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PubMed1996

Is there the creatine kinase equilibrium in working heart cells?

The mathematical model of the compartmentalised energy transfer system in cardiac myocytes, which includes mitochondrial synthesis of ATP by ATP-synthase, phosphocreatine production in the coupled mitochondrial creatine kinase reaction, the myofibrillar and cytoplasmic creatine kinase reactions, ATP utilisation by actomyosin ATPase during contraction cycle, and diffusional exchange of metabolites between different compartments, was used to calculate creatine kinase reaction rates (fluxes) in different cellular compartments at a workload corresponding to the rate of oxygen consumption of 46 micrograms-atom O2 *min-1 * (g wet mass)-1. The results of calculations showed that at this high workload all creatine kinase isoenzymes function most of their time in the cardiac cycle in the steady state far from equilibrium. This mathematical modelling shows that the validity of assumption of creatine kinase equilibrium is limited only to the diastolic phase of the contraction cycle in the working cardiac cells and only to the cytoplasmic compartment. In the systolic phase, due to rapid release of ADP at increased workloads, all creatine kinase isoenzymes are rapidly shifted out of the equilibrium. Cytoplasmic ADP concentration may increase up to 9 times in the systolic phase of the cardiac cycle, correspondingly changing all ADP-dependent parameters. Mitochondrial creatine kinase functions permanently in "metastable" steady state (Jurgen Daut, Biochim. Biophys. Acta 895, 41-62, 1987). It may be proposed that a more precise, in comparison to the equilibrium concept, way of calculating steady state cytoplasmic ADP concentrations at increased workloads is to use kinetic equations and mathematical models of energy metabolism.

Adenosine Diphosphate↗
PubMed1993

Serum proteins bypass the blood-brain fluid barriers for extracellular entry to the central nervous system.

Extracellular pathways circumventing the mammalian blood-brain fluid barriers (e.g., blood-brain and blood-CSF barriers) have been investigated in the rat by immunohistochemical localization of the endogenous serum proteins albumin, IgG, complement C-9, and IgM and by the exogenous tracer protein horseradish peroxidase (HRP). A demonstrable extracellular pathway into the central nervous system (CNS) is evident at the level of the subarachnoid space/pial surface. Immunoreaction products for the serum proteins and reaction product of intravenously administered HRP are identified over the entire pial surface, in the Virchow-Robin spaces and subpial cortical grey matter, and within phagocytes occupying the subarachnoid space/pial surface and perivascular clefts throughout the CNS. From specific circumventricular organs (e.g., median eminence, area postrema, subfornical organ), well known to lie outside the blood-brain barrier (BBB), each of the blood-borne proteins readily enters adjacent white and grey matter and the ventricular system for subsequent rostrocaudal labeling of the ependymal cell lining. Similar immunohistochemical and blood-borne HRP results are obtained in the CNS of the neonatal rat. Peroxidase delivered into the aorta of postmortem adult rats confirms the presence of a BBB in brain sites containing blood vessels impermeable to blood-borne HRP and the absence of a BBB in sites revealed as leaky to blood-borne HRP in the live rat. The results suggest blood-borne macromolecules, including those of the immune and complement systems, have potential widespread, extracellular distribution within the CNS and cerebrospinal fluid from sites deficient in a BBB (e.g., subarachnoid space/pial surface, circumventricular organs). These observations may have important clinical implications regarding experimental and pathologic autoimmune dysfunction within the CNS and impact on the interpretation of potential transcytosis of blood-borne peptides and proteins through the cerebral endothelium in vivo. A summary diagram of suspected extracellular and intracellular pathways circumventing the blood-brain fluid barriers is provided.

Animals↗
PubMed1995

Why do neural transplants survive? An examination of some metabolic and pathophysiological considerations in neural transplantation.

Neural transplantation continues to be a growing field that has advanced beyond animal experimentation and into the clinic where trials in patients with Parkinson's disease are moving forward (14, 30). The remarkable continuity of the brain grafting paradigm owes to the fact that experimentation and data collection may lend themselves to many disciplines and up-to-date technical analyses. Such procedures can represent significant advances in our knowledge of brain development and disorders but extensive investigation remains to be done to ascertain more precisely the cellular and molecular mechanisms by which neural grafts function. There are still many issues in transplantation that need to be resolved, not the least of which is cell survival and enhancement of graft functional capacity. There have been reports that only about 5-10% of dopaminergic neurons in mesencephalic grafts survive (22) and while the numbers of surviving neurons in cortical grafts is not known, recent studies have indicated that surviving neurons may have abnormal cellular aspects such as immature dendrites (32), inhibited axonal outgrowth (47), or reduced glycolytic activity (43). In the following commentary, possible cellular mechanisms of graft survival will be explored. It will be suggested that based on what is known about both cerebrovascular pathology and normal brain metabolic development, coupled with the mechanisms of graft vascularization, it is unlikely that neural grafts should survive or, at best, survive exhibiting only a modicum of activity. It will be further suggested that the answer "...because it is fetal brain ..." to the question--why (or how) do neural grafts survive?--is an inadequate and presently unexplained one.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗
PubMed1997

A statistical analysis of sequences of cardiac interbeat intervals does not support the chaos hypothesis.

Series of cardiac interbeat intervals were recorded in 34 mice and described using an original technique. The different intervals were divided into six classes according to their lengths. The different successions of pairs of intervals were counted with the help of a software programme devoted to lexical analysis. Most of the mice showed a very similar pattern of repeated sequences of interbeat intervals, statistically different from a random distribution. One-, two- or three-dimensional chaotic discrete maps were used to generate series that were then analyzed in the same way. They failed to give a distribution pattern of repeated sequences similar to the biological ones. On the contrary, series generated using a random component, and limited in amplitude by a feed-back correction occurring when the intervals reached a lower or an upper threshold, gave distributions of values very similar to biological ones. Moreover, the natural diversity observed between mice was easily reproduced by fluctuation of these different parameters. It is suggested that a very simple process, not completely deterministic, could better explain interbeat interval regulation in normal mice than did chaotic phenomena, which need complex biological processes.

Animals↗
PubMed1997

Use of serum markers to measure acute myocardial infarct size: lessons of a nonlinear dynamical model.

During acute myocardial infarction, dying cells in the myocardium release a number of chemicals that appear in the blood stream. By sampling the blood and assaying for these markers at intervals after infarction, we obtain a measure of the amount of myocardium lost, and the area under the marker concentration curve with time has been used to estimate the size of infarct. Because many of the important variables in this system are impossible to measure in patients and difficult to measure or control in experimental animals, simulations using a mathematical model provide an important way to learn about the infarct-marker relationship. This paper described a nonlinear dynamical model that allows for continuous changes in coronary flow as well as five key parameters during acute infarction. These five include amount of marker available for release from the myocardium, relative rate of release of marker from the myocardium, rate of degradation of marker in the myocardium, plasma volume, and relative rate of loss of marker from the plasma. By varying these five together with infarct size, simulations using the model demonstrate a noisy relationship between infarct size and area under the plasma marker curve. Mathematically, this noise implies that there is not a one-to-one mapping from marker curve to infarct size, and we should expect no more than a statistical mapping that fails to resolve all the uncertainty. The results do suggest that early reperfusion should reduce, rather than increase the noise in this relationship.

Biomarkers↗
PubMed2000

Characterizing the hemodynamic response: effects of presentation rate, sampling procedure, and the possibility of ordering brain activity based on relative timing.

Rapid-presentation event-related functional MRI (ER-fMRI) allows neuroimaging methods based on hemodynamics to employ behavioral task paradigms typical of cognitive settings. However, the sluggishness of the hemodynamic response and its variance provide constraints on how ER-fMRI can be applied. In a series of two studies, estimates of the hemodynamic response in or near the primary visual and motor cortices were compared across various paradigms and sampling procedures to determine the limits of ER-fMRI procedures and, more generally, to describe the behavior of the hemodynamic response. The temporal profile of the hemodynamic response was estimated across overlapping events by solving a set of linear equations within the general linear model. No assumptions about the shape were made in solving the equations. Following estimation of the temporal profile, the amplitude and timing were modeled using a gamma function. Results indicated that (1) within a region, for a given subject, estimation of the hemodynamic response is extremely stable for both amplitude (r(2) = 0.98) and time to peak (r(2) = 0.95), from one series of measurements to the next, and slightly less stable for estimation of time to onset (r(2) = 0.60). (2) As the trial presentation rate changed (from those spaced 20 s apart to temporally overlapping trials), the hemodynamic response amplitude showed a small, but significant, decrease. Trial onsets spaced (on average) 5 s apart showed a 17-25% reduction in amplitude compared to those spaced 20 s apart. Power analysis indicated that the increased number of trials at fast rates outweighs this decrease in amplitude if statistically reliable response detection is the goal. (3) Knowledge of the amplitude and timing of the hemodynamic response in one region failed to predict those properties in another region, even for within-subject comparisons. (4) Across subjects, the amplitude of the response showed no significant correlation with timing of the response, for either time-to-onset or time-to-peak estimates. (5) The within-region stability of the response was sufficient to allow offsets in the timing of the response to be detected that were under a second, placing event-related fMRI methods in a position to answer questions about the change in relative timing between regions.

Adolescent↗
PubMed2000

Nonlinear responses in fMRI: the Balloon model, Volterra kernels, and other hemodynamics.

There is a growing appreciation of the importance of nonlinearities in evoked responses in fMRI, particularly with the advent of event-related fMRI. These nonlinearities are commonly expressed as interactions among stimuli that can lead to the suppression and increased latency of responses to a stimulus that are incurred by a preceding stimulus. We have presented previously a model-free characterization of these effects using generic techniques from nonlinear system identification, namely a Volterra series formulation. At the same time Buxton et al. (1998) described a plausible and compelling dynamical model of hemodynamic signal transduction in fMRI. Subsequent work by Mandeville et al. (1999) provided important theoretical and empirical constraints on the form of the dynamic relationship between blood flow and volume that underpins the evolution of the fMRI signal. In this paper we combine these system identification and model-based approaches and ask whether the Balloon model is sufficient to account for the nonlinear behaviors observed in real time series. We conclude that it can, and furthermore the model parameters that ensue are biologically plausible. This conclusion is based on the observation that the Balloon model can produce Volterra kernels that emulate empirical kernels. To enable this evaluation we had to embed the Balloon model in a hemodynamic input-state-output model that included the dynamics of perfusion changes that are contingent on underlying synaptic activation. This paper presents (i) the full hemodynamic model (ii), how its associated Volterra kernels can be derived, and (iii) addresses the model's validity in relation to empirical nonlinear characterizations of evoked responses in fMRI and other neurophysiological constraints.

Brain↗
PubMed2002

Bayesian estimation of dynamical systems: an application to fMRI.

This paper presents a method for estimating the conditional or posterior distribution of the parameters of deterministic dynamical systems. The procedure conforms to an EM implementation of a Gauss-Newton search for the maximum of the conditional or posterior density. The inclusion of priors in the estimation procedure ensures robust and rapid convergence and the resulting conditional densities enable Bayesian inference about the model parameters. The method is demonstrated using an input-state-output model of the hemodynamic coupling between experimentally designed causes or factors in fMRI studies and the ensuing BOLD response. This example represents a generalization of current fMRI analysis models that accommodates nonlinearities and in which the parameters have an explicit physical interpretation. Second, the approach extends classical inference, based on the likelihood of the data given a null hypothesis about the parameters, to more plausible inferences about the parameters of the model given the data. This inference provides for confidence intervals based on the conditional density.

Bayes Theorem↗
PubMed2002

A model of the hemodynamic response and oxygen delivery to brain.

A recent nonlinear system by Friston et al. (2000. NeuroImage 12: 466-477) links the changes in BOLD response to changes in neural activity. The system consists of five subsystems, linking: (1) neural activity to flow changes; (2) flow changes to oxygen delivery to tissue; (3) flow changes to changes in blood volume and venous outflow; (4) changes in flow, volume, and oxygen extraction fraction to deoxyhemoglobin changes; and finally (5) volume and deoxyhemoglobin changes to the BOLD response. Friston et al. exploit, in subsystem 2, a model by Buxton and Frank coupling flow changes to changes in oxygen metabolism which assumes tissue oxygen concentration to be close to zero. We describe below a model of the coupling between flow and oxygen delivery which takes into account the modulatory effect of changes in tissue oxygen concentration. The major development has been to extend the original Buxton and Frank model for oxygen transport to a full dynamic capillary model making the model applicable to both transient and steady state conditions. Furthermore our modification enables us to determine the time series of CMRO(2) changes under different conditions, including CO(2) challenges. We compare the differences in the performance of the "Friston system" using the original model of Buxton and Frank and that of our model. We also compare the data predicted by our model (with appropriate parameters) to data from a series of OIS studies. The qualitative differences in the behaviour of the models are exposed by different experimental simulations and by comparison with the results of OIS data from brief and extended stimulation protocols and from experiments using hypercapnia.

Brain↗
PubMed2003

Ideal observer model for detection of blood perfusion and flow using ultrasound.

An ideal observer model is developed for the task of detecting blood perfusing or flowing through tissue. The ideal observer theory relies on a linear systems model that describes tissue and blood object functions and electronic noise as random processes. When aliasing is minimal, the system is characterized by a quantity similar to Noise-Equivalent Quanta used in photon imaging modalities. A simple 1-D model is used to illustrate the effect of the system and object parameters on task performance. Velocity and decorrelation are seen to be advantageous for detection. Aliasing can degrade performance. The ideal observer model provides a framework for assessing the performance of Power Doppler ultrasound systems, and may aid in their design.

Algorithms↗
PubMed2003

Meshfree representation and computation: applications to cardiac motion analysis.

For medical image analysis issues where the domain mappings between images involve large geometrical shape changes, such as the cases of nonrigid motion recovery and inter-object image registration, the finite element methods exhibit considerable loss of accuracy when the elements in the mesh become extremely skewed or compressed. Therefore, algorithmically difficult and computationally expensive remeshing procedures must be performed in order to alleviate the problem. We present a general representation and computation framework which is purely based on the sampling nodal points and does not require the construction of mesh structure of the analysis domain. This meshfree strategy can more naturally handle very large object deformation and domain discontinuity problems. Because of its intrinsic h-p adaptivity, the meshfree framework can achieve desired numerical accuracy through adaptive node and polynomial shape function refinement with minimum extra computational expense. We focus on one of the more robust meshfree efforts, the element free Galerkin method, through the moving least square approximation and the Galerkin weak form formulation, and demonstrate its relevancy to medical image analysis problems. Specifically, we show the results of applying this strategy to physically motivated multiframe motion analysis, using synthetic data for accuracy assessment and for comparison to finite element results, and using canine magnetic resonance tagging and phase contrast images for cardiac kinematics recovery.

Algorithms↗
PubMed2003

Construction of a statistical model for cardiac motion analysis using nonrigid image registration.

In this paper we present a new technique for tracking the movement of the myocardium using a statistical model derived from the motion fields in the hearts of several healthy volunteers. To build the statistical model we tracked the motion of the myocardium in 17 volunteers using a nonrigid registration technique based on free-form deformations and mapped the motion fields obtained into a common reference coordinate system. A principal component analysis (PCA) was then performed on the motion fields to extract the major modes of variation in the fields between the successive time frames. The modes of variation obtained were then used to parametrize the free-form deformations and build our statistical model. The results of using our model to track the motion of the heart in normal volunteers are also presented.

Algorithms↗
PubMed2003

Fast tracking of cardiac motion using 3D-HARP.

MR tagging is considered as a valuable technique to evaluate regional myocardial function quantitatively and noninvasively, however the cumbersome and time-consuming post-processing procedures for cardiac motion tracking still hinder its application to routine clinical examination. We present a fast and semiautomatic method for tracking 3D cardiac motion from short-axis (SA) and long-axis (LA) tagged MRI images. The technique, called 3D-HARP (HARmonic Phase), is based on the HARP method and extends this method to track 3D motion. A material mesh model is built to represent a collection of material points inside the left ventricle (LV) wall. The phase time-invariance property of material points is used to track the mesh points. For a series of 9 timeframe MRI images, the total time required for initializing settings, building the mesh, and tracking 3D cardiac motion is approximately 10 minutes. Further analysis of Langrangian strain and twist angle demonstrates that during systole, the lateral LV wall shows a greater strain values than the septum and the SA slices from the base to the apex show a gradual change in twist pattern.

Algorithms↗
PubMed2003

Estimation of the Hemodynamic Response Function in event-related functional MRI: directed acyclic graphs for a general Bayesian inference framework.

A convenient way to analyze BOLD fMRI data consists of modeling the whole brain as a stationary, linear system characterized by its transfer function: the Hemodynamic Response Function (HRF). HRF estimation, though of the greatest interest, is still under investigation, for the problem is ill-conditioned. In this paper, we recall the most general Bayesian model for HRF estimation and show how it can beneficially be translated in terms of graphical models, leading to (i) a clear and efficient representation of all structural and functional relationships entailed by the model, and (ii) a straightforward numerical scheme to approximate the joint posterior distribution, allowing for estimation of the HRF, as well as all other model parameters. We finally apply this novel technique on both simulations and real data.

Adolescent↗
PubMed2003

Mixed dishomogeneous hemorrhagic brain contusions. Mapping of cerebral blood flow.

The aim of the study was to verify whether regional cerebral blood flow (rCBF) was distributed centrifugally in traumatic hemorrhagic contusions with multiple cores within an oedematous area. Seventeen traumatic brain contusions, from 14 patients with severe head injury (GCS < 9), were analyzed during 39 Xenon-enhanced computerized tomography (Xe-CT) studies. The CBF was measured in 3 concentric regions of interest (ROls): the hemorrhagic core, the intracontusional oedematous low density area and a 1 cm rim of pericontusional normal-appearing brain tissue surrounding the contusion. Differences between rCBFs in the three ROIs were found (p < 0.0001). rCBF in both the hemorrhagic core (21.4 +/- 19.4 ml/ 100gr/min) and the intracontusional low density area (28.4 +/- 19 ml/100gr/min) were lower than rCBF in pericontusional normal-appearing area (41.9 +/- 16 ml/100gr/min) (p < 0.0001). No significant differences were found between rCBF measured in the hemorrhagic core and intracontusional low density area (p = 0.184). Our study suggests that in the mixed density contusions with multiple hemorrhagic cores, the CBF is concentrically distributed, improving from the core to the periphery.

Adult↗
PubMed1996

A mechanical model for the formation of vascular networks in vitro.

Endothelial cells, when cultured on gelled basement membrane matrix exert forces of tension through which they deform the matrix and at the same time they aggregate into clusters. The cells eventually form a network of cord-like structures connecting cell aggregates. In this network, almost all of the matrix has been pulled underneath the cell cords and cell clusters. This phenomenon has been proposed as a possible model for the growth and development of planar vascular systems in vitro. Our hypothesis is that the matrix is reorganized and the cellular networks form as a result of traction forces exerted by the cells on the matrix and the latter's elasticity. We construct and analyze a mathematical model based on this hypothesis and examine conditions necessary for the formation of the pattern. We show cell migration is not necessary for pattern formation and that isotropic, strain-stimulated traction is sufficient to form the observed patterns.

Animals↗