Journal articles: 'Heart Sounds Mathematical models'

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Narváez, Pedro, and Winston S. Percybrooks. "Synthesis of Normal Heart Sounds Using Generative Adversarial Networks and Empirical Wavelet Transform." Applied Sciences 10, no. 19 (October 8, 2020): 7003. http://dx.doi.org/10.3390/app10197003.

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Currently, there are many works in the literature focused on the analysis of heart sounds, specifically on the development of intelligent systems for the classification of normal and abnormal heart sounds. However, the available heart sound databases are not yet large enough to train generalized machine learning models. Therefore, there is interest in the development of algorithms capable of generating heart sounds that could augment current databases. In this article, we propose a model based on generative adversary networks (GANs) to generate normal synthetic heart sounds. Additionally, a denoising algorithm is implemented using the empirical wavelet transform (EWT), allowing a decrease in the number of epochs and the computational cost that the GAN model requires. A distortion metric (mel–cepstral distortion) was used to objectively assess the quality of synthetic heart sounds. The proposed method was favorably compared with a mathematical model that is based on the morphology of the phonocardiography (PCG) signal published as the state of the art. Additionally, different heart sound classification models proposed as state-of-the-art were also used to test the performance of such models when the GAN-generated synthetic signals were used as test dataset. In this experiment, good accuracy results were obtained with most of the implemented models, suggesting that the GAN-generated sounds correctly capture the characteristics of natural heart sounds.

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Tian, Xin, and Zhong Tan. "Analysis and decision of heart sounds via ARMA models." Measurement 5, no. 3 (July 1987): 102–6. http://dx.doi.org/10.1016/s0263-2241(87)80009-x.

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Xin, T. "Analysis and decision of heart sounds via ARMA models." Measurement 5, no. 3 (September 1987): 102–6. http://dx.doi.org/10.1016/0263-2241(87)90011-x.

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Quarteroni, A., A. Manzoni, and C. Vergara. "The cardiovascular system: Mathematical modelling, numerical algorithms and clinical applications." Acta Numerica 26 (May 1, 2017): 365–590. http://dx.doi.org/10.1017/s0962492917000046.

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Mathematical and numerical modelling of the cardiovascular system is a research topic that has attracted remarkable interest from the mathematical community because of its intrinsic mathematical difficulty and the increasing impact of cardiovascular diseases worldwide. In this review article we will address the two principal components of the cardiovascular system: arterial circulation and heart function. We will systematically describe all aspects of the problem, ranging from data imaging acquisition, stating the basic physical principles, analysing the associated mathematical models that comprise PDE and ODE systems, proposing sound and efficient numerical methods for their approximation, and simulating both benchmark problems and clinically inspired problems. Mathematical modelling itself imposes tremendous challenges, due to the amazing complexity of the cardiocirculatory system, the multiscale nature of the physiological processes involved, and the need to devise computational methods that are stable, reliable and efficient. Critical issues involve filtering the data, identifying the parameters of mathematical models, devising optimal treatments and accounting for uncertainties. For this reason, we will devote the last part of the paper to control and inverse problems, including parameter estimation, uncertainty quantification and the development of reduced-order models that are of paramount importance when solving problems with high complexity, which would otherwise be out of reach.

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Price, G. Richard, Joel T. Kalb, and Georges R. Garinther. "Toward a Measure of Auditory Handicap in the Army." Annals of Otology, Rhinology & Laryngology 98, no. 5_suppl (May 1989): 42–52. http://dx.doi.org/10.1177/00034894890980s508.

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The effect of a soldier's ability to hear on the capacity to perform a mission was calculated for a variety of militarily relevant tasks through the use of mathematical models. Changes in hearing can result from organic loss, hearing protectors, the masking effect of noises, etc. The effects were calculated for the detection of sounds of enemy personnel (speech, movement noises) or their equipment (rifle bolt, tank, generator). We also calculated the effects on the ability to control/communicate with troops verbally. The normal ear is highly effective in detecting noises of personnel or their equipment or in understanding speech, even in noise. By contrast, even modest hearing losses and/or the wearing of hearing protectors can have profound effects on military performance, for example, reducing the area that can be monitored acoustically by more than 30-fold or cutting warning times for other sounds by a factor of more than 100. Hearing protectors may have the conflicting effects of protecting hearing while producing unacceptable performance because of their attenuation.

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Zemlyakov, Ivan, Dmitry Zhdanov, Yana Kostelei, Anton Seleznev, and Artem Bureev. "Mathematical model of heart sounds." IOP Conference Series: Materials Science and Engineering 862 (May 28, 2020): 042021. http://dx.doi.org/10.1088/1757-899x/862/4/042021.

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Shahmohammadi, Mehrdad, Hongxing Luo, Philip Westphal, Richard N. Cornelussen, Frits W. Prinzen, and Tammo Delhaas. "Hemodynamics-driven mathematical model of first and second heart sound generation." PLOS Computational Biology 17, no. 9 (September 22, 2021): e1009361. http://dx.doi.org/10.1371/journal.pcbi.1009361.

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We propose a novel, two-degree of freedom mathematical model of mechanical vibrations of the heart that generates heart sounds in CircAdapt, a complete real-time model of the cardiovascular system. Heart sounds during rest, exercise, biventricular (BiVHF), left ventricular (LVHF) and right ventricular heart failure (RVHF) were simulated to examine model functionality in various conditions. Simulated and experimental heart sound components showed both qualitative and quantitative agreements in terms of heart sound morphology, frequency, and timing. Rate of left ventricular pressure (LV dp/dtmax) and first heart sound (S1) amplitude were proportional with exercise level. The relation of the second heart sound (S2) amplitude with exercise level was less significant. BiVHF resulted in amplitude reduction of S1. LVHF resulted in reverse splitting of S2 and an amplitude reduction of only the left-sided heart sound components, whereas RVHF resulted in a prolonged splitting of S2 and only a mild amplitude reduction of the right-sided heart sound components. In conclusion, our hemodynamics-driven mathematical model provides fast and realistic simulations of heart sounds under various conditions and may be helpful to find new indicators for diagnosis and prognosis of cardiac diseases. New & noteworthy To the best of our knowledge, this is the first hemodynamic-based heart sound generation model embedded in a complete real-time computational model of the cardiovascular system. Simulated heart sounds are similar to experimental and clinical measurements, both quantitatively and qualitatively. Our model can be used to investigate the relationships between heart sound acoustic features and hemodynamic factors/anatomical parameters.

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Ryzhov, Oleg S. "Transition length in turbine/compressor blade flows." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2072 (March 7, 2006): 2281–98. http://dx.doi.org/10.1098/rspa.2005.1651.

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High Reynolds number mathematical models for convected vortex impinging against a local hump and sound scattering into Tollmien–Schlichting eigenmodes are introduced to simulate basic mechanisms of the disturbance excitation typical of turbomachinery environments. The streamwise dimension of the transitional flow on the suction side of a blade is evaluated on the assumption that the transition length is of equal order with the extent of viscous/inviscid interaction controlling the boundary-layer response. The triple-deck theory gives a simple power law correlation to express a value of the Reynolds number based on the transition length in terms of the Reynolds number calculated with the blade cord. Precisely the same correlation stems from processing experimental data for both smooth and rough surfaces. The computation shows the explosive development of highly modulated wave packets and their rapid breakdown brought about by erratic short-scaled wiggles riding on the primary long-scaled oscillation cycles. The filling-up of distant parts of the wavenumber spectrum is at the heart of the signal distortion. This process heralds the start of deep transition terminating in fully developed turbulent flow well before reaching the upper stability branch. With the time-harmonic excitation broadly used in experiments, transition requires a much longer distance to complete. An agreement between theoretical predictions based on the assumption of indefinitely large Reynolds numbers and experimental findings from wind-tunnel observations at finite Reynolds numbers is encouraging.

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Rudnitskii, A. G., M. A. Rudnytska, and L. V. Tkachenko. "SINGLE-CHANNEL PROCESSING OF AUSCULTATORY SIGNALS USING METHODS OF MATHEMATICAL MORPHOLOGY." Journal of Numerical and Applied Mathematics, no. 1 (135) (2021): 179–85. http://dx.doi.org/10.17721/2706-9699.2021.1.24.

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The paper considers a new method of separating respiratory sounds from heart sounds in a general signal registered on the surface of the human body. The proposed approach is based on a combination of Bayesian noise suppression techniques and methods of mathematical morphology. The proposed method was tested on real auscultatory signals. Evaluation of the efficiency of the algorithm using auditory, visual and numerical analysis shows that the developed approach is a promising alternative to existing techniques for separating auscultatory signals into its natural components.

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Soto-Murillo, Manuel A., Jorge I. Galván-Tejada, Carlos E. Galván-Tejada, Jose M. Celaya-Padilla, Huizilopoztli Luna-García, Rafael Magallanes-Quintanar, Tania A. Gutiérrez-García, and Hamurabi Gamboa-Rosales. "Automatic Evaluation of Heart Condition According to the Sounds Emitted and Implementing Six Classification Methods." Healthcare 9, no. 3 (March 12, 2021): 317. http://dx.doi.org/10.3390/healthcare9030317.

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The main cause of death in Mexico and the world is heart disease, and it will continue to lead the death rate in the next decade according to data from the World Health Organization (WHO) and the National Institute of Statistics and Geography (INEGI). Therefore, the objective of this work is to implement, compare and evaluate machine learning algorithms that are capable of classifying normal and abnormal heart sounds. Three different sounds were analyzed in this study; normal heart sounds, heart murmur sounds and extra systolic sounds, which were labeled as healthy sounds (normal sounds) and unhealthy sounds (murmur and extra systolic sounds). From these sounds, fifty-two features were calculated to create a numerical dataset; thirty-six statistical features, eight Linear Predictive Coding (LPC) coefficients and eight Cepstral Frequency-Mel Coefficients (MFCC). From this dataset two more were created; one normalized and one standardized. These datasets were analyzed with six classifiers: k-Nearest Neighbors, Naive Bayes, Decision Trees, Logistic Regression, Support Vector Machine and Artificial Neural Networks, all of them were evaluated with six metrics: accuracy, specificity, sensitivity, ROC curve, precision and F1-score, respectively. The performances of all the models were statistically significant, but the models that performed best for this problem were logistic regression for the standardized data set, with a specificity of 0.7500 and a ROC curve of 0.8405, logistic regression for the normalized data set, with a specificity of 0.7083 and a ROC curve of 0.8407, and Support Vector Machine with a lineal kernel for the non-normalized data; with a specificity of 0.6842 and a ROC curve of 0.7703. Both of these metrics are of utmost importance in evaluating the performance of computer-assisted diagnostic systems.

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Noble, Denis. "The development of mathematical models of the heart." Chaos, Solitons & Fractals 5, no. 3-4 (March 1995): 321–33. http://dx.doi.org/10.1016/0960-0779(93)e0025-7.

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Chen, Wei, Qiang Sun, Xiaomin Chen, Gangcai Xie, Huiqun Wu, and Chen Xu. "Deep Learning Methods for Heart Sounds Classification: A Systematic Review." Entropy 23, no. 6 (May 26, 2021): 667. http://dx.doi.org/10.3390/e23060667.

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The automated classification of heart sounds plays a significant role in the diagnosis of cardiovascular diseases (CVDs). With the recent introduction of medical big data and artificial intelligence technology, there has been an increased focus on the development of deep learning approaches for heart sound classification. However, despite significant achievements in this field, there are still limitations due to insufficient data, inefficient training, and the unavailability of effective models. With the aim of improving the accuracy of heart sounds classification, an in-depth systematic review and an analysis of existing deep learning methods were performed in the present study, with an emphasis on the convolutional neural network (CNN) and recurrent neural network (RNN) methods developed over the last five years. This paper also discusses the challenges and expected future trends in the application of deep learning to heart sounds classification with the objective of providing an essential reference for further study.

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Cheng, Xiefeng, Pengfei Wang, and Chenjun She. "Biometric Identification Method for Heart Sound Based on Multimodal Multiscale Dispersion Entropy." Entropy 22, no. 2 (February 20, 2020): 238. http://dx.doi.org/10.3390/e22020238.

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In this paper, a new method of biometric characterization of heart sounds based on multimodal multiscale dispersion entropy is proposed. Firstly, the heart sound is periodically segmented, and then each single-cycle heart sound is decomposed into a group of intrinsic mode functions (IMFs) by improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN). These IMFs are then segmented to a series of frames, which is used to calculate the refine composite multiscale dispersion entropy (RCMDE) as the characteristic representation of heart sound. In the simulation experiments I, carried out on the open heart sounds database Michigan, Washington and Littman, the feature representation method was combined with the heart sound segmentation method based on logistic regression (LR) and hidden semi-Markov models (HSMM), and feature selection was performed through the Fisher ratio (FR). Finally, the Euclidean distance (ED) and the close principle are used for matching and identification, and the recognition accuracy rate was 96.08%. To improve the practical application value of this method, the proposed method was applied to 80 heart sounds database constructed by 40 volunteer heart sounds to discuss the effect of single-cycle heart sounds with different starting positions on performance in experiment II. The experimental results show that the single-cycle heart sound with the starting position of the start of the first heart sound (S1) has the highest recognition rate of 97.5%. In summary, the proposed method is effective for heart sound biometric recognition.

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Denisov, A. M., and V. V. Kalinin. "The inverse problem for mathematical models of heart excitation." Computational Mathematics and Mathematical Physics 50, no. 3 (March 2010): 515–18. http://dx.doi.org/10.1134/s0965542510030127.

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Ghali, Neveen I., Rasha Wahid, and Aboul Ella Hassanien. "Heart Sounds Human Identification and Verification Approaches using Vector Quantization and Gaussian Mixture Models." International Journal of Systems Biology and Biomedical Technologies 1, no. 4 (October 2012): 74–87. http://dx.doi.org/10.4018/ijsbbt.2012100106.

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In this paper the possibility of using the human heart sounds as a human print is investigated. To evaluate the performance and the uniqueness of the proposed approach, tests using a high resolution auscultation digital stethoscope are done for nearly 80 heart sound samples. The verification approach consists of a robust feature extraction with a specified configuration in conjunction with Gaussian mixture modeling. The similarity of two samples is estimated by measuring the difference between their negative log-likelihood similarities of the features. The experimental results obtained show that the overall accuracy offered by the employed Gaussian mixture modeling reach up to 85%. The identification approach consists of a robust feature extraction with a specified configuration in conjunction with LBG-VQ. The experimental results obtained show that the overall accuracy offered by the employed LBG-VQ reach up to 88.7%.

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Ram, Rashmi, Deanne M. Mickelsen, Catherine Theodoropoulos, and Burns C. Blaxall. "New approaches in small animal echocardiography: imaging the sounds of silence." American Journal of Physiology-Heart and Circulatory Physiology 301, no. 5 (November 2011): H1765—H1780. http://dx.doi.org/10.1152/ajpheart.00559.2011.

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Systolic and diastolic dysfunction of the left ventricle (LV) is a hallmark of most cardiac diseases. In vivo assessment of heart function in animal models, particularly mice, is essential to refining our understanding of cardiovascular disease processes. Ultrasound echocardiography has emerged as a powerful, noninvasive tool to serially monitor cardiac performance and map the progression of heart dysfunction in murine injury models. This review covers current applications of small animal echocardiography, as well as emerging technologies that improve evaluation of LV function. In particular, we describe speckle-tracking imaging-based regional LV analysis, a recent advancement in murine echocardiography with proven clinical utility. This sensitive measure enables an early detection of subtle myocardial defects before global dysfunction in genetically engineered and rodent surgical injury models. Novel visualization technologies that allow in-depth phenotypic assessment of small animal models, including perfusion imaging and fetal echocardiography, are also discussed. As imaging capabilities continue to improve, murine echocardiography will remain a critical component of the investigator's armamentarium in translating animal data to enhanced clinical treatment of cardiovascular diseases.

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Legrice, I. J., P. J. Hunter, and B. H. Smaill. "Laminar structure of the heart: a mathematical model." American Journal of Physiology-Heart and Circulatory Physiology 272, no. 5 (May 1, 1997): H2466—H2476. http://dx.doi.org/10.1152/ajpheart.1997.272.5.h2466.

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A mathematical description of cardiac anatomy is presented for use with finite element models of the electrical activation and mechanical function of the heart. The geometry of the heart is given in terms of prolate spheroidal coordinates defined at the nodes of a finite element mesh and interpolated within elements by a combination of linear Lagrange and cubic Hermite basis functions. Cardiac microstructure is assumed to have three axes of symmetry: one aligned with the muscle fiber orientation (the fiber axis); a second set orthogonal to the fiber direction and lying in the newly identified myocardial sheet plane (the sheet axis); and a third set orthogonal to the first two, in the sheet-normal direction. The geometry, fiber-axis direction, and sheet-axis direction of a dog heart are fitted with parameters defined at the nodes of the finite element mesh. The fiber and sheet orientation parameters are defined with respect to the ventricular geometry such that 1) they can be applied to any heart of known dimensions, and 2) they can be used for the same heart at various states of deformation, as is needed, for example, in continuum models of ventricular contraction.

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Álvarez, Alonso, Narcisa Salazar, and José Tinajero. "Scientific Computing and the Huygens' Principle." KnE Engineering 1, no. 2 (January 30, 2018): 44. http://dx.doi.org/10.18502/keg.v1i2.1485.

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Abstract. Mathematics has been present in the development of society since time immemorial; great figures have dedicated their entire life to analysis and research in various branches of this broad science. Scientific Computing is closely related to the design and construction of mathematical models aimed at solving scientific, social and engineering problems. There are several applications of this discipline, for example for mathematical simulations of differential equations in partial derivatives that describe the propagation of a variety of waves such as sound waves, or heat conduction problems in different media, which can be solved using The Fourier Analysis. Through Graphical Computing the Huygens Principle can be verified. All these models can be implemented through the computer in order to facilitate the complex calculations that must be done to solve problems of this type and depending on the case to condense all this information into a graph "A good graph says more than a thousand words (Chinese Proverb) ".

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Zhang, Guo Hua, and Shi Xuan Liu. "Wavelet Packet Algorithm to Feature Extraction of Heart Sound." Advanced Materials Research 317-319 (August 2011): 1211–14. http://dx.doi.org/10.4028/www.scientific.net/amr.317-319.1211.

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In order to extract pathological features of heart sound signal accurately, an algorithm for extracting the sub-band energy is developed based on the wavelet packet. The db6 wavelet is taken as the mother function, and the best wavelet packet basis of heart sound signal is picked out. Then, various heart sound signals are decomposed into four levels and the wavelet packet coefficients of the best basis are obtained. According to the equal-value relation between wavelet packet coefficients and signal energy in time domain, the normalized sub-band energy of the best basis is extracted as the feature vector. Based on BP network, seven identification models for seven kinds of heart sound were trained separately. Then, these models were tested by using 70 heart sounds, and the mean of identification accuracy is 72.9%.

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Cheffer, Augusto, and Marcelo A. Savi. "Random effects inducing heart pathological dynamics: An approach based on mathematical models." Biosystems 196 (October 2020): 104177. http://dx.doi.org/10.1016/j.biosystems.2020.104177.

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BENSA, ELISA, and GIANNI ZANARINI. "LA FISICA DELLA MUSICA." Nuncius 14, no. 1 (1999): 69–111. http://dx.doi.org/10.1163/182539199x00760.

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Abstracttitle SUMMARY /title The scientific revolution of XVII century concerned also the domain of music theory, deeply investigating the nature of musical sounds and the physics of their production. Also the classical explanations of musical consonance were questioned, looking for its hidden causes through physics experiments and mathematical models. The passionating history of musical acoustics from Galileo to the end of XVIII century is revisited, with a particular emphasis on consonance theories.

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Lee, Jang Hyung, Sun Young Kyung, Pyung Chun Oh, Kwang Gi Kim, and Dong Jin Shin. "Heart Sound Classification Using Multi Modal Data Representation and Deep Learning." Journal of Medical Imaging and Health Informatics 10, no. 3 (March 1, 2020): 537–43. http://dx.doi.org/10.1166/jmihi.2020.2987.

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Heart anomalies are an important class of medical conditions from personal, public health and social perspectives and hence accurate and timely diagnoses are important. Heartbeat features two well known amplitude peaks termed S1 and S2. Some sound classification models rely on segmented sound intervals referenced to the locations of detected S1 and S2 peaks, which are often missing due to physiological causes and/or artifacts from sound sampling process. The constituent and combined models we propose are free from segmentation, which consequently is more robust and meritful from reliability aspects. Intuitive phonocardiogram representation with relatively simple deep learning architecture was found to be effective for classifying normal and abnormal heart sounds. A frequency spectrum based deep learning network also produced competitive classification results. When the classification models were merged in one via SVM, performance was seen to improve further. The SVM classification model, comprised of two time domain submodels and a frequency domain submodel, produced 0.9175 sensitivity, 0.8886 specificity and 0.9012 accuracy.

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Biktasheva, I. V., R. D. Simitev, R. Suckley, and V. N. Biktashev. "Asymptotic properties of mathematical models of excitability." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 364, no. 1842 (March 21, 2006): 1283–98. http://dx.doi.org/10.1098/rsta.2006.1770.

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We analyse small parameters in selected models of biological excitability, including Hodgkin–Huxley (Hodgkin & Huxley 1952 J. Physiol. 117 , 500–544) model of nerve axon, Noble (Noble 1962 J. Physiol. 160 , 317–352) model of heart Purkinje fibres and Courtemanche et al . (Courtemanche et al . 1998 Am. J. Physiol. 275 , H301–H321) model of human atrial cells. Some of the small parameters are responsible for differences in the characteristic time-scales of dynamic variables, as in the traditional singular perturbation approaches. Others appear in a way which makes the standard approaches inapplicable. We apply this analysis to study the behaviour of fronts of excitation waves in spatially extended cardiac models. Suppressing the excitability of the tissue leads to a decrease in the propagation speed, but only to a certain limit; further suppression blocks active propagation and leads to a passive diffusive spread of voltage. Such a dissipation may happen if a front propagates into a tissue recovering after a previous wave, e.g. re-entry. A dissipated front does not recover even when the excitability restores. This has no analogy in FitzHugh–Nagumo model and its variants, where fronts can stop and then start again. In two spatial dimensions, dissipation accounts for breakups and self-termination of re-entrant waves in excitable media with Courtemanche et al . kinetics.

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CHAMPNEYS, A. R., D. AVITABILE, M. HOMER, and R. SZALAI. "THE MECHANICS OF HEARING: A COMPARATIVE CASE STUDY IN BIO-MATHEMATICAL MODELLING." ANZIAM Journal 52, no. 3 (January 2011): 225–49. http://dx.doi.org/10.1017/s1446181111000733.

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AbstractA synthesis is presented of two recent studies on modelling the nonlinear neuro-mechanical hearing processes in mosquitoes and in mammals. In each case, a hierarchy of models is considered in attempts to understand data that shows nonlinear amplification and compression of incoming sound signals. The insect’s hearing is tuned to the vicinity of a single input frequency. Nonlinear response occurs via an arrangement of many dual capacity neuro-mechanical units called scolopidia within the Johnston’s organ. It is shown how the observed data can be captured by a simple nonlinear oscillator model that is derived from homogenization of a more complex model involving a radial array of scolopidia. The physiology of the mammalian cochlea is much more complex, with hearing occurring via a travelling wave along a tapered, compartmentalized tube. Waves travel a frequency-dependent distance along the tube, at which point they are amplified and “heard”. Local models are reviewed for the pickup mechanism, within the outer hair cells of the organ of Corti. The current debate in the literature is elucidated, on the relative importance of two possible nonlinear mechanisms: active hair bundles and somatic motility. It is argued that the best experimental agreement can be found when the nonlinear terms include longitudinal coupling, the physiological basis of which is described. A discussion section summarizes the lessons learnt from both studies and attempts to shed light on the more general question of what constitutes a good mathematical model of a complex physiological process.

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Adiban, Mohammad, Bagher BabaAli, and Saeedreza Shehnepoor. "Statistical feature embedding for heart sound classification." Journal of Electrical Engineering 70, no. 4 (August 1, 2019): 259–72. http://dx.doi.org/10.2478/jee-2019-0056.

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Abstract Cardiovascular Disease (CVD) is considered as one of the principal causes of death in the world. Over recent years, this field of study has attracted researchers’ attention to investigate heart sounds’ patterns for disease diagnostics. In this study, an approach is proposed for normal/abnormal heart sound classification on the Physionet challenge 2016 dataset. For the first time, a fixed length feature vector; called i-vector; is extracted from each heart sound using Mel Frequency Cepstral Coefficient (MFCC) features. Afterwards, Principal Component Analysis (PCA) transform and Variational Autoencoder (VAE) are applied on the i-vector to achieve dimension reduction. Eventually, the reduced size vector is fed to Gaussian Mixture Models (GMMs) and Support Vector Machine (SVM) for classification purpose. Experimental results demonstrate the proposed method could achieve a performance improvement of 16% based on Modified Accuracy (MAcc) compared with the baseline system on the Physionet2016 dataset.

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SACHSE, FRANK B., GUNNAR SEEMANN, MATTHIAS B. MOHR, and ARUN V. HOLDEN. "MATHEMATICAL MODELING OF CARDIAC ELECTRO-MECHANICS: FROM PROTEIN TO ORGAN." International Journal of Bifurcation and Chaos 13, no. 12 (December 2003): 3747–55. http://dx.doi.org/10.1142/s0218127403008910.

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Mathematical models of cardiac anatomy and physics provide information, which help to understand structure and behavior of the heart. Miscellaneous cardiac phenomena can only be adequately described by combination of models representing different aspects or levels of detail. Coupling of these models necessitates the definition of appropriate interfaces. Adequateness and efficiency of interfaces is crucial for efficient application of the combined models. In this work an integrated model is presented consisting of several models interconnected by interfaces. The integrated model allows the reconstruction of macroscopic electro-mechanical processes in the heart. The model comprises a three-dimensional are of left ventricular anatomy represented as truncated ellipsoid. The integrated model includes electrophysiological, tension development and elastomechanical models of myocardium at levels of single cell, proteins, and tissue patches, respectively. The model is exemplified by simulations of extracorporated left ventricle of small mammals. These simulations yield temporal distributions of electrophysiological parameters as well as descriptions of electrical propagation and mechanical deformation. The simulations show characteristic macroscopic ventricular function resulting from the interplay between cellular electrophysiology, electrical excitation propagation, tension development, and mechanical deformation.

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ZHANG, WENYING, XINGMING GUO, ZHIHUI YUAN, and XINGHUA ZHU. "HEART SOUND CLASSIFICATION AND RECOGNITION BASED ON EEMD AND CORRELATION DIMENSION." Journal of Mechanics in Medicine and Biology 14, no. 04 (July 3, 2014): 1450046. http://dx.doi.org/10.1142/s0219519414500468.

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Analysis of heart sound is of great importance to the diagnosis of heart diseases. Most of the feature extraction methods about heart sound have focused on linear time-variant or time-invariant models. While heart sound is a kind of highly nonstationary and nonlinear vibration signal, traditional methods cannot fully reveal its essential properties. In this paper, a novel feature extraction approach is proposed for heart sound classification and recognition. The ensemble empirical mode decomposition (EEMD) method is used to decompose the heart sound into a finite number of intrinsic mode functions (IMFs), and the correlation dimensions of the main IMF components (IMF1~IMF4) are calculated as feature set. Then the classical Binary Tree Support Vector Machine (BT-SVM) classifier is employed to classify the heart sounds which include the normal heart sounds (NHSs) and three kinds of abnormal signals namely mitral stenosis (MT), ventricular septal defect (VSD) and aortic stenosis (AS). Finally, the performance of the new feature set is compared with the correlation dimensions of original signals and the main IMF components obtained by the EMD method. The results showed that, for NHSs, the feature set proposed in this paper performed the best with recognition rate of 98.67%. For the abnormal signals, the best recognition rate of 91.67% was obtained. Therefore, the proposed feature set is more superior to two comparative feature sets, which has potential application in the diagnosis of cardiovascular diseases.

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Irons, F. E. "New method for reducing the general formula for lattice specific heat to the Einstein and Nernst-Lindemann approximations." Canadian Journal of Physics 81, no. 8 (August 1, 2003): 1015–36. http://dx.doi.org/10.1139/p03-069.

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To reduce the general formula for lattice specific heat to Einstein's formula of 1907, one traditionally models the spectrum of lattice modes-of-vibration as a set of independent oscillators all of one frequency, ν1. Not only is this a poor representation of a real solid, but no formula is provided for the frequency ν1, which has to be determined empirically. We offer a new and more compelling method for reducing the general formula to Einstein's formula. The reduction involves a simple mathematical approximation, proceeds without any reference to independent oscillators all of one frequency, and leads to a formula for the characteristic frequency, ν1, equal to the mean modal frequency. The mathematical approximation is valid at all but low temperatures, thereby providing insight into the failure of Einstein's formula at low temperatures. A simple extension of the new method leads to the NernstLindemann formula for specific heat, proposed in 1911 on the basis of trial and error and currently without a sound theoretical basis. Empirical values (from the literature) of the frequencies that characterize the Einstein, the NernstLindemann, and also the Debye formulae are all in support of the present theory. PACS Nos.: 65.40.Ba, 01.55.+b

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Acedo, Luis. "A Hidden Markov Model for the Linguistic Analysis of the Voynich Manuscript." Mathematical and Computational Applications 24, no. 1 (January 23, 2019): 14. http://dx.doi.org/10.3390/mca24010014.

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Hidden Markov models are a very useful tool in the modeling of time series and any sequence of data. In particular, they have been successfully applied to the field of mathematical linguistics. In this paper, we apply a hidden Markov model to analyze the underlying structure of an ancient and complex manuscript, known as the Voynich manuscript, which remains undeciphered. By assuming a certain number of internal states representations for the symbols of the manuscripts, we train the network by means of the α and β -pass algorithms to optimize the model. By this procedure, we are able to obtain the so-called transition and observation matrices to compare with known languages concerning the frequency of consonant andvowel sounds. From this analysis, we conclude that transitions occur between the two states with similar frequencies to other languages. Moreover, the identification of the vowel and consonant sounds matches some previous tentative bottom-up approaches to decode the manuscript.

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Stewart, Philip, Oleg V. Aslanidi, Denis Noble, Penelope J. Noble, Mark R. Boyett, and Henggui Zhang. "Mathematical models of the electrical action potential of Purkinje fibre cells." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 367, no. 1896 (June 13, 2009): 2225–55. http://dx.doi.org/10.1098/rsta.2008.0283.

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Early development of ionic models for cardiac myocytes, from the pioneering modification of the Hodgkin–Huxley giant squid axon model by Noble to the iconic DiFrancesco–Noble model integrating voltage-gated ionic currents, ion pumps and exchangers, Ca 2+ sequestration and Ca 2+ -induced Ca 2+ release, provided a general description for a mammalian Purkinje fibre (PF) and the framework for modern cardiac models. In the past two decades, development has focused on tissue-specific models with an emphasis on the sino-atrial (SA) node, atria and ventricles, while the PFs have largely been neglected. However, achieving the ultimate goal of creating a virtual human heart will require detailed models of all distinctive regions of the cardiac conduction system, including the PFs, which play an important role in conducting cardiac excitation and ensuring the synchronized timing and sequencing of ventricular contraction. In this paper, we present details of our newly developed model for the human PF cell including validation against experimental data. Ionic mechanisms underlying the heterogeneity between the PF and ventricular action potentials in humans and other species are analysed. The newly developed PF cell model adds a new member to the family of human cardiac cell models developed previously for the SA node, atrial and ventricular cells, which can be incorporated into an anatomical model of the human heart with details of its electrophysiological heterogeneity and anatomical complexity.

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Kohl, Peter, Peter Hunter, and Denis Noble. "Stretch-induced changes in heart rate and rhythm: clinical observations, experiments and mathematical models." Progress in Biophysics and Molecular Biology 71, no. 1 (January 1999): 91–138. http://dx.doi.org/10.1016/s0079-6107(98)00038-8.

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Rupp, H., and K. Dietz. "Mathematical models of myosin heterodimer formation in the rat heart during thyroid hormone alterations." Circulation Research 68, no. 1 (January 1991): 27–37. http://dx.doi.org/10.1161/01.res.68.1.27.

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Sacks, E., and L. E. Widman. "Nonlinear heart model predicts range of heart rates for 2:1 swinging in pericardial effusion." American Journal of Physiology-Heart and Circulatory Physiology 264, no. 5 (May 1, 1993): H1716—H1722. http://dx.doi.org/10.1152/ajpheart.1993.264.5.h1716.

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We analyze two mathematical models of Rigney and Goldberger (14) of heart swinging in large pericardial effusions. Both models represent the torques due to the outflow of blood from the heart. The first assumes that the duration of systole does not vary with heart rate (in beats/min), whereas the second assumes that it varies linearly with heart rate. We examine the motion of the heart for heart rates between 50 and 200 and for a range of initial positions and velocities. Both models predict that the heart swings once every other beat (2:1 swinging, giving rise to electrical alternans) in a discrete range of heart rates and swings once per beat otherwise; both models explain the appearance and disappearance of 2:1 swinging mathematically. The first model predicts a rate range from 105 to 116 for the occurrence of 2:1 swinging. The second model predicts the same qualitative behavior but with 2:1 swinging occurring at heart rates between 88 and 119, which agrees well with published clinical data showing 2:1 swinging at heart rates between 90 and 144. We describe an analysis program for ordinary differential equations that analyzed the models quickly and automatically.

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Kharun, Makhmud, Sergey Klyuev, Dmitry Koroteev, Paschal C. Chiadighikaobi, Roman Fediuk, Andrej Olisov, Nikolai Vatin, and Nataliya Alfimova. "Heat Treatment of Basalt Fiber Reinforced Expanded Clay Concrete with Increased Strength for Cast-In-Situ Construction." Fibers 8, no. 11 (November 2, 2020): 67. http://dx.doi.org/10.3390/fib8110067.

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Expanded clay concrete (ECC) is a promising structural material for buildings due to its light weight and heat- and sound-insulating properties. Adding basalt fibers (BFs) in ECC reduces its brittleness and enhances its mechanical properties. The heat treatment (HT) of BF-reinforced ECC can significantly accelerate the strength growth during cast-in-situ construction, which allows the reduction of the turnover of the formwork and the construction period, as well as leading to lower construction costs. This paper presents an HT technology for load-bearing structures, containing a BF-reinforced ECC mix and using infrared rays for cast-in-situ construction. The issue of the strength growth of BF-reinforced ECC during HT has been studied. Microsilica and fly ash were added to the ECC mix to obtain a compressive strength of more than 20 MPa. Four different mixes of ECC with chopped BFs in the ratios of 1:0, 1:0.0045, 1:0.009 and 1:0.012 by weight of cement were studied. Test specimens were heated by infrared rays for 7, 9, 11, 13, 16 and 24 h. Then, the heat-treated specimens were tested for compressive strength after 0.5, 4, 12 and 24 h cooling periods. The analysis and evaluation of the experimental data were carried out based on probability theory and mathematical statistics. Mathematical models are proposed for forecasting the strength growth of BF-reinforced ECC during cast-in-situ construction.

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Krasheninnikov, Viktor R., Iulia E. Kuvaiskova, Olga E. Malenova, and Aleksei Iu Subbotin. "THE HYPOTHESIS TEST OF COVARIATION FUNCTIONS OF QUASIPERIODIC PROCESSES SYSTEMS REPRESENTED BY CYLINDRICAL IMAGE MODELS." Автоматизация Процессов Управления 62, no. 4 (2020): 93–102. http://dx.doi.org/10.35752/1991-2927-2020-4-62-93-102.

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The generally accepted mathematical model of a wide variety of natural, technical, economic and other objects that exist in time are random processes, for example sea waves, wind, vibrations of engines and hydraulic units, biorhythms, etc. An object is usually described by several parameters, that is a system of random processes or time series. The processes occurring in many objects have a form close to periodic – quasiperiodic, namely there is a periodicity with an element of unpredictability, for example speech sounds, vibrations of various technical objects, daily temperature fluctuations, etc. In order to formulate the problems of processing the quasiperiodic process systems, their mathematical models are required. For this purpose, authors propose models in which the processes are presented in the form of spiral sweeps on autoregressive cylindrical images. A suitable set of parameter values for these models provides a given degree of quasiperiodicity of individual processes and the given covariance relationships between the processes of the system. A criterion is proposed for testing the hypotheses about the correspondence of the observed system of time series to their model of the described type. The authors provide the examples of the application of this criterion with an analysis of the sensitivity to deviations of the model parameters from the expected ones are given.

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DE OLIVEIRA, H. P., I. DAMIÃO SOARES, and E. V. TONINI. "NONLINEAR RESONANCE IN THE VERY EARLY UNIVERSE: SOUNDS OF THE PRIMORDIAL MUSIC." International Journal of Modern Physics D 17, no. 13n14 (December 2008): 2459–65. http://dx.doi.org/10.1142/s0218271808013959.

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Nonlinear resonance is ubiquitous in nature. Resonance is relevant to understanding phenomena in quite distinct areas such as music, cellular structure, and astrophysics, and in the very early universe. In order to see the crucial role played by resonance in cosmology, we assume that closed FRW universes with a massive inflaton field evolve according to the field equations that contain additional terms arising from high energy corrections to cosmological scenarios. As a consequence, nonsingular bounces in the early evolution of the universe are produced. We have shown that in narrow windows of the parameter space of the models, nonlinear resonance phenomena of KAM tori occur and lead to the destruction of those tori that trap the inflaton, resulting in the escape of the universe into inflation. These resonance windows are labeled by an integer n ≥ 2; n is related to the ratio of the frequencies in the scale factor/scalar field degrees of freedom.

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Shlykov, Vladyslav, Vitalii Kotovskyi, Nikolaj Višniakov, and Andžela Šešok. "Model for Elimination of Mixed Noise from MRI Heart Images." Applied Sciences 10, no. 14 (July 9, 2020): 4747. http://dx.doi.org/10.3390/app10144747.

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A method for the preliminary processing of MRI images of the heart that allows for the elimination of fluctuation and impulse noise from useful signals is proposed. These types of noise are due to the regular geometric structure of the photoelectric elements of the MRI scanner matrix and the structure of the signal transmission channel. The aim of this work is to develop a comprehensive mathematical model for eliminating noise in the signal of an MRI scanner. In this work, mathematical models of linear and median filtering of impulse noise, fluctuation, and geometric noise are implemented. The mathematical models consist of the combined use of linear and median filters for recording MRI images of the heart. In the experiments, real MRI images of the heart from six patients with different diseases were used after noise was added to them. We were able to eliminate the impulse noise, geometric noise, and fluctuation noise in the MRI images by applying our filtering techniques. The filtering technique not only removed the noise, but also increased the contrast of the cancerous volumetric heterogeneous formations in the heart region.

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Namani, Ravi, Yoram Lanir, Lik Chuan Lee, and Ghassan S. Kassab. "Overview of mathematical modeling of myocardial blood flow regulation." American Journal of Physiology-Heart and Circulatory Physiology 318, no. 4 (April 1, 2020): H966—H975. http://dx.doi.org/10.1152/ajpheart.00563.2019.

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The oxygen consumption by the heart and its extraction from the coronary arterial blood are the highest among all organs. Any increase in oxygen demand due to a change in heart metabolic activity requires an increase in coronary blood flow. This functional requirement of adjustment of coronary blood flow is mediated by coronary flow regulation to meet the oxygen demand without any discomfort, even under strenuous exercise conditions. The goal of this article is to provide an overview of the theoretical and computational models of coronary flow regulation and to reveal insights into the functioning of a complex physiological system that affects the perfusion requirements of the myocardium. Models for three major control mechanisms of myogenic, flow, and metabolic control are presented. These explain how the flow regulation mechanisms operating over multiple spatial scales from the precapillaries to the large coronary arteries yield the myocardial perfusion characteristics of flow reserve, autoregulation, flow dispersion, and self-similarity. The review not only introduces concepts of coronary blood flow regulation but also presents state-of-the-art advances and their potential to impact the assessment of coronary microvascular dysfunction (CMD), cardiac-coronary coupling in metabolic diseases, and therapies for angina and heart failure. Experimentalists and modelers not trained in these models will have exposure through this review such that the nonintuitive and highly nonlinear behavior of coronary physiology can be understood from a different perspective. This survey highlights knowledge gaps, key challenges, future research directions, and novel paradigms in the modeling of coronary flow regulation.

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de Bekker, Pieter H. A. M. J., and Jan J. van den Berg. "Modelling and Construction of a Deep Well Aqueous Phase Oxidation Process." Water Science and Technology 27, no. 5-6 (March 1, 1993): 457–68. http://dx.doi.org/10.2166/wst.1993.0523.

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Aqueous phase oxidation is the process in which organic material is oxidized in the liquid phase with gaseous oxygen under elevated temperature and pressure. The VerTech-process uses a vertical subsurface oxidation vessel consisting of two concentric tubes with a length of approximately 1 200 metres. The advantages of which are: an ideal plug flow regime for a high performance, an efficient heat exchange along the reactor length and a less heavy construction compared to surface techniques. The production of residues is minimal and environmentally sound: off-gas consists mostly of carbon dioxide, solid residue is non teachable and the liquid effluent can be purified easily to a high extent. For the design of the oxidation vessel the use of mathematical models is essential: reaction kinetics, hydrodynamics and heat transfer have been brought in models in such a way that up- and downscaling is possible. On the other hand process conditions may be controlled by the model, once it has been approved. The original model has been tested at the demonstration plant at Longmont, Colorado, USA in 1985. A further development will be tested at the first commercial scale plant at Apeldoorn, the Netherlands. This plant will come into full service as of January 1993.

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Narváez, Pedro, Steven Gutierrez, and Winston S. Percybrooks. "Automatic Segmentation and Classification of Heart Sounds Using Modified Empirical Wavelet Transform and Power Features." Applied Sciences 10, no. 14 (July 13, 2020): 4791. http://dx.doi.org/10.3390/app10144791.

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A system for the automatic classification of cardiac sounds can be of great help for doctors in the diagnosis of cardiac diseases. Generally speaking, the main stages of such systems are (i) the pre-processing of the heart sound signal, (ii) the segmentation of the cardiac cycles, (iii) feature extraction and (iv) classification. In this paper, we propose methods for each of these stages. The modified empirical wavelet transform (EWT) and the normalized Shannon average energy are used in pre-processing and automatic segmentation to identify the systolic and diastolic intervals in a heart sound recording; then, six power characteristics are extracted (three for the systole and three for the diastole)—the motivation behind using power features is to achieve a low computational cost to facilitate eventual real-time implementations. Finally, different models of machine learning (support vector machine (SVM), k-nearest neighbor (KNN), random forest and multilayer perceptron) are used to determine the classifier with the best performance. The automatic segmentation method was tested with the heart sounds from the Pascal Challenge database. The results indicated an error (computed as the sum of the differences between manual segmentation labels from the database and the segmentation labels obtained by the proposed algorithm) of 843,440.8 for dataset A and 17,074.1 for dataset B, which are better values than those reported with the state-of-the-art methods. For automatic classification, 805 sample recordings from different databases were used. The best accuracy result was 99.26% using the KNN classifier, with a specificity of 100% and a sensitivity of 98.57%. These results compare favorably with similar works using the state-of-the-art methods.

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Reyes, Alex D. "Mathematical framework for place coding in the auditory system." PLOS Computational Biology 17, no. 8 (August 2, 2021): e1009251. http://dx.doi.org/10.1371/journal.pcbi.1009251.

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In the auditory system, tonotopy is postulated to be the substrate for a place code, where sound frequency is encoded by the location of the neurons that fire during the stimulus. Though conceptually simple, the computations that allow for the representation of intensity and complex sounds are poorly understood. Here, a mathematical framework is developed in order to define clearly the conditions that support a place code. To accommodate both frequency and intensity information, the neural network is described as a space with elements that represent individual neurons and clusters of neurons. A mapping is then constructed from acoustic space to neural space so that frequency and intensity are encoded, respectively, by the location and size of the clusters. Algebraic operations -addition and multiplication- are derived to elucidate the rules for representing, assembling, and modulating multi-frequency sound in networks. The resulting outcomes of these operations are consistent with network simulations as well as with electrophysiological and psychophysical data. The analyses show how both frequency and intensity can be encoded with a purely place code, without the need for rate or temporal coding schemes. The algebraic operations are used to describe loudness summation and suggest a mechanism for the critical band. The mathematical approach complements experimental and computational approaches and provides a foundation for interpreting data and constructing models.

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Torzynska, Katarzyna, Alina Janowska-Kulinska, Alina Markiewicz-Grochowalska, Olga Jerzykowska, Anna Sowinska, Lucyna Kramer, Jerzy Moczko, and Tomasz Siminiak. "Time analysis of heart rate variability in patients with stable angina and 1-vessel coronary heart disease. Novel mathematical models." Journal of Electrocardiology 40, no. 4 (July 2007): S40. http://dx.doi.org/10.1016/j.jelectrocard.2007.03.123.

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Helmreich, Stefan. "Gravity’s Reverb: Listening to Space-Time, or Articulating the Sounds of Gravitational-Wave Detection." Cultural Anthropology 31, no. 4 (October 24, 2016): 464–92. http://dx.doi.org/10.14506/ca31.4.02.

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In February 2016, U.S.-based astronomers announced that they had detected gravitational waves, vibrations in the substance of space-time. When they made the detection public, they translated the signal into sound, a “chirp,” a sound wave swooping up in frequency, indexing, scientists said, the collision of two black holes 1.3 billion years ago. Drawing on interviews with gravitational-wave scientists at MIT and interpreting popular representations of this cosmic audio, I ask after these scientists’ acoustemology—that is, what the anthropologist of sound Steven Feld would call their “sonic way of knowing and being.” Some scientists suggest that interpreting gravitational-wave sounds requires them to develop a “vocabulary,” a trained judgment about how to listen to the impress of interstellar vibration on the medium of the detector. Gravitational-wave detection sounds, I argue, are thus articulations of theories with models and of models with instrumental captures of the cosmically nonhuman. Such articulations, based on mathematical and technological formalisms—Einstein’s equations, interferometric observatories, and sound files—operate alongside less fully disciplined collections of acoustic, auditory, and even musical metaphors, which I call informalisms. Those informalisms then bounce back on the original articulations, leading to rhetorical reverb, in which articulations—amplified through analogies, similes, and metaphors—become difficult to fully isolate from the rhetorical reflections they generate. Filtering analysis through a number of accompanying sound files, this article contributes to the anthropology of listening, positing that scientific audition often operates by listening through technologies that have been tuned to render theories and their accompanying formalisms both materially explicit and interpretively resonant.

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Cherry, Elizabeth M., and Flavio H. Fenton. "A tale of two dogs: analyzing two models of canine ventricular electrophysiology." American Journal of Physiology-Heart and Circulatory Physiology 292, no. 1 (January 2007): H43—H55. http://dx.doi.org/10.1152/ajpheart.00955.2006.

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The extensive development of detailed mathematical models of cardiac myocyte electrophysiology in recent years has led to a proliferation of models, including many that model the same animal species and specific region of the heart and thus would be expected to have similar properties. In this paper we review and compare two recently developed mathematical models of the electrophysiology of canine ventricular myocytes. To clarify their similarities and differences, we also present studies using them in a range of preparations from single cells to two-dimensional tissue. The models are compared with each other and with new and previously published experimental results in terms of a number of their properties, including action potential morphologies; transmembrane currents during normal heart rates and during alternans; alternans onsets, magnitudes, and cessations; and reentry dynamics of spiral waves. Action potential applets and spiral wave movies for the two canine ventricular models are available online as supplemental material. We find a number of differences between the models, including their rate dependence, alternans dynamics, and reentry stability, and a number of differences compared with experiments. Differences between models of the same species and region of the heart are not unique to these canine models. Similar differences can be found in the behavior of two models of human ventricular myocytes and of human atrial myocytes. We provide several possible explanations for the differences observed in models of the same species and region of the heart and discuss the implications for the applicability of models in addressing questions of mechanism in cardiac electrophysiology.

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Garner, D. M., M. Alves, B. P. Da Silva, L. V. De Alcantara Sousa, and V. E. Valenti. "Chaotic global analysis of heart rate variability following power spectral adjustments during exposure to traffic noise in healthy adult women." Russian Journal of Cardiology 25, no. 6 (July 11, 2020): 3739. http://dx.doi.org/10.15829/1560-4071-2020-3739.

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Aim. Previous studies have described the substantial impact of different types of noise on the linear behaviour of heart rate variability (HRV). Yet, there are limited studies about the complexity or nonlinear dynamics of HRV during exposure to traffic noise. Here, we evaluated the complexity of HRV during traffic noise exposure via six power spectra and, when adjusted by the parameters of the Multi-Taper Method (MTM).Material and methods. We analysed 31 healthy female students between 18 and 30 years old. Subjects remained at rest, seated under spontaneous breathing for 20 minutes with an earphone turned off and then the volunteers were exposed to traffic noise through an earphone for a period of 20 minutes. The traffic noise was recorded from a busy urban street and the sound involved car, bus, trucks engineers and horn sounds (71-104 dB).Results. The results stipulate that CFP3 and CFP6 are the best metrics to distinguish the two groups. The most appropriate power spectra were, Welch and MTM. Increasing the DPSS parameter of MTM increased the performance of both CFP3 and CFP6 as mathematical markers. Adaptive was the preferred type for Thomson’s nonlinear combination method.Conclusion. CFP3 with the adaptive option for MTM, and increased DPSS is designated as the best mathematical marker on the basis of five statistical tests.

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Soloveva, I. A. Soloveva, E. A. Sobko Sobko, I. V. Demko Demko, A. Yu Kraposhina Kraposhina, N. V. Gordeeva Gordeeva, N. S. Eydemiller Eydemiller, and A. Yu Burakov Burakov. "Early Diagnostics and Mathematical Prediction Models Remodeling of the Heart at Patients With Atopic Bronchial Asthma." Kardiologiia 4_2016 (April 18, 2016): 64–65. http://dx.doi.org/10.18565/cardio.2016.4.64-65.

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Carley, D. W., and D. C. Shannon. "A minimal mathematical model of human periodic breathing." Journal of Applied Physiology 65, no. 3 (September 1, 1988): 1400–1409. http://dx.doi.org/10.1152/jappl.1988.65.3.1400.

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Numerous mathematical models of periodic breathing (PB) currently exist. These models suggest mechanisms that may underlie many known causes of PB. However, each model that has been shown to simulate PB under reasonable conditions contains greater than 15 physiological parameters. Because some parameters exhibit a wide range of values in a population, such simulations cannot test a model's ability to account for the breathing patterns of individuals. Furthermore it is impractical to perform a direct experimental validation study that would require the estimation of each of 15 or more parameters for each subject. A minimal model of PB is presented that is suitable for direct validation. Analytic expressions are given that define the conditions for PB in terms of the following: 1) CO2 sensitivity, 2) Cardiac output, 3) Mixed venous CO2, 4) Circulation time, and 5) Mean lung volume for CO2. This model is shown to be consistent with previous models and experimental data regarding the degree of hypoxia or congestive heart failure required to produce PB. A quantitative measure of relative stability is defined as a metric of comparison to the human studies described in the accompanying paper (J. Appl. Physiol. 65: 1389-1399, 1988).

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Gerach, Tobias, Steffen Schuler, Jonathan Fröhlich, Laura Lindner, Ekaterina Kovacheva, Robin Moss, Eike Moritz Wülfers, Gunnar Seemann, Christian Wieners, and Axel Loewe. "Electro-Mechanical Whole-Heart Digital Twins: A Fully Coupled Multi-Physics Approach." Mathematics 9, no. 11 (May 29, 2021): 1247. http://dx.doi.org/10.3390/math9111247.

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Mathematical models of the human heart are evolving to become a cornerstone of precision medicine and support clinical decision making by providing a powerful tool to understand the mechanisms underlying pathophysiological conditions. In this study, we present a detailed mathematical description of a fully coupled multi-scale model of the human heart, including electrophysiology, mechanics, and a closed-loop model of circulation. State-of-the-art models based on human physiology are used to describe membrane kinetics, excitation-contraction coupling and active tension generation in the atria and the ventricles. Furthermore, we highlight ways to adapt this framework to patient specific measurements to build digital twins. The validity of the model is demonstrated through simulations on a personalized whole heart geometry based on magnetic resonance imaging data of a healthy volunteer. Additionally, the fully coupled model was employed to evaluate the effects of a typical atrial ablation scar on the cardiovascular system. With this work, we provide an adaptable multi-scale model that allows a comprehensive personalization from ion channels to the organ level enabling digital twin modeling.

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Pooja, S. B., and Siva R. V. Balan. "An Investigation Study on Clustering and Classification Techniques for Weather Forecasting." Journal of Computational and Theoretical Nanoscience 16, no. 2 (February 1, 2019): 417–21. http://dx.doi.org/10.1166/jctn.2019.7742.

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Weather forecasting is the prediction of atmosphere state for particular location by using principles of physics provided by many statistical and empirical techniques. Weather forecasts are frequently made by collecting quantitative data about current state of atmosphere through scientific understanding of atmospheric processes to illustrate how atmosphere changes in future. Current weather conditions are collected through the observation from the ground, ships, aircraft, radio sounds and satellites. The information is transmitted to the meteorological centers where the data are collected and examined for prediction. There are diverse techniques included in weather forecasting, from relatively simple observation of sky to complex computerized mathematical models. But, the existing techniques failed to predict the weather with higher accuracy and lesser time. In order to improve the prediction performance, the machine learning and ensemble techniques are introduced.

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Denisov, A. M., and I. A. Pavel’chak. "A numerical method for determining a localized initial excitation for some mathematical models of the heart excitation." Mathematical Models and Computer Simulations 5, no. 1 (January 2013): 75–80. http://dx.doi.org/10.1134/s2070048213010043.

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Journal articles on the topic 'Heart Sounds Mathematical models'

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