Mechanisms for discordant alternans.

INTRODUCTION: Discordant alternans has the potential to produce larger alternans of the ECG T wave than concordant alternans, but its mechanism is unknown. METHODS AND RESULTS: We demonstrate by one- and two-dimensional simulation of action potential propagation models that discordant alternans can form spontaneously in spatially homogeneous tissue through one of two mechanisms, due to the interaction of conduction velocity and action potential duration restitution at high pacing frequencies or through the dispersion of diastolic interval produced by ectopic foci. In discordant alternans due to the first mechanism, the boundaries marking regions of alternans with opposite phase arise far from the stimulus site, move toward the stimulus site, and stabilize. Dynamic splitting of action potential duration restitution curves due to electrotonic coupling plays a crucial role in this stability. Larger tissues and faster pacing rates are conducive to multiple boundaries, and inhomogeneities of tissue properties facilitate or inhibit formation of boundaries. CONCLUSION: Spatial inhomogeneities of electrical restitution properties are not required to produce discordant alternans.

Alternans and the onset of ventricular fibrillation.

Ventricular fibrillation (VF) remains a major cause of death in the industrialized world. Alternans (a period-doubling bifurcation of cardiac electrical activity) have recently been causally linked to the progression from ventricular tachycardia (VT) to VF, a more spatiotemporally disorganized electrical activity. In this paper, we show how alternans and thus VT degenerate to chaos via multiple, specific dynamical routes, largely associated with spatial components of VF dynamics, explaining failures of many recently proposed antiarrhythmic drugs. Identification of dynamical mechanisms for the onset of VF should lead to the design of future experiments and consequently to more effective antiarrhythmic drugs.

Efficient integration of a realistic two-dimensional cardiac tissue model by domain decomposition.

The size of realistic cardiac tissue models has been limited by their high computational demands. In particular, the Luo-Rudy phase II membrane model, used to simulate a thin sheet of ventricular tissue with arrays of coupled ventricular myocytes, is usually limited to 100 x 100 arrays. We introduce a new numerical method based on domain decomposition and a priority queue integration scheme which reduces the computational cost by a factor of 3-17. In the standard algorithm all the nodes advance with the same time step delta t, whose size is limited by the time scale of activation. However, at any given time, many regions may be inactive and do not require the same small delta t and consequent extensive computations. Hence, adjusting delta t locally is a key factor in improving computational efficiency, since most of the computing time is spent calculating ionic currents. This paper proposes an efficient adaptive numerical scheme for integrating a two-dimensional (2-D) propagation model, by incorporating local adjustments of delta t. In this method, alternating direction Cooley-Dodge and Rush-Larsen methods were used for numerical integration. Between consecutive integrations over the whole domain using an implicit method, the model was spatially decomposed into many subdomains, and delta t adjusted locally. The Euler method was used for numerical integration in the subdomains. Local boundary values were determined from the boundary mesh elements of the neighboring subdomains using linear interpolation. Because delta t was defined locally, a priority queue was used to store and order next update times for each subdomain. The subdomain with the earliest update time was given the highest priority and advanced first. This new method yielded stable solutions with relative errors less than 1% and reduced computation time by a factor of 3-17 and will allow much larger (e.g., 500 x 500) models based on realistic membrane kinetics and realistic dimensions to simulate reentry, triggered activity, and their interactions.

Ventricular fibrillation: one spiral or many?

Ventricular fibrillation is the major cause of sudden cardiac death, the leading cause of death in the industrialized world; however, the mechanisms for its onset are not well understood. To further understand the dynamics of fibrillation at and near its onset, we compared spatial and temporal variability of mean interactivation intervals in a stable canine model for ventricular fibrillation. Temporal variability was very small, suggesting that the relevant physiological parameters remained constant during our experiments. Spatial variability was usually significantly larger and appeared incompatible with the dynamics of a single, meandering spiral wave. This confirmed recent results that a single spiral wave cannot generate ventricular fibrillation. Thus the onset of fibrillation is a multistage process, with spiral-wave breakdown providing a crucial step in the quasi-periodic route to fibrillation.

Expression of interleukin-1beta in human breast carcinoma.

BACKGROUND: Interleukin 1beta (IL-1beta) is a multifunctional cytokine that up-regulates the inflammatory response. It is not known whether IL-1beta plays a major role in human malignancy. To determine whether IL-1beta might be involved in breast carcinoma progression, the authors measured the IL-1beta content in tissue extracts from >200 invasive breast carcinomas and smaller numbers of ductal carcinoma in situ (DCIS) and benign lesions. METHODS: IL-1beta content was measured by an enzyme-linked immunoadsorbent assay and analyzed to determine whether these values were correlated with the contents of scatter factor (SF) (an invasogenic and angiogenic cytokine), von Willebrand's factor (VWF) (a marker of endothelium), thrombospondin-1 (TSP1) (an antiadhesive and antiangiogenic glycoprotein), and tumor necrosis factor-alpha (TNF alpha) (another proinflammatory cytokine). Studies were also performed to determine whether IL-1beta content was correlated with other pathologic and immunochemical variables that have been utilized or proposed as prognostic indicators for breast carcinoma. RESULTS: The most important findings of these studies were: 1) immunoreactive IL-1beta was detected in approximately 90% of invasive breast carcinomas; 2) IL-1beta levels were significantly higher in invasive carcinomas than in a group of DCIS and benign lesions; 3) high IL-1beta content in invasive carcinomas was significantly associated with higher contents of SF, VWF, and TSP1, but not TNF alpha; and 4) there was a trend toward higher IL-1beta content in invasive carcinomas with a group of other parameters that suggest a biologically more aggressive tumor (estrogen receptor negativity, high tumor grade, p53 positivity, and bcl-2 negativity); and the proportion of invasive tumors with these characteristics was significantly increased in a subgroup of tumors having very high IL-1beta content. The authors also found a correlation between high IL-1beta content and CD68 positivity, suggesting that macrophages may account for some of the IL-1beta present in human breast carcinoma tissue. CONCLUSIONS: These findings suggest that significant titers of IL-1beta are present within the microenvironment of most breast carcinomas and that a high IL-1beta content is often associated with tumor invasiveness and with other pathologic features suggestive of an aggressive tumor biology.

Spectral analysis of demodulated ultrasound returns: detection of scatterer periodicity and application to tissue classification.

Ultrasound returns from tissue display variations in amplitude on several spatial scales. Although large-scale variations result from factors such as attenuation, variations on smaller scales are caused by tissue characteristics such as variations in scatterer spacing and reflectance. These small scale variations cause a corresponding variation in the amplitude of the ultrasound return. A simple and direct method for detecting and quantifying periodicity in these variations in the presence of attenuation is described. The radiofrequency ultrasound return is first demodulated by full-wave rectification. The normalized power spectrum of the demodulated return then yields an index that we call the relative Fourier energy. Both computer simulations and in vitro experiments were performed in order to study how relative Fourier energy performed in discriminating between periodic and random scatterer distributions. Computer simulations demonstrated significant differences between the returns from periodic and random scatterer distributions. Ultrasound returns from aortic tissue yielded a relative Fourier energy index that was significantly different between normal vs. atherosclerotic tissue (normal: 0.868 +/- 0.076, mean +/- s.d., fibrofatty plaque: 0.705 +/- 0.109, p < 0.01 vs. normal, calcified plaque: 0.753 +/- 0.078, p < 0.01 vs. normal). In contrast, no difference was found in comparisons of overall reflectance.

Scatter factor protein levels in human breast cancers: clinicopathological and biological correlations.

Scatter factor (SF) is an invasogenic and angiogenic cytokine the cellular receptor of which is encoded by a proto-oncogene (c-met). We measured the immunoreactive SF content (nanograms of SF per milligram of protein) in tissue extracts from 166 breast cancers and correlated the values with various known prognostic parameters. Invasive cancers had nearly four times greater SF content than did ductal carcinoma in situ, and the difference was statistically significant (P < 0.02, two-tailed t-test). However, there were no significant differences in SF content among different histological types of invasive cancer. Invasive cancers that had spread to axillary lymph nodes exhibited higher SF content than did invasive cancers without regional spread (P < 0.02), but the difference in SF content between node-positive and node-negative tumors was not as great as that between invasive and ductal carcinoma in situ tumors. There was a trend toward increased SF content in larger primary tumors as compared with smaller tumors, but statistical comparison revealed borderline significance (0.05 < P < 1.0). There was no significant correlation between SF content and other parameters, including estrogen receptor, progesterone receptor, DNA ploidy, S phase, or Scarff-Bloom-Richardson score. We also measured the content of von Willebrand factor (a marker of blood vessels) and interleukin-1 beta (a pro-inflammatory cytokine) in the same tumor extracts. SF content showed a strong positive correlation with von Willebrand factor content (P < 0.001) but did not appear to be correlated with interleukin-1 beta. These findings suggest that SF is correlated with several other clinicopathological indicators of aggressive tumor behavior, consistent with the hypothesis that SF is a biological factor that may play a role in breast cancer pathogenesis.

Nonlinear dynamics in ventricular fibrillation.

Electrogram recordings of ventricular fibrillation appear complex and possibly chaotic. However, sequences of beat-to-beat intervals obtained from these recordings are generally short, making it difficult to explicitly demonstrate nonlinear dynamics. Motivated by the work of Sugihara on atmospheric dynamics and the Durbin-Watson test for nonlinearity, we introduce a new statistical test that recovers significant dynamical patterns from smoothed lag plots. This test is used to show highly significant nonlinear dynamics in a stable canine model of ventricular fibrillation.

The spatial distribution of pancreatic islets follows a universal power law.

In a previous report we quantified the apparently complex and irregular distribution of pancreatic islets in the guinea pig by showing that they formed a set of cluster or correlation dimension approximately 2.5. Here we show that this distribution holds in a wide range of mammalian species and through ontogenetic development in the guinea pig. These results strongly suggest that islet formation follows an iterative or fractal rule which is universal among mammals.

Statistical geometry of pancreatic islets.

Quantitative histomorphometric studies of the dynamics of growth and development of pancreatic islets in normal and pathological states pose substantial methodological and conceptual problems. We address these problems with the geometry of random fractals, and apply our methods to the analysis of islet regeneration in the alloxan-treated guinea-pig. In both experimental islet-regenerated and control animals, islet centres are found to cluster in similar fractal subsets of dimension strictly less than 3, in agreement with the postulated origin of islets along a system of ductules, and suggesting that regeneration follows the same mathematical dynamics as original islet formation.

Remarks on population planning and control.

We investigate the use of control theory in population planning and show how the use of age at first birth, birth interval, and sex ratio as control variables leads to a practical, fault tolerant approach to population planning and control.

Evolutionary learning and hierarchical Markov systems.

The observation is made that various forms of evolutionary learning systems and classical evolutionary processes can be formally described as hierarchical systems of Markov processes. This leads to a simplification of issues such as convergence criteria and limiting behavior of such systems. The hierarchical structures in question are derived from the notion of rules and meta-rules for moving on graphs studied previously.

Sixty million connections per second.

The purpose of this note is to report processing in a feedforward neural network at a peak speed of 59.9 million connections per second. The network algorithm was coded in Fortran and executed on a CRAY XMP-1, a high speed general purpose vector machine.

Sex and computing.

The computational power of asexual and sexual reproduction is explored with the conclusion that sexual reproduction probably offers significantly greater computational power. This at least partially explains the evolution of sex.

Low dissipation computing in biological systems.

Biological systems frequently need to solve many computationally hard decision and optimization problems. The solution of these problems by digital computers as presently understood requires exponentially large energy dissipation. This severely restricts the ability of digital computers to attack such problems. We shall show that only polynomial dissipation is required to solve these problems adequately by "physical annealing", as realized in the genetic system, making these problems tractable energetically.

Stability of large systems.

We use the May-Wigner Stability Theorem (Geman (1984) preprint, Brown University; Hastings (1984) preprint, Hofstra University), to study the Lyapunov and structural stability of "real" large systems. Here are our new main results. For large systems which satisfy certain natural scaling relations (Harrison, Am. Natur., 113 (1979) 659; May (1979) Blackwell Scientific, Oxford), Lyapunov stability tends to increase with increasing complexity. However, at least one aspect of structural stability decreases: both competitive and cooperative effects can rapidly destabilize such a system. Finally, we observe that random matrices which satisfy the hypotheses and stability criterion of the May-Wigner theorem are asymptotically of the form 'rotation followed by multiplication by lambda,lambda less than 1'. This allows an easy analysis of the effects of noise in these systems. We conclude by briefly discussing applications to analysis of stability of systems such as the world economy, power networks, and the immune system.

Stochastic information processing biological systems.

We propose a simple, biochemically-based model for stochastic information processing in brain, genetic, and, consequently, evolutionary modelling. The essential features of reaction-diffusion processes are realized by intrinsically stochastic probabilistic automata (Shannon and Weaver, 1948; see also Ashby, 1958, von Neumann, 1966; Burks, 1970; Paz, 1971) whose definition extends that of classical automata. (Classical automata are deterministic; earlier work on probabilistic automata focused on error correction and at least approximating deterministic behavior.) We call these probabilistic automata biochemical to emphasize the role of intrinsically stochastic process in biological information processing. Our model yields descriptions of gradualism (Conrad, 1974), learning, and apparent inefficiencies in the brain, and partially resolves the near impossibility of simultaneous point mutations (Conrad, 1972, 1978) in genetics. The genetic model implies an evolutionary dynamics of punctuated equilibria (Gould and Eldredge, 1977).

Time scales, persistence and patchiness.

We consider competition in patch-dynamical and more general diffusion-extinction models. These models identify three time scales in ecology. We begin with a reformulation of Levin's 1978 basic model, using a geometric description of diffusion. As in Levin's model, diffusion drives short-term dynamics, and longer-term dynamics depends upon a diffusion-extinction ratio; maximizing this ratio is shown to be an Evolutionarily Stable Strategy. Over still longer times, the effect of organisms upon their environments becomes paramount. We use Mandelbrot's 1977 fractals to develop these models, and thus relate persistence with relative patchiness. Finally, we propose a numerical measure, the fractal exponent H, of successional stage.