Structure and reactivity of water at biomaterial surfaces

Since its coming of age in the mid 1960s, continuum biomechanics has contributed much to our understanding of human health as well as to disease, injury, and their treatment. Nevertheless, biomechanics has yet to reach its full potential as a consistent contributor to the improvement of health–care delivery. Because of the inherent complexities of the microstructure and biomechanical behaviour of biological cells and tissues, there is a need for new theoretical frameworks to guide the design and interpretation of new classes of experiments. Because of continued advances in experimental technology, and the associated rapid increase in information on molecular and cellular contributions to behaviour at tissue and organ levels, there is a pressing need for mathematical models to synthesize and predict observations across multiple length– and time–scales. And because of the complex geometries and loading conditions, there is a need for new computational approaches to solve the boundaryand initial–value problems of clinical, industrial, and academic importance. Clearly, much remains to be done. The purpose of this paper is twofold: to review a few of the many achievements in the biomechanics of soft tissues and the tools that allowed them, but, more importantly, to identify some of the open problems that merit increased attention from those in applied mechanics, biomechanics, mathematics and mechanobiology.

Review Paper: Continuum biomechanics of soft biological tissues

2 Einstein's Heuristics. 2.1 Einstein's Appraisal of Classical Physics. 2.2 The Discovery of Special Relativity Theory: Removal of the Asymmetry between Classical Mechanics and Electrodynamics. 2.3 The Heuristic Superiority in 7905 of the Relativity Programme: Einstein's Covariance versus Lorentz's Ether. The Power of Einstein's Heuristics: Derivation of a New Relativistic Law of Motion and of E = me. 3 Einstein's Programme Supersedes Lorentz's. 3.1 The Continuity between the Special and General Theories of Relativity. 3.2 The Successful Explanation of the Perihelion of Mercury and its Role in the Further Development of the General Theory.

Why did Einstein's programme supersede lorentz's? (I)

The magnetic field of massive rotating bodies

Summary. 
(a) The problem of temperature coefficients in biology was initiated by chemists and has suffered from the beginning from this circumstance. Attempts to apply chemical temperature-velocity formulae (the Q10 rule and the Van't Hoff-Arrhenius law) to biological processes failed, because none of the temperature constants used in chemistry (Q10, μ) can be said to hold good in biological reactions. It is shown that the value of μ in the Van't Hoff-Arrhenius law varies, in biological processes and in simple enzyme reactions, with the temperature to about the same extent and for the same reasons as tlie value of Q10, these constants being closely related for the zone of biokinetic temperatures. The use of the Van't Hoff-Arrhenius formula in biology, sponsored of late mainly by Crozier, is therefore of no greater advantage than the use of the simpler Q10 formula, both of them presenting the same low degree of accuracy in biology. A new empirical temperature formula, proposed by the writer, is shown to agree in many instances with sufficient accuracy with obscrved data. The constant of this formula (b) remains independent of temperature even in those cases in which the constants Q10 and μ show a steady decrease in value as the temperature increases. When b= 1, the formula becomes identical with the linear relation of Krogh and with the rule of thermal summation, which are thus special instances of a more general interrelation between tcmperature and the velocity of biological phenomena.

None of the temperature formulae proposed up to the present in biology can be said to hold good in every case, nor is there a rational temperature law in biology. Even the constants Q10, and μ are nothing more than empirical and descriptive quantities, which might be used with this restriction so far as they remain relatively constant for the temperatures concerned.

(b) The reason for which the velocity of biological phenomena is influenced by temperature in a way widely different from that commonly found in chemical reactions seems to lie in tlie heterogeneous nature of living matter and in the relatively high viscosity of the reacting protoplasmic phases. Even in enzyme reactions the formulae cited above proved unsatisfactory and one cannot expect that formulae which are not accurate for enzyme reactions should yield better results in biological processes.

Some earlier attempts at a classification of biological phenomena and the undcrlying “master processes” by the aid of the temperature coefficient Q10, as well as a more recent attempt by means of the temperature characteristics μ (Crozier), has necessarily failed for a double reason. First, the formulae used up to now in biology are so inaccurate that they do not permit of any serious analysis. “Breaks” in biological temperature curves at definite “critical” temperatures (Crozier) are artefacts, due to improper use of the chemical temperature formulae in biology, and they do not exist in reality. Second, it is highly probable that diffusion is always or almost always the master process in biological reactions and that thus the viscosity of reacting protoplasmic phases is always or almost always the limiting factor which determines the velocity of biological processes. This thesis is supported by some experimental data from the physico-chemical literature. If this is so, then the temperature coefficients of biological phenomena are merely temperature coefficients of the viscosity of reacting protoplasmic phases.

(c) If this hypothesis is correct, it follows that temperature coefficients of analogous biological processes are indicators of protoplasmic viscosity. This is made probable by an analysis of J. Loeb's data on the viscosity of gelatin solutions, which shows that the temperature coefficient of viscosity regularly increases with concentration.

The hypothesis can be tested on abundant numerical material, furnished by numerous investigators. It is shown that the temperature coefficients increase when a rise in protoplasmic viscosity may be assumed to take place. This is illustrated by the following facts: (1) the temperature coefficients of the heart-beat frequency in various animals, of the developmental processes in vertebrates and invertebrates, and of the metabolic rate of animals and plants vary systematically with the age of the organisms; (2) insect development in dry air gives a higher temperature coefficient than when it takes place in a humid atmosphere; (3) the temperature coefficient of successive periods of the mitotic process changes in accordance with the variations of protoplasmic viscosity which have been shown to take place during mitosis.

Temperature coefficients in biology

In an elastic balloon the relation between the internal excess pressure and the tension of the wall can be readily calculated if we assume that the balloon is spherical and that the material is homogeneous and of negligible weight. If we suppose the balloon divided into two hemispheres by a plane horizontal partition, the area of this partition will be πr 2 and the downward force on the upper surface due to the excess pressure p will be πr 2 p . The balloon wall meets the partition at right angles along a length 2 πr . Hence if T is the tension in the wall, the upward force exerted by this tension on the partition is 2 πr T. But as these two forces must be equal we have πr 2 p = 2 π T r , so that p = 2 T/ r . (1) When such a balloon is filled without stretching the wall the pressure inside is equal to the prevailing atmospheric, and the radius r may be termed the initial radius. If we assume that the balloon is perfectly obedient to Hooke's law, then T1 = K ( r 1 — r )/ r ; but from (1) we learn that p 1 = 2 T1/ r 1; hence, by substitution, p 1 = 2 K/ r —2 K/ r 1, or r 1 (2K/ r — p 1) = 2 K. (2)

The Elasticity of Rubber Balloons and Hollow Viscera

IN recent issues of NATURE and the Philosophical Magazine, Profs. Larmor and Fitzgerald and Lord Kelvin have expressed themselves as if satisfied that the negative result of the celebrated Michelson and Morley experiment as to a relative motion of earth and ether is genuinely decisive, and as if the only present escape from the dilemma between this experiment and the bulk of the evidence which necessitates a relative motion of earth and ether is to be found in a possible change of the dimensions of bodies caused by changes in their motion through ether.

Relative Motion of the Earth and the Ether

T HE electrical properties of nerve have received so much attention that it is necessary to preface the following seemingly purely mechanical theory of the propagation of nerve excitation with a few words of explanation. I have recently, in the “ Philosophical Magazine,” shown that cohesion and rigidity are essentially electrical properties of matter; so that in the tracing of the “ conductivity ” of nerve to the rigidity of its substance, as I propose to do, the electric properties of nerve are not ignored, but their principal effect is conceived in the simpler and more direct terms of mechanics instead of the ultimate electrical ones. A complete electrical theory of elasticity will have to account for the piezoelectricity of quartz, as well as for the electrical properties of nerve. Two lines of thought lead to a conception of the possible importance of rigidity in the phenomena of nerve and muscle. In the first place it is known that a jelly offers but little more resistance to the passage of a small ion than does pure water at the same temperature, despite the enormous difference in the large scale viscosities of the two media. This proves that in a jelly the molecules of the gelatine form a mesh dividing the jelly into compartments with net-work walls which confine the molecules of water in batches. The cellular structure gives to the jelly its rigidity, yet the meshes are so open that an ion urged forward by electric force has little difficulty in passing from one compartment to another, and encounters most of the resistance to its motion in passing through the batches of water molecules. Thus the jelly has rigidity on the molar scale, and fluidity on the molecular. Now the rigidity of the jelly is the outcome of the elastic properties of the fibres forming the meshes. Just as an ion moves through the jelly almost independently of the presence of the network, there ought to be phenomena of the jelly confined to the network as regards cause and effect. How would it be possible to

The nature of the propagation of nerve impulse

A possible cause of the Earth's magnetism is the rotation of an electrostatic field within the Earth, as Rowland's experiments have proved (Phil. Mag. [5] xxvii) that a moving charge of electricity produces a magnetic field analogous to that of a current. If the Earth carries round an electrostatic field in its rotation, then it will have the axis of its magnetic field identical with the axis of rotation which is the chief approximate fact of the Earth's magnetism. The actual obliquity of the magnetic to the rotational axis is traced to unsymmetrical magnetic permeability of the Earth, which also causes the induction of Earth currents, the secular variation of whose tracks is the cause of magnetic secular variation.

The theory advanced to account for daily variation is that under the action of the Sun's rays the oxygen and ozone of the atmosphere become the active substance of a large secondary battery or accumulator whose alternate charge and discharge are the cause of the daily variations.

A possible cause of the earth's magnetism and a theory of its variations

I N two communications to this journal 1 I have given a physical theory of the propagation and electric properties of nerve impulse. That theory is a deduction from the general physical principle which I have sought to establish, namely, that all rigidity is of electric origin. In nerve there are two broad classes of electric action to be distinguished, first, that in which, for instance, a wireless telegraphic signal passes unnoticed through the body of a living animal, nerve behaving like any ordinary substance; and, second, that occurring when the electricity of a nerve is displaced so as to displace also the protein molecule with which the displaced electricity is associated. In this second case the main electric disturbance and the associated elastic disturbance in the nerve are propagated together as two aspects of the same occurrence. In this way the conclusion is reached that the velocity of propagation of nerve impulse is that of a shear in the substance of the nerve. It follows, then, that to a first approximation the change in the velocity of nerve impulse with temperature ought to be equal to the change in the velocity of a shear. But with lowering of temperature most substances, including protein jellies, become more rigid and therefore transmit a shear more quickly. Hence it appears from this physical theory that nerve impulse ought to travel faster at lower temperatures than at higher. But within the range of temperatures physiologically permissible, say from o” to 4o”, the change to be expected on the physical theory must be small, because the change in the rigidity of nerve within these temperatures is small. The original observation of Helmholtz on the effect of temperature on nerve velocities seemed to contradict this theoretical deduction flatly, but in my first paper I mentioned that Weiss claimed to have shown,

William Sutherland

Papers

The Elasticity of Rubber Balloons and Hollow Viscera

Relative Motion of the Earth and the Ether

The nature of the propagation of nerve impulse

A possible cause of the earth's magnetism and a theory of its variations

The nature of the conduction of nerve impulse