Mathematical birth of Early Afterdepolarizations in a cardiomyocyte model

Early Afterdepolarizations (EADs) are abnormal behaviors that can lead to cardiac failure and even cardiac death. In this paper we investigate the occurrence and development of these phenomena in a reduced Luo-Rudy cardiac model. Through a comprehensive dynamical analysis, we map out the distinct patterns observed in the parametric plane, differentiating between normal beats without EADs and pathological beats with EADs. By examining the bifurcation structure of the model, we elucidate the dynamical elements associated with these patterns and their transitions. Using a fast-slow analysis, we explore the emergence and evolution of EADs in the model. Notably, our approach combines the two commonly used fast-slow approaches (1-slow-2-fast and 2-slow-1-fast), and we show how both approaches together provide a more complete understanding of this phenomenon.

Evaluación de la dinámica cardiaca con la aplicación de metodologías basadas en entropía proporcional y la ley Zipf-Mandelbrot

Introducción

Las metodologías fisicomatemáticas son de utilidad para el diagnóstico de la dinámica cardiaca.

Objetivo

Comparar la aplicación de dos métodos matemáticos de evaluación de la dinámica cardiaca. Una basada en proporciones de la entropía y otra en la ley de Zipf-Mandelbrot.

Método

Se tomaron 10 registros Holter, cinco de pacientes con enfermedad aguda y cinco normales. Se construyó un atractor numérico, se evaluó la probabilidad, entropía y proporciones de entropía. Para aplicar la segunda metodología se agruparon los valores de frecuencia cardiaca en rangos de 15 latidos/minuto y se aplicó la ley de Zipf-Mandelbrot para obtener la dimensión fractal estadística. Finalmente se comparó la evaluación matemática obtenida por ambas metodologías.

Resultados

La metodología basada en las proporciones de la entropía diferenció normalidad, enfermedad y estados intermedios. La segunda metodología diferenció normalıdad de enfermedad aguda mediante el grado de complejidad.

Conclusión

Ambas metodologías establecen evaluaciones de ayuda diagnóstica de la dinámica cardiaca de forma objetiva y reproducible. La entropía proporcional permite cuantificar normalidad, enfermedad y evolución entre estados con carácter predictivo y mayor precisión.

Introduction

Physical-mathematical methodologies have been useful for the diagnosis of cardiac dynamics.

Objective

To compare the application of two mathematical methodologies for cardiac dynamics evaluation, one of them based on entropy proportions and the other based on of Zipf-Mandelbrot law.

Method

10 Holter, 5 acute disease dynamics and 5 normal records were taken. A numerical attractor was constructed; probability, entropy and entropy proportions were evaluated. To apply the second methodology, heart rate values were grouped in 15-beat/min ranges, and Zipf-Mandelbrot’s law was applied in order for the statistical fractal dimension to be obtained. Finally, the mathematical evaluation obtained by both methodologies was compared.

Results

The methodology based on entropy proportions differentiated normality, disease and intermediate states. The second methodology differentiated normality from acute disease through the degree of complexity.

Conclusion

Both methodologies establish diagnostically helpful evaluations of cardiac dynamics in an objective and reproducible way. Proportional entropy allows normality, disease and evolution between states to be quantified in a predictive manner and with higher accuracy.

Extracting cardiac dynamics within ECG signal for human identification and cardiovascular diseases classification

Cardiac characteristics underlying the time/frequency domain features are limited and not comprehensive enough to reflect the temporal/dynamical nature of ECG patterns. This paper proposes a dynamical ECG recognition framework for human identification and cardiovascular diseases classification via a dynamical neural learning mechanism. The proposed method consists of two phases: a training phase and a test phase. In the training phase, cardiac dynamics within ECG signals is extracted (approximated) accurately by using radial basis function (RBF) neural networks through deterministic learning mechanism. The obtained cardiac system dynamics is represented and stored in constant RBF networks. An ECG signature is then derived from the extracted cardiac dynamics along the periodic ECG state trajectories. A bank of estimators is constructed using the extracted cardiac dynamics to represent the trained gait patterns. In the test phase, recognition errors are generated and taken as the similarity measure by comparing the cardiac dynamics of the trained ECG patterns and the dynamics of the test ECG pattern. Rapid recognition of a test ECG pattern begins with measuring the state of test pattern, and automatically proceeds with the evolution of the recognition error system. According to the smallest error principle, the test ECG pattern can be rapidly recognized. This kind of cardiac dynamics information represents the beat-to-beat temporal change of ECG modifications and the temporal/dynamical nature of ECG patterns. Therefore, the amount of discriminability provided by the cardiac dynamics is larger than the original signals. This paper further discusses the extension of the proposed method for cardiovascular diseases classification. The constructed recognition system can distinguish and assign dynamical ECG patterns to predefined classes according to the similarity of cardiac dynamics. Experiments are carried out on the FuWai and PTB ECG databases to demonstrate the effectiveness of the proposed method.

A note on stress-driven anisotropic diffusion and its role in active deformable media

We introduce a new model to describe diffusion processes within active deformable media. Our general theoretical framework is based on physical and mathematical considerations, and it suggests to employ diffusion tensors directly influenced by the coupling with mechanical stress. The proposed generalised reaction-diffusion-mechanics model reveals that initially isotropic and homogeneous diffusion tensors turn into inhomogeneous and anisotropic quantities due to the intrinsic structure of the nonlinear coupling. We study the physical properties leading to these effects, and investigate mathematical conditions for its occurrence. Together, the mathematical model and the numerical results obtained using a mixed-primal finite element method, clearly support relevant consequences of stress-driven diffusion into anisotropy patterns, drifting, and conduction velocity of the resulting excitation waves. Our findings also indicate the applicability of this novel approach in the description of mechano-electric feedback in actively deforming bio-materials such as the cardiac tissue.

Optogenetic Light Crafting Tools for the Control of Cardiac Arrhythmias

The control of spatiotemporal dynamics in biological systems is a fundamental problem in nonlinear sciences and has important applications in engineering and medicine. Optogenetic tools combined with advanced optical technologies provide unique opportunities to develop and validate novel approaches to control spatiotemporal complexity in neuronal and cardiac systems. Understanding of the mechanisms and instabilities underlying the onset, perpetuation, and control of cardiac arrhythmias will enable the development and translation of novel therapeutic approaches. Here we describe in detail the preparation and optical mapping of transgenic channelrhodopsin-2 (ChR2) mouse hearts, cardiac cell cultures, and the optical setup for photostimulation using digital light processing.

Mechanistic insights into hypothermic ventricular fibrillation: the role of temperature and tissue size

AIMS

Hypothermia is well known to be pro-arrhythmic, yet it has beneficial effects as a resuscitation therapy and valuable during intracardiac surgeries. Therefore, we aim to study the mechanisms that induce fibrillation during hypothermia. A better understanding of the complex spatiotemporal dynamics of heart tissue as a function of temperature will be useful in managing the benefits and risks of hypothermia.

METHODS AND RESULTS

We perform two-dimensional numerical simulations by using a minimal model of cardiac action potential propagation fine-tuned on experimental measurements. The model includes thermal factors acting on the ionic currents and the gating variables to correctly reproduce experimentally recorded restitution curves at different temperatures. Simulations are implemented using WebGL, which allows long simulations to be performed as they run close to real time. We describe (i) why fibrillation is easier to induce at low temperatures, (ii) that there is a minimum size required for fibrillation that depends on temperature, (iii) why the frequency of fibrillation decreases with decreasing temperature, and (iv) that regional cooling may be an anti-arrhythmic therapy for small tissue sizes however it may be pro-arrhythmic for large tissue sizes.

CONCLUSION

Using a mathematical cardiac cell model, we are able to reproduce experimental observations, quantitative experimental results, and discuss possible mechanisms and implications of electrophysiological changes during hypothermia.

Cardiac electrophysiological dynamics from the cellular level to the organ level

Cardiac alternans describes contraction of the ventricles in a strong-weak-strong-weak sequence at a constant pacing frequency. Clinically, alternans manifests as alternation of the T-wave on the ECG and predisposes individuals to arrhythmia and sudden cardiac death. In this review, we focus on the fundamental dynamical mechanisms of alternans and show how alternans at the cellular level underlies alternans in the tissue and on the ECG. A clear picture of dynamical mechanisms underlying alternans is important to allow development of effective anti-arrhythmic strategies.

Nuclear Medicine Physics: The Basics. 7th ed

Nuclear Medicine Physics: The Basics. 7th ed. Ramesh Chandra, Lippincott Williams and Wilkins, a Wolters Kluwer Business. Philadelphia, 2012. Softbound, 224 pp. Price: $69.99. ISBN: 9781451109412.

WE-G-218-01: Management of RT Patients with Implanted Cardiac Devices: Updated Recommendations?

It has been long time since AAPM published TG-34 on cardiac pacemakers of older technology, which has been the standard document for clinical use, even today, for pacemakers (ICPs) and for defibrillators (ICDs), alike. Management of RT patients with recent technology cardiac devices has been widely published in literature without the provision of a new comprehensive and concise set of recommendations. The various effects of interaction of non-ionizing and ionizing radiations with those devices are crucial to be studied and accounted for during RT treatment deliveries. Thus, AAPM has formed the new TG-203 to work on this issue and provide recommendations to the clinical user for management of patients with cardiac devices when receiving RT. It has been numerous postings that we see in medical physics list server groups inquiring advices on dealing with these devices during patient imaging and radiation treatments. As treatment delivery technologies (IMRT, SBRT, dose escalations, proton beams, etc) and ICP/ICD technology advance, the need to address the management of patients with such devices receiving radiation treatment becomes increasingly important. ICDs offer the same functionality as ICPs, but they are also able to deliver a high-voltage shock to the heart, if needed. Finally, major discrepancies exist among manufacturer recommendations and wide variations exist among radiation therapy facilities regarding patient management precautions.

LEARNING OBJECTIVES

1. Provide a review on sources of potential malfunctions of modern ICPs and ICDs, including malfunction mechanisms from high-LET radiations and transient effects attributed to medical imaging procedures for radiotherapy. 2. Provide a review on management of radiotherapy patients with cardiac implanted devices. 3. Utilize recently available data and computation methods of out-of-field/peripheral dose by scattered photons and secondary neutrons in order to assess cumulative doses on the ICPs and ICDs, during current treatment deliveries (IMRT, SBRT, proton beam therapy, etc). Risk of failure associated with these doses will be discussed. 4. Provide recommendations for management of radiotherapy patients with implanted cardiac devices including the initial patient evaluation stage, dosimetric evaluation to the ICP/ICD during treatment simulation, treatment planning and treatment delivery. Recommendations for the final evaluation of the integrity and functionality of the device after treatment completion will be assessed.

TU-E-211-01: Establishing Multidisciplinary Collaboration as a Medical Physicist

Many medical physicists are scientists at heart and their career fulfillment includes a balance of clinical service and research development. Multidisciplinary collaboration is a great way for the medical physicists to advance science and technology of our fields and the fields of our collaborators. Cross-pollination among scientists of different fields has been the key for some of the most significant breakthroughs in science and medicine and produced some of the most rewarding experiences for the individuals involved. However, medical physicists face unique challenges in establishing multidisciplinary collaboration because our time and resources for research are often quite limited compared to basic scientists. Yet we medical physicists are uniquely positioned and have a tremendous opportunity to create/contribute to multidisciplinary research: our fields are already multidisciplinary in nature and hospital environment is problem rich. How do we establish and carry out research collaboration with scientists of other fields? How to balance research with your higher priority clinical service? How do you find the right multidisciplinary collaboration in your own environment? We will discuss the challenges, provide real exemplary solutions to the above questions, and offer advise to medical physicists who are interested in starting or improving their multidisciplinary collaboration. There are different kinds of multidisciplinary collaborations a medical physicist can create and participate at different involvement levels. Multidisciplinary collaboration is not for every medical physicist but for those who seek and devote time to it, the experience can be truly rewarding and the impact can be enormous.

LEARNING OBJECTIVES

1. Learn the types of multidisciplinary collaboration medical physicists can created/participated 2. Learn the approaches and strategies to develop collaborations with scientists and professional of other fields3. Understand the challenges and different approaches to balance clinical service and multidisciplinary research collaboration.

SU-E-I-35: Experience with Th Zero Gravity Suit

PURPOSE

To compare the effectiveness of the Zero Gravity Suit (CFI Medical Solutions) in reducing the annual dose received by one physician in the Cardiac Catheterization Lab.

METHODS

A physician with a history of receiving high annual dose equivalents was purchased a Zero Gravity Suit. Film badges (Landauer) were worn at the collar and waist and monitored monthly. Previous dose history was acquired via the Landauer Exposure Report Archive. Annual values for Deep Dose Equivalent (DDE), Eye Dose Equivalent (LDE), and Shallow Dose Equivalent (SDE) were compared for the first full year of the Zero Gravity Suit (2011) to the previous four years (2007-2010). Readings for 2009 and 2007 were corrected for improper wear of the film badges.

RESULTS

The reduction in dose equivalent for DDE ranged from 70%-87%. The reduction in dose equivalent for LDE ranged from 16%-60%. The reduction in dose equivalent for SDE ranged from 16%-60%.

CONCLUSIONS

It was determined that the Zero Gravity Suit is effective at reducing the exposure of a physician with a history of high annual dose equivalents in our facilities Cardiac Catheterization Lab. While the suit did reduce the LDE and SDE it was more effective at reducing the DDE. During 2010 the suit was acquired midyear. The dose equivalent values would likely be similar to 2011 if the suit was introduced at the beginning of the year. In 2009 the physician was pregnant and attempting a reduced workload. The physician only uses the suit if a procedure is expected to take longer than fifteen minutes. The accuracy of the study is dependent upon the physician wearing the badges consistently and correctly and the physician using the Zero Gravity Suit consistently.

SU-E-E-05: An Educational Physical Environment Concept with Close Research and Clinical Collaborations

PURPOSE

To create a physical environment where imaging medical physicists can be educated in a real-work, clinical and research setting in close collaboration with professionals such as physicians, biomédical engineers, and other medical personnel.

METHODS

A single building structure has been designed where medical physics students can be immersed in a collaborative clinical and research educational environment.

RESULTS

A Clinical Translational Research Center has been constructed on the top four floors over a new Global Vascular Institute (GVI) which is connected to the main university hospital complex and adjacent to radiation therapy facilities. The research and educational component including offices, labs, and conference rooms for the Medical Physics Program is on the top floor and dedicated research imaging suites (fluoroscopic interventional systems, CT, PET/CT, and MRI) along with complete animal facilities and additional research labs for cardiac and vascular investigators are on the two top floors. An atrium and numerous meeting spaces are in place to encourage informal communication among students and science and clinical investigators. The clinical GVI, which occupies the lower four floors, has a full upper floor containing 15 vascular imaging suites for cardiac, neuro, and peripheral vascular imaging and interventions while the floors below have short-term hotel-like patient and family rooms favoring ambulatory patients having minimally invasive procedures. Medical physics didactic education is designed to take place in modern meeting rooms; however, because of the close proximity to research labs and clinical suites, students are expected to get a unique perspective on how research is done and how it is translated into clinical practice.

CONCLUSIONS

A new physical structure has been built which enables medical physics education to be an integral part of a highly collaborative clinical translational research environment. Research funds provided by NIH grants and equipment grants from Toshiba Medical Systems Corp.