dp/dtmax),Tau was the catheter-derived time constant (Taucatheter).Aortic regurgitation spectrum of original audio data was post-processed with MATLAB mathematical software.The spectral lines refresh time of about 300 μs was chosen to form a new Doppler spectrum.Three points:(t1,1 m/s),(t2,2 m/s) and (t3,3 m/s) were selected in aortic regurgitation velocity spectrum and tl,t2 and t3 was put into the corresponding Tau formula:Tau=(t2-t1)/ln[(ADP-C-4)/(ADP-C-16)],Tau=(t3-t1)/ln[(ADP-C-4)/(ADP-C-36)].Tau was the aortic regurgitant time constant (Tauultrasound).The difference between Taucatheter and Tauultrasound was compared by paired t test.The correlation between Taucatheter and Tauultrasound was analyzed by Pearson correlation analysis.Results Twelve dogs were successfully produced aortic regurgitation model.Two dogs died of ventricular fibrillation during the procedure of acute ischemic left ventricular diastolic dysfunction.The range of the Taucatheter was between 27.12 ms and 86.88 ms with an average of (48.973± 14.667) ms;the range of the Tauultrasound was between 28.13 ms and 90.18 ms with an average of (51.236± 15.146) ms.The difference was not statistically significant (t=1.841,P ＞ 0.05).Pearson correlation analysis showed that Taucatheter was positively correlated with Tatultrasound (r=0.89,P=0.000).Conclusion Choosing three points:(t1,1 m/s),(t2,2 m/s) and (t3,3 m/s) in aortic regurgitant velocity spectrum and putting into the corresponding formula,we can calculate Tau,which had a good correlation with the catheter-derived Tau.

Calculation of left ventricular relaxation time constant (Tau) in dogs with mitral regurgitation by continuous-wave Doppler / 中华医学超声杂志（电子版）

Objective To explore the new method for noninvasively measuring the time constant of left ventricular relaxation (Tau) in animals with mitral regurgitation by continuous-wave Doppler.Methods The acute ischaemic left diastolic heart failure with mitral regurgitation was produced in 9 dogs.Dobutamine hydrochloride or esmolol hydrochloride had been applied to change the hemodynamic states.In different hemodynamic states,left ventricular pressures,left atrial pressures,curves of dP/dt and continuous-wave mitral regurgitant spectra were synchronously recorded.Doppler spectra were laterly processed through Matlab workstation.Paired t-test was used to compare the difference between Tau-catheter (Tau-c) and Tau-doppler ultrasound (Tau-d),and the correlation between Tau-c and Tau-d was analyzed by Pearson correlation analysis.Results Thirty-nine hemodynamic status had been obtained in 9 dogs.Tau-c was 21.03-78.45 ms and the average was (48.76± 17.60) ms.Tau-d was 21.24-94.60 ms and the average was (49.33 ± 18.79) ms.There was no significant difference (t=0.353,P=0.726) between Tau-d and Tau-c.The correlation analysis between Tau-d and Tau-c suggested a strong positive relationship with the correlation coefficient (r=0.85,P ＜ 0.001).Conclusions The dog aortic regurgitation model under ultrasound guidance is less traumatic.The method of inducing left ventricular diastolic dysfunction by repeatedly injecting microspheres into the left coronary sinus is safe and reliable.Choosing three points (t1,1 m/s;t2,2 m/s;t3,3 m/s) in aortic regurgitant velocity spectrum and putting them into the corresponding formula,we can obtain Tau,which had a good correlation with the catheter-derived Tau.

Effect of pressure phase plane derived τ and K on evaluation of left ventricular diastolic function in isolated rat heart during ischemia/reperfusion / 中国病理生理杂志

AIM: To analyze and compare the changes of pressure phase plane(PPP) derived τ and K on isolated rat heart during ischemia/reperfusion, and to explore the value of PPP derived τ and K for evaluation of left ventricular diastolic dysfunction. METHODS: LVEDP, -d(p/dt)_(max), τ and K were measured and calculated during ischemia/reperfusion in Sprague-Dawley rat hearts. Meanwhile, the level of lactate dehydrogenase (LDH) in the coronary effluent was measured, and the ultrastructure changes in myocardium were observed under electron microscope. RESULTS: Compared with control group, τ increased and K reduced significantly in each ischemic group in a time dependent manner (P<0.05). With prolonged ischemia, τ was even higher and K was even lower (P<0.05). Compared with control group, except ischemia 15 min, LDH in other groups increased significantly at 10 min and 20 min after reperfusion (P<0.05). Compared with ischemia 30 min, LDH of ischemia 45 min and ischemia 60 min were even higher at 10 min and 20 min after reperfusion (P<0.05). With prolonged ischemia, the abnormal changes of the myocardial ultrastructure were observed. CONCLUSION: PPP derived τ and K may be promising indexes for quantitative assessment of left ventricular diastolic function on isolated) rat heart during ischemia/reperfusion, and indication of the severity of ischemia/reperfusion injury.

Variação diurna e resposta da cinética do VO2 de ciclistas durante exercício muito intenso / Diurnal variation and Vo2 kinetic response of cyclists during heavy exercise

O objetivo do presente estudo foi avaliar a influência da hora do dia nos parâmetros da cinética do consumo de oxigênio de ciclistas durante exercício muito intenso. Nove voluntários do sexo masculino realizaram exercícios de carga constante às 08:00, 13:00 e 18:00 h, em dias diferentes. Estes exercícios foram realizados duas vezes em cada visita, com um intervalo de 1 h entre eles. A intensidade usada foi de 75 por centoΔ (75 por cento da diferença entre o VO2 no limiar de lactato e o VO2max. A amplitude do componente primário do VO2 (2597 ± 273 ml.min-1, 2513 ± 268 ml.min-1 e 2609 ± 370 ml.min-1), a constante de tempo do componente primário do VO2 (19.3 ± 2.5 s, 18.4 ± 3.0 s e 19.7 ± 3.9 s), o componente lento do VO2 (735 ± 81 ml.min-1, 764 ± 99 ml.min-1 e 680 ± 121 ml.min-1) e o tempo de resposta média (51.8 ± 4.2 s, 51.2 ± 4.2 s e 51.4 ± 3.4 s) não apresentaram diferenças significativas entre os diferentes horários do dia (08:00, 13:00 e 18:00 h), assim como os demais parâmetros da cinética do VO2. Estes resultados sugerem que a resposta da cinética do VO2 de ciclistas durante exercício muito intenso (75 por centoΔ) não é influenciada pela hora do dia.

The objective of the present study was to evaluate the influence of the time of day on the parameters of oxygen uptake kinetics of trained cyclists during high intensity exercise. Nine male volunteers repeated bouts at constant loads at 08:00, 13:00 and 18:00 h on different days. These exercise bouts were performed twice on each occasion, with an interval of 1 h between them. The load intensity used was 75 percentΔ (75 percent of the difference between the VO2 at the lactate threshold and the VO2max). The primary VO2 amplitude (2597 ± 273 ml.min-1, 2513 ± 268 ml.min-1 and 2609 ± 370 ml.min-1), the primary VO2 time constant (19.3 ± 2.5 s, 18.4 ± 3.0 s and 19.7 ± 3.9 s), the VO2 slow component (735 ± 81 ml.min-1, 764 ± 99 ml.min-1 and 680 ± 121 ml.min-1) and the mean response time (51.8 ± 4.2 s, 51.2 ± 4.2 s and 51.4 ± 3.4 s) did not present significant differences at the different times (08:00, 13:00 and 18:00 h), neither did the other parameters of the VO2 kinetics. These results suggest that the response of the VO2 kinetics of cyclists exercising at high intensity (75 percentΔ) is not influenced by the time of day.

EFFECT ON DECLINE IN HEART RATE INDUCED BY OCULAR COMPRESSION AND APNEA AFTER EXERCISE / 体力科学

<b>Object </b>: The purpose of this study was to test the response of the decline in heart rate (HR) induced by compression on the eyeball (eyeball pressure : EP) and voluntary non breath (VNB) after pedaling exercise. <b>Methods </b>: EP ; Nine male subjects performed exercise for 3 min in a supine position using a bicycle ergometer. Immediately after the exercise all subjects received EP for 10 seconds. After that, subjects undertook the same protocol without EP (CON-E). VNB ; Four male and two female subjects performed exercise for 5 minutes using a bicycle ergometer. Immediately after the exercise subjects received VNB for 7 seconds. After that subjects undertook the same protocol without VNB (CON-V). <b>Results </b>: The slope of the decline in HR recovery (HR_DS) after exercise in EP increased significantly more than that in CON-E (p<0.05). However, time constant (HR_TC) in CON-E declined faster than that in EP. Thereby, the relationship between HR_DS in EP and HR_TC in CON-E correlated (r=-0.562). The HR_DS of VNB was greater than that of EP and CON-V. However the relationship between HR_DS in VNB and HR_TC in CON-V did not correlate. <b>Conclusion </b>: We suggest that EP affects vagal nervous activity and VNB affects strength of baroreflex sensitivity. Therefore HR_DS of EP might evaluate vagal nervous activity.

Changes in Cardiac Autonomic Nervous Activity During Menstrual Cycle of Young Women / 体力科学

The purpose of this study was to evaluate the function of cardiac autonomic nervous activity and post-exercise vagal reaction during the menstrual cycle. The subjects were healthy young women (n=13, age 19.9±0.6 years) with normal menstrual cycles. Power spectral analysis of heart rate variability was used to examine cardiac autonomic nervous activity. In addition, the time con stant of heart rate decline for the first 30 sec (T<SUB>30</SUB>) after exercise was used to examine post-exercise vagal reactivation.<BR>Results show that the cardiac autonomic nervous activity changes during the menstrual cycle. Also, T<SUB>30</SUB> shows significant change during the menstrual cycle, especially T<SUB>30</SUB> retardation in the early luteal phase. These results suggest that an imbalance of estradiol and progesterone hormones may be responsible for these changes in cardiac autonomic nervous activity during the menstrual cycle.

The Temperature Effects on Motor Nerve Conduction Parameters by Different Warming Methods

OBJECTIVE: To investigate the patterns of the temperature effect on motor nerve conduction parameters according to various warming methods and to obtain the most valuable method of warming in clinical setting. METHOD: Twenty normal subjects were studied. After limb cooling in cold water, the cooled hands were warmed by hot pack, fan heater, and whirl pool. The median motor responses were recorded at abdnctor pollicis brevis after the stimulation at the wrist during warming at 1 min interval until the temperature increment reached plateau. We measured the temperature changes and conduction parameters were measured at each examination. RESULTS: The time constants for temperature increment and distal motor latency, duration, area of compound muscle action potentials showed shorter tendency by hot pack and whirl pool than by fan heater (p<0.05). For the measurement of distal motor latency, time constant of whirl pool (2.49 1.21 min) was shorter than that of fan heater (7.12 3.12 min) or hot pack (5.96 1.98 min) (p<0.05). CONCLUSION: These findings suggest that the use of whirl pool is the most effective method for warming of the cooled limb.

Electrodiagnostic Alteration to Temperature Effect in Demyelinating Peripheral Neuropathy

OBJECTIVE: The purpose of this study was to determine the difference of temperature effects on the nerve conduction variables and to obtain correction factors for temperature in demyelinated and normal peripheral nerves. METHOD: The compound muscle action potentials (CMAPs) were recorded with wrist stimulation during cooling and warming in 10 control subjects and 13 subjects with demyelinating neuropathies. The temperature of cooling and warming were 18degrees C and 40degrees C, respectively. The time of cooling and warming were 60 minutes and composed of successive 4 sessions of 15 minutes. The skin temperature of thenar area, latency, amplitude, duration, and area of CMAPs were measured before and after each session of 15 minutes of cooling or warming. RESULTS: The time constants of parameters of CMAPs were of higher tendency in cooling than in warming. The time constants of latency of CMAP were higher in subjects with demyelinating neuropathy than in controls (p<0.05): 33.3+/-4.0 minutes versus 27.2+/-2.2 minutes in cooling; 30.0+/-7.8 minutes versus 19.6+/-3.3 minutes in warming. The temperature correction factor of latency of CMAPs was 0.23+/-0.03 msec/degrees C in control and 0.33+/-0.06 msec/degrees C in subjects with demyelinating neuropathies (p<0.05). CONCLUSION: When studying a subject with demyelinating neuropathies, we should warm the extremity for more sufficient time than in normal subject, or may applicate a differenct temperature correction factors.

COMPUTATION OF TIME-CONSTANT HISTOGRAMS FROM THE FORCED EXPIRED VOLUME-TIME CURVES / 第二军医大学学报

An efficient BASIC program was established on Apple-Ⅱ microcomputer with the CHESTAC-3EF pulmonary function testing system to calculate the time-constant histogram from the spirogram.By a set of analogue studies, we confirmed that the recovered time-constant histogrgram was within one compartment of the assumed one and that the root of mean square values of the residuals between the experimental and model volume-time curves was 0.02. In four adult healthy subjects, the mean value of time-constant histograms (TCx ) had the variation coefficient (6.6%). The results show that our method is reliable and reproducible, and it can be used for clinical investigation.

Anaerobic threshold, O2 deficit and response time of O2 uptake in long, middle and short distance runners / 体力科学

Subjects were long distance runners (n=6), middle distance runners (n=6), and sprinters (n=4) . They exercised in incremental exercise and steady state exercise. The anaerobic thershold (AT), O<SUB>2</SUB>deficit at AT (AT-O<SUB>2</SUB>df), and time constant of Vo<SUB>2</SUB> (τ) which were obtained from these exercise tests were compared among three groups of runners, and the interrelationship of three parameters was elucidated. The results were as follows.<BR>1) AT-Vo<SUB>2</SUB>of long distance runners was the highest followed by the values of middle distance runners and sprinters, successively. The AT-Vo<SUB>2</SUB>per weight and per Vo<SUB>2</SUB>max also decreased in the same order.<BR>2) AT-O<SUB>2</SUB>df per weight of long distance runners was as high as that of middle distance runners, and was significantly higher than that of sprinters.<BR>3) τ of long distance runners was shorter than that of middle distance runners, but was not significantly shorter than that of sprinters. τ of long distance runners was shorter than the reported one of untrained people.<BR>4) ΔAT-Vo<SUB>2</SUB> (difference between AT-Vo<SUB>2</SUB>and Vo<SUB>2</SUB>at rest) related to neither AT-O<SUB>2</SUB>df nor τ. However, the ratio of AT-O<SUB>2</SUB>df/τ significantly related to the ΔAT-Vo<SUB>2</SUB> (r=0.795, n=16, p<0.001) . From these results, the highest values of AT-Vo<SUB>2</SUB>obtained in long distance runners would be due to both high AT-O<SUB>2</SUB>df and short τ.

EFFECTS OF TEMPERATURE AND ANESTHESIA ON VARIOUS EXCITABILITY INDEXES OF SCIATIC--PERONEAL NERVE IN TOADS / 西安交通大学学报(医学版)

Effects of temperature and anesthesia on various excitability indexes of sciatic—peronael nerve were observed in toads. The results show that standard electrical quantity(a) changes regularly with the change of excitability. The higher excitability, the less the "a" value. But "b" in Weiss's fomula, chronaxie (Chr), rheobase (Rh), and intensity-duration curve do not indicate excitability. The time constant (RC)of the cell membrane is not related to the changes of excitability. Thus, "a" is an actual index of measuring excitability.