Miroslav Holeček

Biomedical Thermodynamics and Implantology Aspects of Biocompatible Glass-Ceramics and Otherwise Modified Inorganic Materials and Surfaces

Some historical and recent attitudes aimed to bioactive inorganic materials are reviewed. The theory of bridging and non-bridging oxygen is reconsidered as well as the acid and alkali treatment of titanium surface necessary to achieve a good osteointegration. Some theoretical models to characterize mechanical properties are also reviewed.

Scale continuum approach in biomechanics: a simple simulation of a microstructural control of tissues' stiffness

We construct a simple model of an elastic material whose stiffness can be effectively controlled by an appropriately chosen set of microstructural parameters. The model is based on ideas of the scale-dependent continuum description and might play an important role in modelling of muscle tissues in biomechanics.

Self-measurability in rapid thermal processes

The dynamics of heat conduction may be interpreted (at least in special situations) as the process in which small pieces of media measure a delayed temperature of their surroundings. This “self-measurability” is a very useful concept when interpreting measurements of temperature in rapid thermal processes, e.g., for the use of thermal analysis. The self-measurability condition describes the temperature equilibrating in much general situations than the classical Fourier law. As an example, we analyze the rapid thermal process on a metal sample when the electron gas is immediately heated while the metal lattice remains cold.

Modelling the Smooth Muscle Tissue as a Dissipative Microstructured Material

A highly simplified model of the smooth muscle tissue is formed to study a special form of viscous effects occurring in living tissues. Namely, when a sample of the tissue is deformed, the fluid in the extracellular matrix has to move because it is extruded from one places into others. This phenomenon contributes into the global viscous properties of the tissue. That contribution is studied by means of a simplified model of smooth muscle tissue regarded as a regular lattice of elastic inclusions. An expression of the dissipation due to the fluid flow around the inclusions is found out. At the macroscopic (continuum) level, the idea of constitutive model with internal variables is used. As a result, a differential form of the viscoelastic behaviour is derived. The model is solved numerically and fitted by a confrontation with experiment performed on gastropod smooth muscle tissue.

Stereological Assessment, Mechanical Measurement and Computer Modelling of Smooth Muscle

We used mechanical measurements and unbiased statistical morphometry in order to supply the computer model of smooth muscle cells (SMC) and collagen connective tissue of a gastropod Arion sp. with sufficient input data. We identified the elasticity modulus for both living (34 kPa) and formalin-fixed samples (440 kPa). The relative volume proportion of SMC was 57.8%, their numerical density was 425 925 mm-3, surface density of SMC was 405.9 mm-1 and the mean cell volume was 1 358 .m3.

Scale Axis, Fractals and Some Thermal Phenomena

In this paper, the idea of an objective scale axis enriching Nature with a new dimension is explicated and illustrated on the problem of heat conduction. Physical description of Nature thus has to be formulated on individual scale levels parametrized by points of the scale axis), space and time are intrinsic parameters of each level. A ‘global’space-time then becomes a useful construction expressing a possibility of a scale-independent description. Consequently, the cases in which such a description is not possible (e.g. the problem of thermal waves) might lead to a contradiction with the concept of a global space-time, which may manifest itself by a presence of some fractal structures.

Some Aspects of Vitrification, Amorphisation and Disordering and the Generated Extent of Nano-Crystallinity

Historically, glass is often viewed as a remarkable translucent substance though usually made from the simplest raw materials upon the effect of firing. Nature, itself, is the best instance to learn how different temperature changes can provide various glassy states, altering from very slow rates occurring within geological time scales (e.g. obsidians – glassy volcanic rocks consisting of natural acidic silicate glasses) to extremely fast, occurring as a result of fast energetically driven collapse (e.g., by impact of meteorites, yielding melted droplets then cooled to various tektites). Mimicking evolution, however, man became responsible for the creation of further families of a wide variety of glassy and amorphous materials (geopolymers), which have gradually appeared through human creativity, particularly during last 100 years. Properly chosen procedure of rapid extraction of heat (often called quenching) turned up to be a efficient route for successful glass-formation (vitrification, as a repeatable process) of almost all substances (thus allowing for the preparation of glasses from different sorts of various inorganic materials, including metals) in contrast to the traditional chemical approach, seeking just for an appropriate composition to vitrify under a customary self-cooling procedure [1,2].

The simple model of cell prestress maintained by cell incompressibility

Living cells are reinforced by polymer fibers (the so-called cytoskeleton) which are responsible for their mechanical behaviour. There are many evidences that these fibres are prestressed without an external load. To include this prestress into mechanical models of living tissues is not an easy task. We propose an approach in which the intracellular prestress is maintained by the incompressibility of cells. A simple illustrative structure is studied in order to determine the dependence of stiffness on the level of prestress. Some macroscopic models of living tissues with prestressed cells are formulated. The results show a clear dependence of the macroscopic mechanical response on the level of prestress at microscale. The model exhibits some features of living cells (prestress-induced stiffening, strain hardening).

What Is the Physical and Operational Meaning of Temperature and Its Self-Measurability During Unsteady Thermal Processes Within Thermodynamic Concepts?

Historical maturity of terms temperatura and thermoscope is sketched. Problem of temperature definition and observation (measurement) is studied in detail. Temperature is a typical averaged quantity clear-cut under equilibrium only. A self-measurability condition is implied, and some consequences are outlined. Physical and operational meaning of temperature and its self-measurability during unsteady thermal processes is analysed. Particular case of thermal analysis often idealized under constant temperature changes is thermodynamically examined. For extreme temperature changes as that during quenching, a novel term “tempericity” is proposed. Branched view to the spheres of alternative thermodynamics is shown locating thermal analysis as thermotics and quenching as thermokinetics. Non-equilibrium thermodynamics under a non-constant rate of temperature changes is analysed. Practical aspects of non-equilibrium temperatures due to heat inertia and thermal gradients are specified including cases of modulated experiments. Textbook thermodynamic description under the perceptible impact of second temperature derivatives becomes ambiguous and associated tabular values are unclear. Thermotics, thermokinetics, and the validity of the first and second thermodynamic laws are discussed bringing another dimension of the thermodynamic legacy. The concept of equivalence of work and heat is questioned. The chapter contains 126 references.

GRID CONTINUUM DESCRIPTION: A NOVEL APPROACH IN TWO-SCALE HYPERELASTICITY

In this paper, a generalization of the standard continuum theory is proposed in order to describe materials with a more complex microstructure. The key idea consists in dividing the studied body onto a set of small but finite disjunct cells whose boundaries form what is called the grid. The state of the grid is described by macroscopically smooth functions. The interior of each cell, on the other hand, is described by an additional field that may be discontinuous or highly oscillating. Such an approach allows us to include non-trivial effects of the microstructure in resulting material models of macroscopic bodies. The theory is illustrated on two examples of two-scale hyperelastic models. The first one represents a crystalline material with a failure of the Cauchy-Born rule. The second one, motivated by an arrangement of soft tissues, includes prestress at the reference state as well as non-trivial response caused by a collapse of micro-constituents. Transparent physical meaning of several material parameters of the latter model provides for their direct identification instead of the least-squares fitting.