The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Mohammad M. Hamasha - One of the best experts on this subject based on the ideXlab platform.
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mathematical approximation of single and double sided truncated normal distribution using Logistic Function
International Journal of Industrial Engineering-theory Applications and Practice, 2020Co-Authors: Mohammad M. HamashaAbstract:This article provides a mathematical approximation model of the general double-sided truncated normal distribution. The right and left-sided cases are included in the model as special cases. The double-sided truncated normal distribution is important for many applications in industrial and systems engineering. For example, in quality control, production engineers maybe interested in scrapping the unfit products. The distribution of product variations after this scrapping is basically double-sided truncated normal distribution. A full analysis of deviation of the introduced approximation’s results from the actual results is provided. Further, recommendations for the use of the model are provided.
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Practitioner advice: Approximation of the cumulative density of left-sided truncated normal distribution using Logistic Function and its implementation in Microsoft Excel
Quality Engineering, 2017Co-Authors: Mohammad M. HamashaAbstract:? 2016 Taylor & Francis Group, LLCThe left-sided truncated normal distribution is especially important in quality engineering where we remove the left side of the distribution, for example, due to estimation of the life of used products. Although the theoretical background of truncated normal distribution is already established, there is very little work on mathematical approximation of the probability density and the cumulative probability density Functions. In this article, a high accuracy mathematical approximation of the left-sided truncated normal distribution is proposed. A full analysis of errors and recommendations for implementation using Microsoft Excel are provided at the end of this article.
Ju Mizuno - One of the best experts on this subject based on the ideXlab platform.
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half Logistic Function model for first half of descending phase of cardiomyocyte cytoplasmic ca 2 concentration ca 2 i time curve catciii in isolated aequorin injected mouse left ventricular papillary muscle
Acta Cardiologica Sinica, 2016Co-Authors: Ju Mizuno, Mikiya Otsuji, Hideko Arita, Takeshi Yokoyama, Kazuo HanaokaAbstract:Background: Myocardial contraction and relaxation are regulated by increases and decreases in cytoplasmic calcium concentration ([Ca^(2+)]_i). In previous studies, we found that a half-Logistic (h-L) Function, which represents a half-curve of a symmetrical sigmoid Logistic Function with a boundary at the inflection point, curve-fits the first half of the ascending phase and the second half of the descending phase of the [Ca^(2+)]_i transient curve better than a mono-exponential (m-E) Function. In the present study,we investigated the potential application of an h-L Function to analyse the first half of the descending phase of CaTC (CaTCIII). Methods: The [Ca^(2+)]_i was measured using the Ca^(2+)-sensitive aequorin, which was microinjected into 15 isolated mouse left ventricular (LV) papillary muscles. The observed CaTCIII data in the interval from the point corresponding to the peak [Ca^(2+)]_i to the point corresponding to dCa/dtmin was curve-fitted using the h-L and m-E Function equations by the least-squares method. Results: The mean correlation coefficient (r) values of the h-L and m-E Function best curve-fits for 11 CaTCIIIs were 0.9986 and 0.9982, respectively. The Z transformation of h-L r (3.64 ± 0.45) was larger than that of m-E r (3.50 ± 0.33) (p ＜ 0.05). Conclusions: The h-L Function can evaluate most CaTCIIIs more accurately than the m-E Function in isolated aequorin-injected mouse LV papillary muscle. The three calculated h-L parameters i.e., amplitude constant, time constant, and non-zero asymptote, are more reliable indices than m-E for evaluating the magnitude and time course of the change in the decrease in [Ca^(2+)]_i.
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intracellular ca 2 transient phase ii can be assessed by half Logistic Function model in isolated aequorin injected mouse left ventricular papillary muscle
Acta Cardiologica Sinica, 2013Co-Authors: Ju Mizuno, Mikiya Otsuji, Kazuo Hanaoka, Hideko Arita, Takeshi YokoyamaAbstract:Background: Myocardial contraction and relaxation are regulated by increases and decreases in intracellular cytoplasmic calcium (Ca^2+) concentration ([Ca^2+]i). In previous studies, we found that a half-Iogistic (h-L) Function, which represents a half-curve of a symmetrical sigmoid Logistic Function with a boundary at the inflection point, curve-fits the first half of the ascending phase (CaTI) and the second half of the descending phase of the [Ca^2+]i transient curve (CaTIV) better than a mono-exponential (m-E) Function. In the present study, we investigated the potential application of an h-L Function to the analysis of the second half of the ascending phase of the [Ca^2+]i transient curve (CaTII).Methods: The [Ca^2+]i transient was measured using the Ca^2+ -sensitive photoprotein aequorin, which was microinjected into 15 isolated left ventricular (LV) papillary muscles of mice. The observed CaTII data during the time duration from the point corresponding to the maximum of the first-order time derivative of Ca^2+ concentration (dCa/dtmax) to the point corresponding to the peak Ca^2+ concentration was curve-fitted by the least-squares method using the h-L and m-E Function equations.Results: The mean correlation coefficient (r) values of the h-L and m-E curve-fits for CaTlI were 0.9996 and 0.9984, respectively. The Z transformation of h-L r was larger than that of m-E r (p ＜ 0.0001). H-L residual mean square (RMS) was smaller than m-E RMS (p ＜ 0.001).Conclusions: The h-L Function tracks the magnitudes and time courses of CaTII more accurately than the m-E Function in isolated aequorin-injected mouse LV papillary muscle. Compared with the m-E time constant, the h-L time constant of CaTl1 is a more reliable index for evaluating the time duration of the change in the increase in [Ca^2+]i during the combination of the middle part of the contraction process and the early part of the relaxation process. CaTII can be assessed by the h-L Function model in cardiac muscles. The h-L approach may provide a more useful model for studying each process in myocardial Ca^2+ handling.
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calcium induced calcium release from the sarcoplasmic reticulum can be evaluated with a half Logistic Function model in aequorin injected cardiac muscles
Journal of Anesthesia, 2011Co-Authors: Ju Mizuno, Mikiya Otsuji, Kazuo Hanaoka, Hideko Arita, Hidetoshi Sakamoto, Satoru Fukuda, Shigehito SawamuraAbstract:Purpose Release of calcium (Ca2+) from the sarcoplasmic reticulum (SR) induced by Ca2+ influx through voltage-dependent sarcolemmal L-type Ca2+ channels (CICR) in cardiac muscle cells has been implicated as a potential target contributing to anesthetic-induced myocardial depression. In an earlier study, we found that (1) a half-Logistic (h-L) Function, which represents a half-curve of a sigmoid Logistic Function with a boundary at the inflection point, curve-fits the first half of the ascending phases of the isometric myocardial tension and isovolumic left ventricular (LV) pressure waveforms better than a mono-exponential (m-E) Function and (2) the h-L time constants are useful as inotropic indices. We report here our investigation of the potential application of an h-L Function to the analysis of the first half of the ascending phase of the Ca2+ transient curve (faCaT) that precedes and initiates myocardial contraction and the increase in LV pressure.
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curve fit with hybrid Logistic Function for intracellular calcium transient
Masui. The Japanese journal of anesthesiology, 2009Co-Authors: Ju Mizuno, Mikiya Otsuji, Kazuo Hanaoka, Shigeho Morita, Junichi Araki, Satoshi KuriharaAbstract:As the left ventricular (LV) pressure curve and myocardial tension curve in heart are composed of contraction and relaxation processes, we have found that hybrid Logistic (HL) Function calculated as the difference between two Logistic Functions curve-fits better the isovolumic LV pressure curve and the isometric twitch tension curve than the conventional polynomial exponential and sinusoidal Functions. Increase and decrease in intracellular Ca2+ concentration regulate myocardial contraction and relaxation. Recently, we reported that intracellular Ca2+ transient (CaT) curves measured using the calcium-sensitive bioluminescent protein, aequorin, were better curve-fitted by HL Function compared to the polynomial exponential Function in the isolated rabbit RV and mouse LV papillary muscles. We speculate that the first Logistic component curve of HL fit represents the concentration of the Ca2+ inflow into the cytoplasmic space, the concentration of Ca2+ released from sarcoplasmic reticulum (SR), the concentration of Ca2+ binding to troponin C (TnC), and the attached number of cross-bridge (CB) and their time courses, and that the second Logistic component curve of HL fit represents the concentration of Ca2+ sequestered into SR, the concentration of Ca2+ removal from the cytoplasmic space, the concentration of Ca2+ released from TnC, and the detached number of CB and their time courses. This HL approach for CaT curve may provide a more useful model for investigating Ca2+ handling, Ca(2+) -TnC interaction, and CB cycling.
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novel assessment of intracellular calcium transient decay in cardiac muscle by curve fitting with half Logistic Function
Masui. The Japanese journal of anesthesiology, 2008Co-Authors: Ju Mizuno, Kazuo Hanaoka, Hideko Arita, Yoichiro Kusakari, Satoshi KuriharaAbstract:A decrease in intracellular calcium (Ca2+) concentration in the cardiac muscle is one of the important factors to induce myocardial relaxation. A mono-exponential (m-E) Function has been used for assessing myocardial relaxation curve of isometric tension and intracellular calcium transient (CaT) decay, and the m-E time constants for the relaxation curve of isometric tension (F tau E) and CaT decay (Ca tau E) have been recognised as lusitropic indices. However, we found that a half-Logistic (h-L) Function fits the relaxation curve of isometric tension much more precisely than the conventional m-E Function in the ferret right ventricular (RV) papillary muscle. Moreover, we demonstrated that the goodness of the h-L fits for CaT decays was superior to the goodness of the m-E fits in the rabbit RV and murine left ventricular papillary muscles. The changes in the h-L time constants for the relaxation curves of isometric tension (F tau L) and CaT decays (Ca tau L) with the different onsets were significantly smaller than the changes in F tau E and Ca tau E, respectively. The differences in the h-L non-zero asymptotes for the relaxation curves of isometric tension and CaT decays with the different onsets were smaller than the changes in the m-E non-zero asymptotes. The h-L Function model characterises the amplitudes and time courses of the relaxation curve of isometric tension and CaT decay more precisely than the m-E Function model, and thus F tau L and Ca tau L serve as more novel and reliable lusitropic indices. Simultaneous analysis of myocardial relaxation curve of isometric tension and CaT decay using h-L Functions can become a useful method for assessment of myocardial calcium handling.
Hiroyuki Suga - One of the best experts on this subject based on the ideXlab platform.
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hybrid Logistic characterization of isometric twitch force curve of isolated ferret right ventricular papillary muscle
Japanese Journal of Physiology, 1999Co-Authors: Ju Mizuno, Junichi Araki, Satoshi Kurihara, Takeshi Mikane, Mineko Hatashima, Toshiyuki Moritan, Tetsuya Ishikawa, Kimiaki Komukai, Masahisa Hirakawa, Hiroyuki SugaAbstract:We previously found that the isovolumic pressure curve of the left ventricle and the isometric twitch force curve of the right ventricular in situ papillary muscle, both of the blood-perfused canine heart, were precisely fitted by our newly proposed hybrid Logistic Function. This Function describes the difference between the two S-shaped Logistic Functions for the rising and falling components: A/[1+exp{-(4B/A)(t-C)}]-D/[1+exp{-(4E/D)(t-F)}]+G. This Function characterizes comprehensively both ventricular and in situ papillary muscle contraction and relaxation. In the present study, we hypothesized that this Function could also characterize the force curve of the most popular, standard-type, isolated and Tyrode-superfused papillary muscle preparation. To test this hypothesis, we investigated how precisely the hybrid Logistic Function could fit 112 isometric twitch force curves observed in eight isolated and Tyrode-superfused ferret right ventricular papillary muscles at different muscle lengths and extracellular Ca2+ concentrations. We always obtained a precise curve fitting with a correlation coefficient above 0.9987. This fitting was much more precise than sinusoidal and polynomial exponential Function curve fittings. These results supported the present hypothesis. We conclude that our hybrid Logistic Function reasonably characterizes the force curve of the isolated myocardial preparation. This result broadens the generality of the hybrid Logistic characterization of ventricular isovolumic pressure and myocardial isometric twitch force generation. The hybrid Logistic characterization seems to be an integrative expression of contractile processes in myocardial twitch contraction.
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hybrid Logistic characterization of isometric twitch force time curve of intact blood perfused canine right ventricular papillary muscle
Japanese Journal of Physiology, 1997Co-Authors: Taisuke Sakamoto, Junichi Araki, Miyako Takaki, Yoshiki Hata, Hiromi Matsubara, Hiroyuki SugaAbstract:We previously found that a ventricular isovolumic pressure-time curve could be well fitted by the difference between two S-shaped Logistic curves for the pressure rising and falling components, and called it "hybrid Logistic" Function: P(t)=A/[1+exp[-(4B/A)(t-C)]]-D/[1+exp[-(4E/D)(t-F)]]+G. We reported that the parameters of this hybrid Logistic Function are useful to characterize left ventricular contraction and relaxation comprehensively. In this study, we investigated how well this hybrid Logistic Function could fit the isometric twitch force-time curves of cross-circulated right ventricular papillary muscles of 7 dogs. This Function precisely fitted the isometric force curves with correlation coefficients above 0.9996, much better than another fitting Function (F(t)=C(t/A)(B)exp[1-(t/A)(B)]) proposed by Nwasokwa. The present results indicate that our hybrid Logistic Function can also reasonably express the canine right ventricular papillary muscle isometric twitch force-time curve. We suggest the possibility that the parameters of this hybrid Logistic Function are also useful to comprehensively characterize right ventricular papillary muscle twitch contraction and relaxation.
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Logistic characterization of left ventricular isovolumic pressure time curve
Japanese Journal of Physiology, 1995Co-Authors: Hiromi Matsubara, Junichi Araki, Miyako Takaki, S T Nakagawa, Hiroyuki SugaAbstract:Although some investigators have attempted to express the left ventricular pressure-time curve by mathematical Functions such as exponential and sinusoidal Functions, none of them reasonably fits the left ventricular pressure-time curve. In the present study, we hypothesized that a ventricular isovolumic pressure-time curve could be expressed as the difference between two S-shaped curves for pressure rising and falling, and proposed a new "hybrid Logistic" Function to express the left ventricular isovolumic pressure-time curve. We investigated how well this hybrid Logistic Function fits left ventricular isovolumic pressure curves experimentally observed under physiological preload and contractility in the excised cross-circulated left ventricles of 10 dogs. The new Function precisely fitted the isovolumic pressure curves regardless of preload and contractility with correlation coefficients above 0.9996, much better than the previously proposed Functions. The observed values characterizing the magnitude and time course of the isovolumic pressure curve such as peak +/- dP/dt also closely correlated with the corresponding theoretical values calculated by the present best-fit Function. We conclude that our new hybrid Logistic Function reasonably characterizes the canine left ventricular isovolumic pressure-time curve within physiological ranges of preload and contractility. The present results indicate that this hybrid Logistic Function is useful to evaluate left ventricular contraction and relaxation comprehensively.
Junichi Araki - One of the best experts on this subject based on the ideXlab platform.
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curve fit with hybrid Logistic Function for intracellular calcium transient
Masui. The Japanese journal of anesthesiology, 2009Co-Authors: Ju Mizuno, Mikiya Otsuji, Kazuo Hanaoka, Shigeho Morita, Junichi Araki, Satoshi KuriharaAbstract:As the left ventricular (LV) pressure curve and myocardial tension curve in heart are composed of contraction and relaxation processes, we have found that hybrid Logistic (HL) Function calculated as the difference between two Logistic Functions curve-fits better the isovolumic LV pressure curve and the isometric twitch tension curve than the conventional polynomial exponential and sinusoidal Functions. Increase and decrease in intracellular Ca2+ concentration regulate myocardial contraction and relaxation. Recently, we reported that intracellular Ca2+ transient (CaT) curves measured using the calcium-sensitive bioluminescent protein, aequorin, were better curve-fitted by HL Function compared to the polynomial exponential Function in the isolated rabbit RV and mouse LV papillary muscles. We speculate that the first Logistic component curve of HL fit represents the concentration of the Ca2+ inflow into the cytoplasmic space, the concentration of Ca2+ released from sarcoplasmic reticulum (SR), the concentration of Ca2+ binding to troponin C (TnC), and the attached number of cross-bridge (CB) and their time courses, and that the second Logistic component curve of HL fit represents the concentration of Ca2+ sequestered into SR, the concentration of Ca2+ removal from the cytoplasmic space, the concentration of Ca2+ released from TnC, and the detached number of CB and their time courses. This HL approach for CaT curve may provide a more useful model for investigating Ca2+ handling, Ca(2+) -TnC interaction, and CB cycling.
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Logistic time constant of isometric relaxation force curve of ferret ventricular papillary muscle reliable index of lusitropism
Japanese Journal of Physiology, 2000Co-Authors: Ju Mizuno, Junichi Araki, Satoshi Kurihara, Hiromi Matsubara, Takeshi Mikane, Satoshi Mohri, Takeshi Imaoka, Hiroshi Okuyama, Tohru Ohe, Masahisa HirakawaAbstract:We have found that a Logistic Function fits the left ventricular isovolumic relaxation pressure curve in the canine excised, cross-circulated heart more precisely than a monoexponential Function. On this basis, we have proposed a Logistic time constant (tau(L)) as a better index of ventricular isovolumic lusitropism than the conventional monoexponential time constant (tau(E)). We hypothesize in the present study that this tau(L) would also be a better index of myocardial isometric lusitropism than the conventional tau(E). We tested this hypothesis by analyzing the isometric relaxation force curve of 114 twitches of eight ferret isolated right ventricular papillary muscles. The muscle length was changed between 82 and 100% L(max) and extracellular Ca(2+) concentrations ([Ca(2+)](o)) between 0.2 and 8 mmol/l. We found that the Logistic Function always fitted the isometric relaxation force curve much more precisely than the monoexponential Function at any muscle length and [Ca(2+)](o) level. We also found that tau(L) was independent of the choice of the end of isometric relaxation but tau(E) was considerably dependent on it as in ventricular relaxation. These results validated our present hypothesis. We conclude that tau(L) is a more reliable, though still empirical, index of lusitropism than conventional tau(E) in the myocardium as in the ventricle.
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hybrid Logistic characterization of isometric twitch force curve of isolated ferret right ventricular papillary muscle
Japanese Journal of Physiology, 1999Co-Authors: Ju Mizuno, Junichi Araki, Satoshi Kurihara, Takeshi Mikane, Mineko Hatashima, Toshiyuki Moritan, Tetsuya Ishikawa, Kimiaki Komukai, Masahisa Hirakawa, Hiroyuki SugaAbstract:We previously found that the isovolumic pressure curve of the left ventricle and the isometric twitch force curve of the right ventricular in situ papillary muscle, both of the blood-perfused canine heart, were precisely fitted by our newly proposed hybrid Logistic Function. This Function describes the difference between the two S-shaped Logistic Functions for the rising and falling components: A/[1+exp{-(4B/A)(t-C)}]-D/[1+exp{-(4E/D)(t-F)}]+G. This Function characterizes comprehensively both ventricular and in situ papillary muscle contraction and relaxation. In the present study, we hypothesized that this Function could also characterize the force curve of the most popular, standard-type, isolated and Tyrode-superfused papillary muscle preparation. To test this hypothesis, we investigated how precisely the hybrid Logistic Function could fit 112 isometric twitch force curves observed in eight isolated and Tyrode-superfused ferret right ventricular papillary muscles at different muscle lengths and extracellular Ca2+ concentrations. We always obtained a precise curve fitting with a correlation coefficient above 0.9987. This fitting was much more precise than sinusoidal and polynomial exponential Function curve fittings. These results supported the present hypothesis. We conclude that our hybrid Logistic Function reasonably characterizes the force curve of the isolated myocardial preparation. This result broadens the generality of the hybrid Logistic characterization of ventricular isovolumic pressure and myocardial isometric twitch force generation. The hybrid Logistic characterization seems to be an integrative expression of contractile processes in myocardial twitch contraction.
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hybrid Logistic characterization of isometric twitch force time curve of intact blood perfused canine right ventricular papillary muscle
Japanese Journal of Physiology, 1997Co-Authors: Taisuke Sakamoto, Junichi Araki, Miyako Takaki, Yoshiki Hata, Hiromi Matsubara, Hiroyuki SugaAbstract:We previously found that a ventricular isovolumic pressure-time curve could be well fitted by the difference between two S-shaped Logistic curves for the pressure rising and falling components, and called it "hybrid Logistic" Function: P(t)=A/[1+exp[-(4B/A)(t-C)]]-D/[1+exp[-(4E/D)(t-F)]]+G. We reported that the parameters of this hybrid Logistic Function are useful to characterize left ventricular contraction and relaxation comprehensively. In this study, we investigated how well this hybrid Logistic Function could fit the isometric twitch force-time curves of cross-circulated right ventricular papillary muscles of 7 dogs. This Function precisely fitted the isometric force curves with correlation coefficients above 0.9996, much better than another fitting Function (F(t)=C(t/A)(B)exp[1-(t/A)(B)]) proposed by Nwasokwa. The present results indicate that our hybrid Logistic Function can also reasonably express the canine right ventricular papillary muscle isometric twitch force-time curve. We suggest the possibility that the parameters of this hybrid Logistic Function are also useful to comprehensively characterize right ventricular papillary muscle twitch contraction and relaxation.
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Logistic characterization of left ventricular isovolumic pressure time curve
Japanese Journal of Physiology, 1995Co-Authors: Hiromi Matsubara, Junichi Araki, Miyako Takaki, S T Nakagawa, Hiroyuki SugaAbstract:Although some investigators have attempted to express the left ventricular pressure-time curve by mathematical Functions such as exponential and sinusoidal Functions, none of them reasonably fits the left ventricular pressure-time curve. In the present study, we hypothesized that a ventricular isovolumic pressure-time curve could be expressed as the difference between two S-shaped curves for pressure rising and falling, and proposed a new "hybrid Logistic" Function to express the left ventricular isovolumic pressure-time curve. We investigated how well this hybrid Logistic Function fits left ventricular isovolumic pressure curves experimentally observed under physiological preload and contractility in the excised cross-circulated left ventricles of 10 dogs. The new Function precisely fitted the isovolumic pressure curves regardless of preload and contractility with correlation coefficients above 0.9996, much better than the previously proposed Functions. The observed values characterizing the magnitude and time course of the isovolumic pressure curve such as peak +/- dP/dt also closely correlated with the corresponding theoretical values calculated by the present best-fit Function. We conclude that our new hybrid Logistic Function reasonably characterizes the canine left ventricular isovolumic pressure-time curve within physiological ranges of preload and contractility. The present results indicate that this hybrid Logistic Function is useful to evaluate left ventricular contraction and relaxation comprehensively.
Hiromi Matsubara - One of the best experts on this subject based on the ideXlab platform.
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Logistic time constant of isometric relaxation force curve of ferret ventricular papillary muscle reliable index of lusitropism
Japanese Journal of Physiology, 2000Co-Authors: Ju Mizuno, Junichi Araki, Satoshi Kurihara, Hiromi Matsubara, Takeshi Mikane, Satoshi Mohri, Takeshi Imaoka, Hiroshi Okuyama, Tohru Ohe, Masahisa HirakawaAbstract:We have found that a Logistic Function fits the left ventricular isovolumic relaxation pressure curve in the canine excised, cross-circulated heart more precisely than a monoexponential Function. On this basis, we have proposed a Logistic time constant (tau(L)) as a better index of ventricular isovolumic lusitropism than the conventional monoexponential time constant (tau(E)). We hypothesize in the present study that this tau(L) would also be a better index of myocardial isometric lusitropism than the conventional tau(E). We tested this hypothesis by analyzing the isometric relaxation force curve of 114 twitches of eight ferret isolated right ventricular papillary muscles. The muscle length was changed between 82 and 100% L(max) and extracellular Ca(2+) concentrations ([Ca(2+)](o)) between 0.2 and 8 mmol/l. We found that the Logistic Function always fitted the isometric relaxation force curve much more precisely than the monoexponential Function at any muscle length and [Ca(2+)](o) level. We also found that tau(L) was independent of the choice of the end of isometric relaxation but tau(E) was considerably dependent on it as in ventricular relaxation. These results validated our present hypothesis. We conclude that tau(L) is a more reliable, though still empirical, index of lusitropism than conventional tau(E) in the myocardium as in the ventricle.
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hybrid Logistic characterization of isometric twitch force time curve of intact blood perfused canine right ventricular papillary muscle
Japanese Journal of Physiology, 1997Co-Authors: Taisuke Sakamoto, Junichi Araki, Miyako Takaki, Yoshiki Hata, Hiromi Matsubara, Hiroyuki SugaAbstract:We previously found that a ventricular isovolumic pressure-time curve could be well fitted by the difference between two S-shaped Logistic curves for the pressure rising and falling components, and called it "hybrid Logistic" Function: P(t)=A/[1+exp[-(4B/A)(t-C)]]-D/[1+exp[-(4E/D)(t-F)]]+G. We reported that the parameters of this hybrid Logistic Function are useful to characterize left ventricular contraction and relaxation comprehensively. In this study, we investigated how well this hybrid Logistic Function could fit the isometric twitch force-time curves of cross-circulated right ventricular papillary muscles of 7 dogs. This Function precisely fitted the isometric force curves with correlation coefficients above 0.9996, much better than another fitting Function (F(t)=C(t/A)(B)exp[1-(t/A)(B)]) proposed by Nwasokwa. The present results indicate that our hybrid Logistic Function can also reasonably express the canine right ventricular papillary muscle isometric twitch force-time curve. We suggest the possibility that the parameters of this hybrid Logistic Function are also useful to comprehensively characterize right ventricular papillary muscle twitch contraction and relaxation.
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Logistic characterization of left ventricular isovolumic pressure time curve
Japanese Journal of Physiology, 1995Co-Authors: Hiromi Matsubara, Junichi Araki, Miyako Takaki, S T Nakagawa, Hiroyuki SugaAbstract:Although some investigators have attempted to express the left ventricular pressure-time curve by mathematical Functions such as exponential and sinusoidal Functions, none of them reasonably fits the left ventricular pressure-time curve. In the present study, we hypothesized that a ventricular isovolumic pressure-time curve could be expressed as the difference between two S-shaped curves for pressure rising and falling, and proposed a new "hybrid Logistic" Function to express the left ventricular isovolumic pressure-time curve. We investigated how well this hybrid Logistic Function fits left ventricular isovolumic pressure curves experimentally observed under physiological preload and contractility in the excised cross-circulated left ventricles of 10 dogs. The new Function precisely fitted the isovolumic pressure curves regardless of preload and contractility with correlation coefficients above 0.9996, much better than the previously proposed Functions. The observed values characterizing the magnitude and time course of the isovolumic pressure curve such as peak +/- dP/dt also closely correlated with the corresponding theoretical values calculated by the present best-fit Function. We conclude that our new hybrid Logistic Function reasonably characterizes the canine left ventricular isovolumic pressure-time curve within physiological ranges of preload and contractility. The present results indicate that this hybrid Logistic Function is useful to evaluate left ventricular contraction and relaxation comprehensively.
