Tricuspid Chordae Tendineae Mechanics: Insertion Site,Leaflet, and Size-Specific Analysis and Constitutive Modelling

Background: Tricuspid valve chordae tendineae play a vital role in our cardiovascular system. They function as “parachute cords” to the tricuspid leaflets to prevent prolapse during systole. However, in contrast to the tricuspid annulus and leaflets, the tricuspid chordae tendineae have received little attention. Few previous studies have described their mechanics and their structure-function relationship. Objective: In this study, we aimed to quantify the mechanics of tricuspid chordae tendineae based on their leaflet of origin, insertion site, and size. Methods: Specifically, we uniaxially stretched 53 tricuspid chordae tendineae from sheep and recorded their stress-strain behavior. We also analyzed the microstructure of the tricuspid chordae tendineae based on two-photon microscopy and histology. Finally, we compared eight different hyperelastic constitutive models and their ability to fit our data. Results: We found that tricuspid chordae tendineae are highly organized collageneous tissues, which are populated with cells throughout their thickness. In uniaxial stretching, this microstructure causes the classic J-shaped nonlinear stress-strain response known from other collageneous tissues. We found differences in stiffness between tricuspid chordae tendineae from the anterior, posterior, or septal leaflets only at small strains. Similarly, we found significant differences based on their insertion site or size also only at small strains. Of the models we fit to our data, we recommend the Ogden two-parameter model. This model fit the data excellently and required a minimal number of parameters. For future use, we identified and reported the Ogden material parameters for an average data set. Conclusion: The data presented in this study help to explain the mechanics and structure-function relationship of tricuspid chordae tendineae and provide a model recommendation (with parameters) for use in computational simulations of the tricuspid valve.

     

Bios data analyzer

The Bios Data Analyzer (BDA) is a set of computer programs (CD-ROM, in Sabelli et al., Bios. A Study of Creation, 2005) for new time series analyses that detects and measures creative phenomena, namely diversification, novelty, complexes, nonrandom complexity. We define a process as creative when its time series displays these properties. They are found in heartbeat interval series, the exemplar of bios .just as turbulence is the exemplar of chaos, in many other empirical series (galactic distributions, meteorological, economic and physiological series), in biotic series generated mathematically by the bipolar feedback, and in stochastic noise, but not in chaotic attractors. Differencing, consecutive recurrence and partial autocorrelation indicate nonrandom causation, thereby distinguishing chaos and bios from random and random walk. Embedding plots distinguish causal creative processes (e.g. bios) that include both simple and complex components of variation from stochastic processes (e.g. Brownian noise) that include only complex components, and from chaotic processes that decay from order to randomness as the number of dimensions is increased. Varying bin and dimensionality show that entropy measures symmetry and variety, and that complexity is associated with asymmetry. Trigonometric transformations measure coexisting opposites in time series and demonstrate bipolar, partial, and uncorrelated opposites in empirical processes and bios, supporting the hypothesis that bios is generated by bipolar feedback, a concept which is at variance with standard concepts of polar and complementary opposites.