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ABSTRACT: A striking feature of stress relaxation in biological soft tissue is that it frequently follows a power law in time with an exponent that is independent of strain even when the elastic properties of the tissue are highly nonlinear. This kind of behavior is an example of quasi-linear viscoelasticity, and is usually modeled in a purely empirical fashion. The goal of the present study was to account for quasi-linear viscoelasticity in mechanistic terms based on our previously developed hypothesis that it arises as a result of isolated micro-yield events occurring in sequence throughout the tissue, each event passing the stress it was sustaining on to other regions of the tissue until they themselves yield. We modeled stress relaxation computationally in a collection of stress-bearing elements. Each element experiences a stochastic sequence of either increases in elastic equilibrium length or decreases in stiffness according to the stress imposed upon it. This successfully predicts quasi-linear viscoelastic behavior, and in addition predicts power-law stress relaxation that proceeds at the same slow rate as observed in real biological soft tissue.
Annals of biomedical engineering 03/2013; · 2.41 Impact Factor
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ABSTRACT: The current standard of care for patients suffering from acute respiratory distress syndrome (ARDS) is ventilation with a tidal volume of 6 ml/kg predicted body weight (PBW), but variability remains in the tidal volumes that are actually used. This study aims to identify patient scenarios for which there is discordance between physicians in choice of tidal volume and positive end-expiratory pressure (PEEP) in ARDS patients. We developed an algorithm based on fuzzy logic for encapsulating the expertise of individual physicians regarding their use of tidal volume and PEEP in ARDS patients. The algorithm uses three input measurements: (1) peak airway pressure (PAP), (2) PEEP, and (3) arterial oxygen saturation (SaO2). It then generates two output parameters: (1) the deviation of tidal volume from 6 ml/kg PBW, and (2) the change in PEEP from its current value. We captured 6 realizations of intensivist expertise in this algorithm and assessed their degree of concordance using a Monte Carlo simulation. Variability in the tidal volume recommended by the algorithm increased for PAP > 30 cmH2O and PEEP > 5 cmH2O. Tidal volume variability decreased for SaO2 > 90 %. Variability in the recommended change in PEEP increased for PEEP > 5 cmH2O and for SaO2 near 90 %. Intensivists vary in their management of ARDS patients when peak airway pressures and PEEP are high, suggesting that the current goal of 6 ml/kg PBW may need to be revisited under these conditions.
International Journal of Clinical Monitoring and Computing 03/2013;
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ABSTRACT: Allergic inflammation is a general host-defense mechanism for dealing with perceived foreign invaders. Although most effort has been directed toward understanding how this response gets turned on, how it gets turned off again when no longer needed is just as important to an organism's survival. We postulate that the control of the allergic inflammatory response is achieved via frequency modulation whereby a sequence of self-resolving events is repetitively invoked only so long as Ag is present. This leads to the notion of a unitary inflammatory event that we argue has formal similarity to the skeletal muscle twitch, albeit manifest over a much longer time scale. To test the plausibility of this hypothesis, we created an agent-based computational model of the allergic inflammatory response in the lungs. Continual stimulation of the model results in cycles of tissue damage and repair interspersed with periods of nonresponsiveness indicative of a refractory period. These findings are consistent with the inflammatory twitch hypothesis and the notion that the allergic inflammatory response is controlled via frequency modulation. We speculate that chronic inflammatory diseases may represent a failure of the inflammatory twitch to resolve toward baseline.
The Journal of Immunology 02/2013; · 5.79 Impact Factor
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ABSTRACT: Management of ALI/ARDS involves supportive ventilation at low tidal volumes (V (t)) to minimize the rate at which ventilator induced lung injury (VILI) develops while the lungs heal. However, we currently have few details to guide the minimization of VILI in the ALI/ARDS patient. The goal of the present study was to determine how VILI progresses with time as a function of the manner in which the lung is ventilated in mice. We found that the progression of VILI caused by over-ventilating the lung at a positive end-expiratory pressure of zero is accompanied by progressive increases in lung stiffness as well as the rate at which the lung derecruits over time. We were able to accurately recapitulate these findings in a computational model that attributes changes in the dynamics of recruitment and derecruitment to two populations of lung units. One population closes over a time scale of minutes following a recruitment maneuver and the second closes in a matter of seconds or less, with the relative sizes of the two populations changing as VILI develops. This computational model serves as a basis from which to link the progression of VILI to changes in lung mechanical function.
Annals of biomedical engineering 11/2012; · 2.41 Impact Factor
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ABSTRACT: The explanted lung slice has become a popular in vitro system for studying how airways contract. Because the forces of airway-parenchymal interdependence are such important modulators of airway narrowing, it is of significant interest to understand how the parenchyma around a constricting airway in a lung slice behaves. We have previously shown that the predictions of the 2-dimensional distortion field around a constricting airway are substantially different depending on whether the parenchyma is modeled as an elastic continuum versus a network of hexagonally arranged springs, which raises the question as to which model best explains the lung slice. We treated lung slices with methacholine and then followed the movement of a set of parenchymal landmarks around the airway as it narrowed. The resulting parenchymal displacement field was compared to the displacement fields predicted by the continuum and hexagonal spring network models. The predictions of the continuum model were much closer to the measured data than were those of the hexagonal spring network model, suggesting that the parenchyma in the lung slice behaves like an elastic continuum rather than a network of discrete springs. This may be because the alveoli of the lung slice are filled with agarose in order to provide structural stability, causing the parenchyma in the slice to act like a true mechanical continuum. How the air-filled parenchyma in the intact lung behave in vivo remains an open question.
Respiratory Physiology & Neurobiology 11/2012; · 2.24 Impact Factor
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ABSTRACT: Catheter ablation strategies for treatment of cardiac arrhythmias are quite successful when targeting spatially constrained substrates. Complex, dynamic, and spatially varying substrates, however, pose a significant challenge for ablation, which delivers spatially fixed lesions. We describe tissue excitation using concepts of surface topology which provides a framework for addressing this challenge. The aim of this study was to test the efficacy of mechanism-based ablation strategies in the setting of complex dynamic substrates.
We used a computational model of propagation through electrically excitable tissue to test the effects of ablation on excitation patterns of progressively greater complexity, from fixed rotors to multi-wavelet re-entry. Our results indicate that (i) focal ablation at a spiral-wave core does not result in termination; (ii) termination requires linear lesions from the tissue edge to the spiral-wave core; (iii) meandering spiral-waves terminate upon collision with a boundary (linear lesion or tissue edge); (iv) the probability of terminating multi-wavelet re-entry is proportional to the ratio of total boundary length to tissue area; (v) the efficacy of linear lesions varies directly with the regional density of spiral-waves.
We establish a theoretical framework for re-entrant arrhythmias that explains the requirements for their successful treatment. We demonstrate the inadequacy of focal ablation for spatially fixed spiral-waves. Mechanistically guided principles for ablating multi-wavelet re-entry are provided. The potential to capitalize upon regional heterogeneity of spiral-wave density for improved ablation efficacy is described.
Europace 11/2012; 14 Suppl 5:v106-v111. · 1.98 Impact Factor
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ABSTRACT: The outward tethering forces exerted by the lung parenchyma on the airways embedded within it are potent modulators of the ability of the airway smooth muscle to shorten. Much of our understanding of these tethering forces is based on treating the parenchyma as an elastic continuum; yet, on a small enough scale, the lung parenchyma in two dimensions would seem to be more appropriately described as a discrete spring network. We therefore compared how the forces and displacements in the parenchyma surrounding a contracting airway are predicted to differ depending on whether the parenchyma is modeled as an elastic continuum or as a spring network. When the springs were arranged hexagonally to represent alveolar walls, the predicted parenchymal stresses and displacements propagated substantially farther away from the airway than when the springs were arranged in a triangular pattern or when the parenchyma was modeled as a continuum. Thus, to the extent that the parenchyma in vivo behaves as a hexagonal spring network, our results suggest that the range of interdependence forces due to airway contraction may have a greater influence than was previously thought.
Journal of Applied Physiology 04/2012; 113(1):124-9. · 3.75 Impact Factor
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ABSTRACT: Airway hyperresponsiveness (AHR), a characteristic of asthma that involves an excessive reduction in airway caliber, is a complex mechanism reflecting multiple processes that manifest over a large range of length and time scales. At one extreme, molecular interactions determine the force generated by airway smooth muscle (ASM). At the other, the spatially distributed constriction of the branching airways leads to breathing difficulties. Similarly, asthma therapies act at the molecular scale while clinical outcomes are determined by lung function. These extremes are linked by events operating over intermediate scales of length and time. Thus, AHR is an emergent phenomenon that limits our understanding of asthma and confounds the interpretation of studies that address physiological mechanisms over a limited range of scales. A solution is a modular computational model that integrates experimental and mathematical data from multiple scales. This includes, at the molecular scale, kinetics, and force production of actin-myosin contractile proteins during cross-bridge and latch-state cycling; at the cellular scale, Ca(2+) signaling mechanisms that regulate ASM force production; at the tissue scale, forces acting between contracting ASM and opposing viscoelastic tissue that determine airway narrowing; at the organ scale, the topographic distribution of ASM contraction dynamics that determine mechanical impedance of the lung. At each scale, models are constructed with iterations between theory and experimentation to identify the parameters that link adjacent scales. This modular model establishes algorithms for modeling over a wide range of scales and provides a framework for the inclusion of other responses such as inflammation or therapeutic regimes. The goal is to develop this lung model so that it can make predictions about bronchoconstriction and identify the pathophysiologic mechanisms having the greatest impact on AHR and its therapy.
Frontiers in physiology. 01/2012; 3:191.
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ABSTRACT: Fractionated electrograms are used by some as targets for ablation in atrial and ventricular arrhythmias. Fractionation has been demonstrated to result when there is repetitive or asynchronous activation of separate groups of cells within the recording region of a mapping electrode(s).
Using a computer model, we generated tissue activation patterns with increasing spatiotemporal variation and calculated virtual electrograms from electrodes with decreasing resolution. We then quantified electrogram fractionation. In addition, we recorded unipolar electrograms during atrial fibrillation in 20 patients undergoing atrial fibrillation ablation. From these we constructed bipolar electrograms with increasing interelectrode spacing and quantified fractionation. During modeling of spatiotemporal variation, fractionation varied directly with electrode length, diameter, height, and interelectrode spacing. When resolution was held constant, fractionation increased with increasing spatiotemporal variation. In the absence of spatial variation, fractionation was independent of resolution and proportional to excitation frequency. In patients with atrial fibrillation, fractionation increased as interelectrode spacing increased.
We created a model for distinguishing the roles of spatial and temporal electric variation and electrode resolution in producing electrogram fractionation. Spatial resolution affects fractionation attributable to spatiotemporal variation but not temporal variation alone. Electrogram fractionation was directly proportional to spatiotemporal variation and inversely proportional to spatial resolution. Spatial resolution limits the ability to distinguish high-frequency excitation from overcounting. In patients with atrial fibrillation, complex fractionated atrial electrogram detection varies with spatial resolution. Electrode resolution must therefore be considered when interpreting and comparing studies of fractionation.
Circulation Arrhythmia and Electrophysiology 12/2011; 4(6):909-16. · 6.46 Impact Factor
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06/2011; , ISBN: 9780470650714
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ABSTRACT: We have developed a straightforward, physiologically based mathematical in silico model of cardiac electric activity to facilitate understanding of the fundamental principles that determine how excitation propagates through the heart. Despite its simplicity, the model provides a very powerful teaching tool. In fact, its simplicity is integral to the model's utility. The contrast between the minimal set of rules that govern the model's function and the widely varied complex behaviors it can manifest offers insight into the nature of emergent behavior in wave propagation. Emergence in this context refers to the richness of the tissue activation patterns that arise from the aggregate behavior of the simple cells that comprise the tissue. Each cell can be active, inactive, or refractory and interacts only with its immediate neighbors. From these simple building blocks, very elaborate global behaviors emerge.
Circulation Arrhythmia and Electrophysiology 06/2011; 4(4):586-91. · 6.46 Impact Factor
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Andrew J E Seely,
Stuart A Kauffman, Jason H T Bates,
Peter T Macklem,
Béla Suki,
John C Marshall,
Andriy I Batchinsky,
Jose Luis Perez-Velazquez,
Adam Seiver,
Carolyn McGregor, [......],
Martin G Frasch,
Christian Straus,
Leon Glass,
Paul J Godin,
John A Morris,
Daby Sow,
Vera Nenadovic,
Ryan C Arnold,
Patrick Norris,
J Randall Moorman
Journal of critical care 06/2011; 26(3):325-7. · 2.13 Impact Factor
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03/2011; , ISBN: 9780470650714
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AJP Lung Cellular and Molecular Physiology 03/2011; 300(3):L506; author reply L507. · 3.66 Impact Factor
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ABSTRACT: Variable (or noisy) ventilation (VV) has been demonstrated in animal models of acute lung injury to be superior to constant (or conventional) ventilation (CV), in terms of improved gas exchange and mitigation of lung injury, for reasons that are not entirely clear. We hypothesized that the efficacy of VV is related to the fact that recruitment and derecruitment of lung units are dynamic processes. To test this hypothesis, we modeled the lung computationally as a symmetrically bifurcating airway tree terminating in elastic units. Each airway was fully open or completely closed, at any point in time, according to its pressure history. The model is able to accurately mimic previous experimental measurements showing that the lungs of mice injured by acid aspiration are better recruited after 60 min of VV than CV. The model also shows that recruitment/derecruitment dynamics contribute to the relative efficacy of VV, provided lung units open more rapidly than they close once a critical opening or closing pressure threshold has been crossed. We conclude that the dynamics of recruitment and derecruitment in the lung may be important factors responsible for the benefits of VV compared with CV.
Journal of Applied Physiology 03/2011; 110(5):1319-26. · 3.75 Impact Factor
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Journal of Applied Physiology 02/2011; 110(4):1109-10. · 3.75 Impact Factor
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ABSTRACT: Multi-scale modeling of biological systems has recently become fashionable due to the growing power of digital computers as well as to the growing realization that integrative systems behavior is as important to life as is the genome. While it is true that the behavior of a living organism must ultimately be traceable to all its components and their myriad interactions, attempting to codify this in its entirety in a model misses the insights gained from understanding how collections of system components at one level of scale conspire to produce qualitatively different behavior at higher levels. The essence of multi-scale modeling thus lies not in the inclusion of every conceivable biological detail, but rather in the judicious selection of emergent phenomena appropriate to the level of scale being modeled. These principles are exemplified in recent computational models of the lung. Airways responsiveness, for example, is an organ-level manifestation of events that begin at the molecular level within airway smooth muscle cells, yet it is not necessary to invoke all these molecular events to accurately describe the contraction dynamics of a cell, nor is it necessary to invoke all phenomena observable at the level of the cell to account for the changes in overall lung function that occur following methacholine challenge. Similarly, the regulation of pulmonary vascular tone has complex origins within the individual smooth muscle cells that line the blood vessels but, again, many of the fine details of cell behavior average out at the level of the organ to produce an effect on pulmonary vascular pressure that can be described in much simpler terms. The art of multi-scale lung modeling thus reduces not to being limitlessly inclusive, but rather to knowing what biological details to leave out.
Journal of Applied Physiology 02/2011; 110(5):1466-72. · 3.75 Impact Factor
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ABSTRACT: Management of patients with acute lung injury (ALI) rests on achieving a balance between the gas exchanging benefits of mechanical ventilation and the exacerbation of tissue damage in the form of ventilator-induced lung injury (VILI). Optimizing this balance requires an injury cost function relating injury progression to the measurable pressures, flows, and volumes delivered during mechanical ventilation. With this in mind, we mechanically ventilated naive, anesthetized, paralyzed mice for 4 h using either a low or high tidal volume (Vt) with either moderate or zero positive end-expiratory pressure (PEEP). The derecruitability of the lung was assessed every 15 min in terms of the degree of increase in lung elastance occurring over 3 min following a recruitment maneuver. Mice could be safely ventilated for 4 h with either a high Vt or zero PEEP, but when both conditions were applied simultaneously the lung became increasingly unstable, demonstrating worsening injury. We were able to mimic these data using a computational model of dynamic recruitment and derecruitment that simulates the effects of progressively increasing surface tension at the air-liquid interface, suggesting that the VILI in our animal model progressed via a vicious cycle of alveolar leak, degradation of surfactant function, and increasing tissue stress. We thus propose that the task of ventilating the injured lung is usefully understood in terms of the Vt-PEEP plane. Within this plane, non-injurious combinations of Vt and PEEP lie within a "safe region", the boundaries of which shrink as VILI develops.
Annals of biomedical engineering 01/2011; 39(5):1505-16. · 2.41 Impact Factor
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ABSTRACT: The mechanical properties of the lung are embodied in its mechanical input impedance, which it is interpreted in physiological terms by being fit with a mathematical model. The normal lung is extremely well described by a model consisting of a single uniformly ventilated compartment comprised of tissue having a constant-phase impedance, but to describe the abnormal lung it frequently becomes necessary to invoke additional compartments. To date, all evidence of regional mechanical heterogeneity in the mouse lung has been assumed to be of the parallel variety. We therefore investigated the use of a serial heterogeneity model, relative to parallel heterogeneity and homogeneous models, for describing impedance spectra in mice subjected to a variety of interventions designed to make their lungs heterogeneous. We found that functional evidence of the finite stiffness of the airway wall in mice with airways obstruction can sometimes be apparent in lung impedance below 20 Hz. The model estimates of airway stiffness were smaller than direct estimates obtained from micro-CT images of the lung in vivo, suggesting that the conducting airways alone are likely not the precise anatomical correlate of proximal functional stiffness in the lung. Nevertheless, we conclude that central airway shunting in mice can sometimes be an important physiological phenomenon.
Annals of biomedical engineering 01/2011; 39(1):497-507. · 2.41 Impact Factor
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ABSTRACT: The mechanical properties of lung parenchymal tissue are both elastic and dissipative, as well as being highly nonlinear. These properties cannot be fully understood, however, in terms of the individual constituents of the tissue. Rather, the mechanical behavior of lung tissue emerges as a macroscopic phenomenon from the interactions of its microscopic components in a way that is neither intuitive nor easily understood. In this review, we first consider the quasi-static mechanical behavior of lung tissue and discuss computational models that show how smooth nonlinear stress-strain behavior can arise through a percolation-like process in which the sequential recruitment of collagen fibers with increasing strain causes them to progressively take over the load-bearing role from elastin. We also show how the concept of percolation can be used to link the pathologic progression of parenchymal disease at the micro scale to physiological symptoms at the macro scale. We then examine the dynamic mechanical behavior of lung tissue, which invokes the notion of tissue resistance. Although usually modeled phenomenologically in terms of collections of springs and dashpots, lung tissue viscoelasticity again can be seen to reflect various types of complex dynamic interactions at the molecular level. Finally, we discuss the inevitability of why lung tissue mechanics need to be complex.
Journal of Applied Physiology 01/2011; 110(4):1111-8. · 3.75 Impact Factor
