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Knowledge of how a population of cancerous cells progress through the cell cycle is vital if the population is to be treated effectively, as treatment outcome is dependent on the phase distributions of the population. Estimates on the phase distribution may be obtained experimentally however the errors present in these estimates may effect treatment efficacy and planning. If mathematical models are to be used to make accurate, quantitative predictions concerning treatments, whose efficacy is phase dependent, knowledge of the phase distribution is crucial. In this paper it is shown that two different transition rates at the - checkpoint provide a good fit to a growth curve obtained experimentally. However, the different transition functions predict a different phase distribution for the population, but both lying within the bounds of experimental error. Since treatment outcome is effected by the phase distribution of the population this difference may be critical in treatment planning. Using an age-structured population balance approach the cell cycle is modelled with particular emphasis on the - checkpoint. By considering the probability of cells transitioning at the - checkpoint, different transition functions are obtained. A suitable finite difference scheme for the numerical simulation of the model is derived and shown to be stable. The model is then fitted using the different probability transition functions to experimental data and the effects of the different probability transition functions on the model's results are discussed. [ABSTRACT FROM AUTHOR]

Sudden cardiac death is often caused by cardiac arrhythmias. Recently, special attention has been given to a certain arrhythmogenic condition, the long-QT syndrome, which occurs as a result of genetic mutations or drug toxicity. The underlying mechanisms of arrhythmias, caused by the long-QT syndrome, are not fully understood. However, arrhythmias are often connected to special excitations of cardiac cells, called early afterdepolarizations (EADs), which are depolarizations during the repolarizing phase of the action potential. So far, EADs have been studied mainly in isolated cardiac cells. However, the question on how EADs at the single-cell level can result in fibrillation at the tissue level, especially in human cell models, has not been widely studied yet. In this paper, we study wave patterns that result from single-cell EAD dynamics in a mathematical model for human ventricular cardiac tissue. We induce EADs by modeling experimental conditions which have been shown to evoke EADs at a single-cell level: by an increase of L-type Ca currents and a decrease of the delayed rectifier potassium currents. We show that, at the tissue level and depending on these parameters, three types of abnormal wave patterns emerge. We classify them into two types of spiral fibrillation and one type of oscillatory dynamics. Moreover, we find that the emergent wave patterns can be driven by calcium or sodium currents and we find phase waves in the oscillatory excitation regime. From our simulations we predict that arrhythmias caused by EADs can occur during normal wave propagation and do not require tissue heterogeneities. Experimental verification of our results is possible for experiments at the cell-culture level, where EADs can be induced by an increase of the L-type calcium conductance and by the application of I blockers, and the properties of the emergent patterns can be studied by optical mapping of the voltage and calcium. [ABSTRACT FROM AUTHOR]

In this paper we introduce a new method to expressly use live/corporeal data in quantifying differences of time series data with an underlying limit cycle attractor; and apply it using an example of gait data. Our intention is to identify gait pattern differences between diverse situations and classify them on group and individual subject levels. First we approximated the limit cycle attractors, from which three measures were calculated: δM amounts to the difference between two attractors (a measure for the differences of two movements), δD computes the difference between the two associated deviations of the state vector away from the attractor (a measure for the change in movement variation), and δF, a combination of the previous two, is an index of the change. As an application we quantified these measures for walking on a treadmill under three different conditions: normal walking, dual task walking, and walking with additional weights at the ankle. The new method was able to successfully differentiate between the three walking conditions. Day to day repeatability, studied with repeated trials approximately one week apart, indicated excellent reliability for δM (ICCave > 0.73 with no differences across days; p > 0.05) and good reliability for δD (ICCave  =  0.414 to 0.610 with no differences across days; p > 0.05). Based on the ability to detect differences in varying gait conditions and the good repeatability of the measures across days, the new method is recommended as an alternative to expensive and time consuming techniques of gait classification assessment. In particular, the new method is an easy to use diagnostic tool to quantify clinical changes in neurological patients. [ABSTRACT FROM AUTHOR]

We solve the local and global structural identifiability problems for viscoelastic mechanical models represented by networks of springs and dashpots. We propose a very simple characterization of both local and global structural identifiability based on identifiability tables, with the purpose of providing a guideline for constructing arbitrarily complex, identifiable spring-dashpot networks. We illustrate how to use our results in a number of examples and point to some applications in cardiovascular modeling. [ABSTRACT FROM AUTHOR]

The photoplethysmogram (PPG) obtained from pulse oximetry measures local variations of blood volume in tissues, reflecting the peripheral pulse modulated by heart activity, respiration and other physiological effects. We propose an algorithm based on the correntropy spectral density (CSD) as a novel way to estimate respiratory rate (RR) and heart rate (HR) from the PPG. Time-varying CSD, a technique particularly well-suited for modulated signal patterns, is applied to the PPG. The respiratory and cardiac frequency peaks detected at extended respiratory (8 to 60 breaths/min) and cardiac (30 to 180 beats/min) frequency bands provide RR and HR estimations. The CSD-based algorithm was tested against the Capnobase benchmark dataset, a dataset from 42 subjects containing PPG and capnometric signals and expert labeled reference RR and HR. The RR and HR estimation accuracy was assessed using the unnormalized root mean square (RMS) error. We investigated two window sizes (60 and 120 s) on the Capnobase calibration dataset to explore the time resolution of the CSD-based algorithm. A longer window decreases the RR error, for 120-s windows, the median RMS error (quartiles) obtained for RR was 0.95 (0.27, 6.20) breaths/min and for HR was 0.76 (0.34, 1.45) beats/min. Our experiments show that in addition to a high degree of accuracy and robustness, the CSD facilitates simultaneous and efficient estimation of RR and HR. Providing RR every minute, expands the functionality of pulse oximeters and provides additional diagnostic power to this non-invasive monitoring tool. [ABSTRACT FROM AUTHOR]

We describe the construction of a fully tractable mathematical model for intracellular pH. This work is based on coupling the kinetic equations depicting the molecular mechanisms for pumps, transporters and chemical reactions, which determine this parameter in eukaryotic cells. Thus, our system also calculates the membrane potential and the cytosolic ionic composition. Such a model required the development of a novel algebraic method that couples differential equations for slow relaxation processes to steady-state equations for fast chemical reactions. Compared to classical heuristic approaches based on fitted curves and ad hoc constants, this yields significant improvements. This model is mathematically self-consistent and allows for the first time to establish analytical solutions for steady-state pH and a reduced differential equation for pH regulation. Because of its modular structure, it can integrate any additional mechanism that will directly or indirectly affect pH. In addition, it provides mathematical clarifications for widely observed biological phenomena such as overshooting in regulatory loops. Finally, instead of including a limited set of experimental results to fit our model, we show examples of numerical calculations that are extremely consistent with the wide body of intracellular pH experimental measurements gathered by different groups in many different cellular systems. [ABSTRACT FROM AUTHOR]

Numerical integration of mathematical models of heart cell electrophysiology provides an important computational tool for studying cardiac arrhythmias, but the abundance of available models complicates selecting an appropriate model. We study the behavior of two recently published models of human ventricular action potentials, the Grandi-Pasqualini-Bers (GPB) and the O'Hara-Virág-Varró-Rudy (OVVR) models, and compare the results with four previously published models and with available experimental and clinical data. We find the shapes and durations of action potentials and calcium transients differ between the GPB and OVVR models, as do the magnitudes and rate-dependent properties of transmembrane currents and the calcium transient. Differences also occur in the steady-state and S1–S2 action potential duration and conduction velocity restitution curves, including a maximum conduction velocity for the OVVR model roughly half that of the GPB model and well below clinical values. Between single cells and tissue, both models exhibit differences in properties, including maximum upstroke velocity, action potential amplitude, and minimum diastolic interval. Compared to experimental data, action potential durations for the GPB and OVVR models agree fairly well (although OVVR epicardial action potentials are shorter), but maximum slopes of steady-state restitution curves are smaller. Although studies show alternans in normal hearts, it occurs only in the OVVR model, and only for a narrow range of cycle lengths. We find initiated spiral waves do not progress to sustained breakup for either model. The dominant spiral wave period of the GPB model falls within clinically relevant values for ventricular tachycardia (VT), but for the OVVR model, the dominant period is longer than periods associated with VT. Our results should facilitate choosing a model to match properties of interest in human cardiac tissue and to replicate arrhythmia behavior more closely. Furthermore, by indicating areas where existing models disagree, our findings suggest avenues for further experimental work. [ABSTRACT FROM AUTHOR]

Increased oxygen tension influences bone metabolism. This study comprised two main experiments: one aimed to determine the bone mineral apposition and bone formation rates in vivo under hyperbaric hyperoxia (HBO), and the other aimed to evaluate the effects of exposure to HBO on fracture healing. In experiment 1, male mice were exposed to HBO [90 min/day at 90% O2 at 2 atmospheres absolute (ATA) for 5 days]. In experiment 2, an open femur fracture model was created in mice, followed by exposure to HBO 5 times/week (90 min/day at 90% O2 at 2 ATA) for 6 weeks after surgery. In experiment 1, HBO treatment significantly increased the mineral apposition and bone formation rates in the lumbar vertebra and femur and type 1 collagen alpha 1 and alkaline phosphatase mRNA expression in the lumbar vertebra. In experiment 2, at 2 weeks after fracture, the fracture callus was significantly larger in the HBO group than in the non-HBO group. Furthermore, at 4 and 6 weeks after fracture, radiographic findings showed accelerated fracture healing in the HBO group. At 6 weeks after fracture, femur stiffness and maximum load were significantly higher in the HBO group than in the non-HBO group. Urinary 8-hydroxy-2′-deoxyguanosine and plasma calcium concentrations were not significantly different between groups. These results suggest that exposure to HBO enhances bone anabolism and accelerates fracture healing without causing oxidative DNA damage or disruption of plasma calcium homeostasis. [ABSTRACT FROM AUTHOR]

Snowflake Vitreoretinal Degeneration (SVD) is associated with the R162W mutation of the Kir7.1 inwardly-rectifying potassium channel. Kir7.1 is found at the apical membrane of Retinal Pigment Epithelial (RPE) cells, adjacent to the photoreceptor neurons. The SVD phenotype ranges from RPE degeneration to an abnormal b-wave to a liquid vitreous. We sought to determine how this mutation alters the structure and function of the human Kir7.1 channel. In this study, we expressed a Kir7.1 construct with the R162W mutation in CHO cells to evaluate function of the ion channel. Compared to the wild-type protein, the mutant protein exhibited a non-functional Kir channel that resulted in depolarization of the resting membrane potential. Upon co-expression with wild-type Kir7.1, R162W mutant showed a reduction of IKir7.1 and positive shift in ‘0’ current potential. Homology modeling based on the structure of a bacterial Kir channel protein suggested that the effect of R162W mutation is a result of loss of hydrogen bonding by the regulatory lipid binding domain of the cytoplasmic structure. [ABSTRACT FROM AUTHOR]

Human aging into senescence diminishes the capacity of the postural control system to adapt to the stressors of everyday life. Diminished adaptive capacity may be reflected by a loss of the fractal-like, multiscale complexity within the dynamics of standing postural sway (i.e., center-of-pressure, COP). We therefore studied the relationship between COP complexity and adaptive capacity in 22 older and 22 younger healthy adults. COP magnitude dynamics were assessed from raw data during quiet standing with eyes open and closed, and complexity was quantified with a new technique termed empirical mode decomposition embedded detrended fluctuation analysis (EMD-DFA). Adaptive capacity of the postural control system was assessed with the sharpened Romberg test. As compared to traditional DFA, EMD-DFA more accurately identified trends in COP data with intrinsic scales and produced short and long-term scaling exponents (i.e., αShort, αLong) with greater reliability. The fractal-like properties of COP fluctuations were time-scale dependent and highly complex (i.e., αShort values were close to one) over relatively short time scales. As compared to younger adults, older adults demonstrated lower short-term COP complexity (i.e., greater αShort values) in both visual conditions (p>0.001). Closing the eyes decreased short-term COP complexity, yet this decrease was greater in older compared to younger adults (p<0.001). In older adults, those with higher short-term COP complexity exhibited better adaptive capacity as quantified by Romberg test performance (r2 = 0.38, p<0.001). These results indicate that an age-related loss of COP complexity of magnitude series may reflect a clinically important reduction in postural control system functionality as a new biomarker. [ABSTRACT FROM AUTHOR]

We introduce an electromechanical model for human cardiac tissue which couples a biophysical model of cardiac excitation (Tusscher, Noble, Noble, Panfilov, 2006) and tension development (adjusted Niederer, Hunter, Smith, 2006 model) with a discrete elastic mass-lattice model. The equations for the excitation processes are solved with a finite difference approach, and the equations of the mass-lattice model are solved using Verlet integration. This allows the coupled problem to be solved with high numerical resolution. Passive mechanical properties of the mass-lattice model are described by a generalized Hooke's law for finite deformations (Seth material). Active mechanical contraction is initiated by changes of the intracellular calcium concentration, which is a variable of the electrical model. Mechanical deformation feeds back on the electrophysiology via stretch-activated ion channels whose conductivity is controlled by the local stretch of the medium. We apply the model to study how stretch-activated currents affect the action potential shape, restitution properties, and dynamics of spiral waves, under constant stretch, and dynamic stretch caused by active mechanical contraction. We find that stretch conditions substantially affect these properties via stretch-activated currents. In constantly stretched medium, we observe a substantial decrease in conduction velocity, and an increase of action potential duration; whereas, with dynamic stretch, action potential duration is increased only slightly, and the conduction velocity restitution curve becomes biphasic. Moreover, in constantly stretched medium, we find an increase of the core size and period of a spiral wave, but no change in rotation dynamics; in contrast, in the dynamically stretching medium, we observe spiral drift. Our results may be important to understand how altered stretch conditions affect the heart's functioning. [ABSTRACT FROM AUTHOR]

Here we investigate how ß-adrenergic stimulation of the heart alters regulation of ryanodine receptors (RyRs) by intracellular Ca2+ and Mg2+ and the role of these changes in SR Ca2+ release. RyRs were isolated from rat hearts, perfused in a Langendorff apparatus for 5 min and subject to 1 min perfusion with 1 µM isoproterenol or without (control) and snap frozen in liquid N2 to capture their phosphorylation state. Western Blots show that RyR2 phosphorylation was increased by isoproterenol, confirming that RyR2 were subject to normal ß-adrenergic signaling. Under basal conditions, S2808 and S2814 had phosphorylation levels of 69% and 15%, respectively. These levels were increased to 83% and 60%, respectively, after 60 s of ß-adrenergic stimulation consistent with other reports that ß-adrenergic stimulation of the heart can phosphorylate RyRs at specific residues including S2808 and S2814 causing an increase in RyR activity. At cytoplasmic [Ca2+] <1 µM, ß-adrenergic stimulation increased luminal Ca2+ activation of single RyR channels, decreased luminal Mg2+ inhibition and decreased inhibition of RyRs by mM cytoplasmic Mg2+. At cytoplasmic [Ca2+] >1 µM, ß-adrenergic stimulation only decreased cytoplasmic Mg2+ and Ca2+ inhibition of RyRs. The Ka and maximum levels of cytoplasmic Ca2+ activation site were not affected by ß-adrenergic stimulation. Our RyR2 gating model was fitted to the single channel data. It predicted that in diastole, ß-adrenergic stimulation is mediated by 1) increasing the activating potency of Ca2+ binding to the luminal Ca2+ site and decreasing its affinity for luminal Mg2+ and 2) decreasing affinity of the low-affinity Ca2+/Mg2+ cytoplasmic inhibition site. However in systole, ß-adrenergic stimulation is mediated mainly by the latter. [ABSTRACT FROM AUTHOR]

The dwell times between two successive steps of the two-headed molecular motor myosin V are governed by non-exponential distributions. These distributions have been determined experimentally for various control parameters such as nucleotide concentrations and external load force. First, we use a simplified network representation to determine the dwell time distributions of myosin V, with the associated dynamics described by a Markov process on networks with absorbing boundaries. Our approach provides a direct relation between the motor’s chemical kinetics and its stepping properties. In the absence of an external load, the theoretical distributions quantitatively agree with experimental findings for various nucleotide concentrations. Second, using a more complex branched network, which includes ADP release from the leading head, we are able to elucidate the motor’s gating effect. This effect is caused by an asymmetry in the chemical properties of the leading and the trailing head of the motor molecule. In the case of an external load acting on the motor, the corresponding dwell time distributions reveal details about the motor’s backsteps. [ABSTRACT FROM AUTHOR]