Simulation of Biological Processes phần 6

GENERAL DISCUSSION II 127 Subramaniam: Not necessarily. You can have emergent properties as a conse-quenceofintegration. Noble: Andyoumayeven bepuzzledastowhy. Thisisnotyetanexplanation. Boissel: The next term is ‘robustness’. Yesterday, again, I heard two di¡erent de¢nitions.First, insensitivityto parametervalues;second,insensitivity touncer- tainty.Ilikethesecondbutnotthe¢rst. Noble:Insomecasesyouwouldwantsensitivity.NoHodgkin^Huxleyanalysis ofanerveimpulsewouldbecorrectwithoutitbeingthecasethatatacertaincritical pointthewholethingtakeso¡.Wewillneedtohavesensitivitytosomeparameter values. Boissel: For me, insensitivity to parameter values means that the parameters are uselessinthemodel. Cassman:Inthosecases(atleast,thefairlylimitednumberwherethisseemstobe true) it is the architecture of the system that determines the output and not the speci¢c parameter values. It seems likely this is only true for certain characteristic phenotypicoutcomes.Insomecasesitexists,inothersitdoesn’t. Hinch:Perhapsabetterwayofsayingthisisinsensitivitytoill-de¢nedparameter values.Insomemodelsthereareparametersthatarenotwellde¢ned,whichisthe case in a lot of signalling networks. In contrast, in a lot of electrophysiology they are well de¢ned and then the model doesn’t have to be robust to a well de¢ned parameter. Loew: Rather than uncertainty, a better concept for our discussion might be variability. That is, because of di¡erences in the environment and natural variability.Weareoftendealingwithasmallnumberofmolecules.Thereisthere-fore a certain amount of uncertainty or variability that is built into biology. If a biological system is going to work reliably, it has to be insensitive to this variability. Boissel: Thatisdi¡erentfromuncertainty,soweshouldaddvariabilityhere. Paterson:Itisthedi¡erencebetweenrobustnessofapredictionversusrobustness of a system design. Robustness of a system design would be insensitivity to variability.Robustnessof aprediction,where youaretrying tomakeaprediction basedonamodelwithincompletedataismoretheuncertaintyissue. Maini:Italldependswhatyoumeanbyparameter.Parametercanalsorefertothe topologyandnetworkingofthesystem,ortoboundaryconditions.Thereisalink between the parameter values and the uncertainty. If your model only worked if a certain parameter was 4.6, biologically you could never be certain that this parameter was 4.6. It might be 4.61. In this case you would say that this was not a goodmodel. Boissel: There is another issue regarding uncertainty, which is the strength of evidence of the data that have been used to parameterize the model. This is a di⁄cultissue. 128 GENERAL DISCUSSION II References BoydCAR,NobleD1993Thelogicoflife.OxfordUniversityPress,Oxford Loew L 2002 The Virtual Cell project. In: ‘In silico’ simulation of biological processes. Wiley, Chichester (NovartisFoundSymp247) p151^161 Winslow RL, Helm P, Baumgartner W Jr et al 2002 Imaging-based integrative models of the heart: closing the loop between experiment and simulation. In: ‘In silico’ simulation of biologicalprocesses. Wiley,Chichester (NovartisFoundSymp247) p129^143 ‘In Silico’ Simulation of Biological Processes: Novartis Foundation Symposium, Volume 247 Edited by Gregory Bock and Jamie A. Goode Copyright ¶ Novartis Foundation 2002. ISBN: 0-470-84480-9 Imaging-basedintegrativemodelsof theheart:closingtheloopbetween experimentandsimulation Raimond L. Winslow*, Patrick Helm*, William Baumgartner Jr.*, Srinivas Peddi{, Tilak Ratnanather{, Elliot McVeigh{ and Michael I. Miller{ *TheWhitakerBiomedicalEngineeringInstituteCenterforComputationalMedicine&Biology and {Center for Imaging Sciences, {NIH Laboratory of Cardiac Energetics: Medical Imaging Section3,JohnsHopkinsUniversity,BaltimoreMD21218,USA Abstract.Wedescribemethodologiesfor:(a)mappingventricularactivationusinghigh-densityepicardialelectrodearrays;(b)measuringandmodellingventriculargeometryand ¢bre orientation at high spatial resolution using di¡usion tensor magnetic resonance imaging (DTMRI); and (c) simulating electrical conduction; using comprehensive data setscollected fromindividualcanine hearts.We demonstrate thatcomputational models basedontheseexperimentaldatasetsyieldreasonablyaccuratereproductionofmeasured epicardial activation patterns. We believe this ability to electrically map and model individual hearts will lead to enhanced understanding of the relationship between anatomicalstructure,andelectricalconduction inthecardiacventricles. 2002 ‘In silico’ simulation of biological processes. Wiley, Chichester (Novartis Foundation Symposium247)p129^143 Cardiacelectrophysiologyisa¢eldwitharichhistoryofintegrativemodelling.A criticalmilestoneforthe¢eldwasthedevelopmentofthe¢rstbiophysicallybased cell model describing interactions between voltage-gated membrane currents, pumps and exchangers, and intracellular calcium (Ca2+) cycling processes (DiFrancesco & Noble 1985), and the subsequent elaboration of this model to describe the cardiac ventricular myocyte action potential (Noble et al 1991, Luo & Rudy 1994). The contributions of these and other models to understanding of myocyte function have been considerable, and are due in large part to a rich interplay between experiment and modellingöan interplay in which experimentsinformmodelling,andmodelling suggestsnewexperiments. Modelling of cardiac ventricular conduction has to a large extent lacked this interplay. While it is now possible to measure electrical activation of the epicardium at relatively high spatial resolution, the di⁄culty of measuring the geometry and ¢bre structure of hearts which have been electrically mapped has 129 130 WINSLOW ET AL limited our ability to relate ventricular structure to conduction via quantitative models. We believe there are four major tasks that must be accomplished if we are to understand this structure^function relationship. First, we must identify an appropriate experimental preparationöone which a¡ords the opportunity to study e¡ects of remodelling of ventricular geometry and ¢bre structure on ventricular conduction. Second, we must develop rapid, accurate methods for measuring both electrical conduction, ventricular geometry and ¢bre structure in the same heart. Third, we must develop mathematical approaches for identifying statistically signi¢cant di¡erences in geometry and ¢bre structure between hearts. Fourth, once identi¢ed, these di¡erences in geometry and ¢bre structure must be relatedtodi¡erencesinconductionproperties. We are pursuing these goals by means of coordinated experimental and modelling studies of electrical conduction in normal canine heart, and canine hearts in which failure is induced using the tachycardia pacing-induced procedure (Williams et al 1994). In the following sections, we describe the ways in which we: (a) map ventricular activation using high-density epicardial electrode arrays; (b) measure and model ventricular geometry and ¢bre orientation at high spatial resolution using di¡usion tensor magnetic resonance imaging (DTMRI); and (c) construct computational models of the imaged hearts; and (d) compare simulated conduction properties with those measured in thesameheart. Mappingofepicardialconduction innormalandfailingcanineheart In each of the three normal and three failing canine hearts studied to date, we have, prior to imaging, performed electrical mapping studies in which epicardial conduction in response to various current stimuli are measured using multi-electrode epicardial socks consisting of a nylon mesh with 256 electrodes and electrode spacing of 5mm sewn around its surface. Bipolar epicardial twisted-pair pacing electrodes are sewn onto the right atrium (RA) and the right ventricular (RV) free-wall. Four to 10 glass beads ¢lled with gadolinium-DTPA(5mM)areattachedtothesockaslocalizationmarkers,andresponsesto di¡erent pacing protocols are recorded. Figure 1A shows an example of measurement of activation time (colour bar, in ms) measured in response to an RV stimulus pulse applied at the epicardial locations marked in red. After all electrical recordings are obtained, the animal is euthanatized with a bolus of potassium chloride, and the heart is then scanned with high-resolution T1-weighted imaging in order to locate the gadolinium-DTPA ¢lled beads in scanner coordinates. The heart is then excised, sock electrode locations are determined using a 3D digitizer (MicroScribe 3DLX), and the heart is formalin-¢xed in preparation for DTMRI. MODELS OF THE HEART 131 FIG.1. (A)Electricalactivationtimes(indicatedbygreyscale)inresponsetorightRVpacingas recorded using electrode arrays. Data was obtained from a normal canine heart that was subsequently reconstructed using DTMRI. Activation times are displayed on the epicardial surfaceofa¢nite-elementmodel¢ttotheDTMRIreconstructiondata.Fibreorientationonthe epicardial surface, as ¢t to the DTMRI data by the FEM model, is shown by the short line segments.(B)Activationtimespredictedusingacomputationalmodeloftheheartmappedin(A). Measuringthe¢brestructureofthecardiacventriclesusingDTMRI DTMRI is based on the principle that proton di¡usion in the presence of a magnetic ¢eld gradient causes signal attenuation, and that measurement of this attenuation in several di¡erent directions can be used to estimate a di¡usion tensor at each image voxel (Skejskal 1965, Basseret al 1994). Several studies have now con¢rmed that the principle eigenvector of the di¡usion tensor is locally aligned with the long-axis of cardiac ¢bres (Hsu et al 1998, Scollan et al 1998, Holmesetal2000). Use of DTMRI for reconstruction of cardiac ¢bre orientation provides several advantages over traditional histological methods. First, DTMRI yields estimates of the absolute orientation of cardiac ¢bres, whereas histological methods yield estimates of only ¢bre inclination angle. Second, DTMRI performed using formalin-¢xed tissue: (a) yields high resolution images of the cardiac boundaries, thus enabling precise reconstruction of ventricular geometry using image segmentation software; and (b) eliminates £ow artefacts present in perfused heart, enabling longer imaging times, increased signal-to-noise (SNR) ratio and improved spatial resolution. Third, DTMRI provides estimates of ¢bre orientation at greater than one order of magnitude more points than possible with histological methods. Fourth, reconstruction time is greatly reduced (60h versusweekstomonths)relativetothatforhistologicalmethods. ... - tailieumienphi.vn