The modelling of fibre reorientation in soft tissue

In this paper, a hyperelastic and thermodynamically consistent model for soft tissue is developed that is able to describe the change of the initial orientation of the collagen fibres. Full numerical implementation is considered as well. The collagen architecture is assumed to reorient driven by a specific thermodynamical force. The anisotropy is described by a strain energy function, which is decomposed into a part related to the matrix and a part related to the fibres. The initial fibre orientation is defined by a structural tensor, while the current orientation is described by a time-dependent structural tensor, which results from the initial one by a rotational transformation. The rotation tensor is obtained via an integration process of a rate tensor, which depends on an adequately defined thermodynamical force. The integration is achieved via an exponential map algorithm, where it is shown that the rotation is necessarily a two-parametric one. Efficiency of the proposed formulation is demonstrated using some numerical examples.     

Effect of binding on melting transitions in polymer–diluent systems

An expression is derived for the melting point of a polymer when in equilibrium with a solution in which binding of low molecular weight compounds to the polymer takes place. Allowance is made for the possibility that the crystalline polymer itself is a complex. The argument is a purely thermodynamic one and is based on a consideration of the change in free energy as a result of a change in binding. Allowance is made also for non-specific polymer–solvent interactions, in which the mixture of low molecular weight solvents is treated as a single solvent. Special attention is paid to “inverted” melting transitions, i.e., cases in which the melting point increases with increasing dilution of the polymer. It is shown that as a rule this is accompanied by a corresponding, inverted effect of the solvent composition on the melting point. It is further shown that-in the absence of binding, “normal” behavior at the critical point (i.e., phase separation is induced by lowering the temperature) is always accompanied by “normal” melting behavior (i.e., a decrease in melting point when the polymer is diluted). Also, “inverted” melting always implies that phase separation at the critical point is induced by heating, but the reverse is not necessarily true.     

The Influence of Temperature on the Effect of Bacteriostatic Concentrations of Phenol Against Escherichia coli

S ummary . During early exponential growth of Escherichia coli in the absence of phenol there is a natural death rate at 20, 30, and 44° but at the optimum temperature around 37° there is little if any significant death. The influence of a rise in temperature from 20 to 44° is to decrease the generation time and at 44° the lower generation time compensates for a reduced generation index. The main effect of sub-bacteriostatic concentrations of phenol is to increase the generation time but at 30, 37 and 44° there is a significant reduction in the generation index at the higher concentrations resulting in a dynamic bacteriostasis. At 20° bacteriostasis is due mainly to a large generation time but there is a little growth and so bacteriostasis is essentially dynamic. There is also evidence to suggest that the effect of a particular concentration of phenol on the generation index is not merely influenced by the temperature but by the generation time under the particular set of conditions. If phenol is added to rapidly growing cultures of E. coli the effect of a rise in temperature is to reduce the concentration required for bacteriostasis but if it is added during the lag phase there is a maximum in the bacteriostatic concentration between 20 and 37°.     

Design‐based inference on Bernstein type estimators for continuous populations

The estimation of the values of a variable at any point of a study area is performed using Bernstein polynomials when the sampling scheme is implemented by selecting a point in each polygon of a regular grid overimposed onto the area. The evaluation of the precision of the resulting estimates is investigated under a completely design‐based framework. Moreover, as the main contribution to the mean squared error of the Bernstein‐type estimator is due to the bias, also a pseudo‐jackknife estimator is proposed. The performance of both estimators is investigated theoretically and by means of a simulation study. An application to a soil survey performed in Berkshire Downs in Oxfordshire (UK) is considered.     

A contribution to the mathematical biology of the rates of historical development

The paper is a second step toward a biomathematical theory of the rates of spread of new nonconformist ideas or behaviors in a society. It is intended as a preliminary and purely theoretical study of a very oversimplified case. An equation which determines the distribution function of the tendencies toward conformist and nonconformist behaviors is set up under a number of oversimplified assumptions, and a solution by successive approximations is indicated. The expression for the first approximation is given, and an estimate of the order of magnitude of the rates of changes is made. In conclusion an outline is given for further improvement of the theory.     

Toward an optimal design principle in relational biology

A vulnerability criterion is posed for a biological system within the context of representing the system as a relational set, i.e., a collection of components whose interdependency is described by means of a set of binary relations. The criterion provides a numerical value for each representation and therefore a means for comparing one representation against another. Choice of the criterion is such that the larger a numerical value a representation has then the less vulnerable to destruction is the system represented. Other things being equal, it is argued that the representation which endows the system with the least vulnerability is more likely to be a valid representation. A selection criterion is thereby achieved for narrowing down the choice ofa priori representations.     

A graph theoretic approach to the development of minimal phylogenetic trees

Summary The problem of determining the minimal phylogenetic tree is discussed in relation to graph theory. It is shown that this problem is an example of the Steiner problem in graphs which is to connect a set of points by a minimal length network where new points can be added. There is no reported method of solving realistically-sized Steiner problems in reasonable computing time. A heuristic method of approaching the phylogenetic problem is presented, together with a worked example with 7 mammalian cytochrome c sequences. It is shown in this case that the method develops a phylogenetic tree that has the smallest possible number of amino acid replacements. The potential and limitations of the method are discussed. It is stressed that objective methods must be used for comparing different trees. In particular it should be determined how close a given tree is to a mathematically determined lower bound. A theorem is proved which is used to establish a lower bound on the length of any tree and if a tree is found with a length equal to the lower bound, then no shorter tree can exist.     

The optical near-field and cell biology

A new form of scanning light microscopy is described in which the lens is replaced by a point of light that is smaller than the wavelength. Resolution is obtained that is defined not by the wavelength but by the size of the spot of light. This is the case so long as the point of light is within the dimension of a wavelength from the surface that is to imaged or within the optical near-field. This new form of light microscopy is called near-field scanning optical microscopy (NSOM). Resolutions are being obtained with NSOM that are similar to scanning electron microscopy but without the destructive effects of a vacuum or of an electron beam. In addition such a microscope is readily interfaced with fluorescent and non-fluorescent contrast enhancing stains that are commonly used in cell biology. The possibility of a near-field/far-field microscope is discussed with overlapping resolutions from a few hundred of a conventional microscope to the tens of thousand that can be obtained with NSOM.     

Rhesus monkey apolipoprotein(a). Sequence, evolution, and sites of synthesis

Human lipoprotein(a) is a low density lipoprotein-like lipoprotein whose concentration in plasma is correlated with atherosclerosis. The characteristic protein component of lipoprotein(a) is apolipoprotein(a) (apo(a)) which is disulfide-linked to apolipoprotein B-100. Sequencing of rhesus monkey apo(a) cDNA suggests that this protein, like human apo(a), is highly similar to plasminogen. Sequence data suggests that a plasminogen-like protease activity and kringle 1-, 2-, 3-, and 5-like domains are unnecessary for apo(a) function, but a highly repeated kringle four-like domain is important. Liver is the major site of apo(a) RNA synthesis; reduced amounts of message were also found in testes and brain. Co-expression with apoB-100 and plasminogen in rhesus tissues is not mandatory.     

Competition in chemostat-type equations with two habitats

Competition on a model with nutrient recycling is considered. The model is based on a chemostat-type equation which is used to study population dynamics of microorganisms. The model consists of four organisms competing for a limiting nutrient. Nutrient is supplied both from the in-flow of medium and a recycling with delay, the latter is generated from dead organisms by bacterial decomposition. This paper shows that the model undergoes a Hopf bifurcation through a critical value of time delay when the in-flow is small. Coexistence of four organisms competing for one limiting nutrient is indicated by numerical simulation results.     

A physical characterization of biological information and communication system model of ecosystems

What is information for living organisms? An answer to this question is given on a physical basis and a contrast between genetic information and sensory information is stressed with a relation to information theory. A simple model of an environment of living organisms is investigated on the basis of communication systems model proposed by the author and a cost of information transmission is taken into consideration through capacity cost theory. It is shown that channel capacity of information theory can be interpreted as an environment, and furthermore that a large diversity of genetic messages needs a large capacity of the environment. In addition, a definition of life in terms of information is proposed and a unified view on life processes is suggested.     

A moral argument for frozen human embryo adoption

Some people (e.g., Drs. Paul and Susan Lim) and, with them, organizations (e.g., the National Embryo Donation Center) believe that, morally speaking, the death of a frozen human embryo is a very bad thing. With such people and organizations in mind, the question to be addressed here is as follows: if one believes that the death of a frozen embryo is a very bad thing, ought, morally speaking, one prevent the death of at least one frozen embryo via embryo adoption? By way of a three-premise argument, one of which is a moral principle first introduced by Peter Singer, my answer to this question is: at least some of those who believe this ought to. (Just who the “some” are is identified in the paper.) If this is correct, then, for said people, preventing the death of a frozen embryo via embryo adoption is not a morally neutral matter; it is, instead, a morally laden one. Specifically, their intentional refusal to prevent the death of a frozen embryo via embryo adoption is, at a minimum, morally criticizable and, arguably, morally forbidden. Either way, it is, to one extent or another, a moral failing.     

Detection and Prediction of Tooth Mobility During the Periodontitis Healing Process

The focus of the article is on a generic approach to prediction of a healing process based on automatic measurement and modelling of mechanical disease indicators. As a specific example the healing process after treatment of advanced periodontitis is characterised and predicted based on measurement of tooth mobility (TM). For the measurement a new mechatronic instrument was developed that includes a pneumatically driven probe with incorporated sensors of tooth displacement and loading force. TM is measured by a computer controlled data acquisition system and predicted by a non-parametric regression. Similarly as in the characterisation of technical processes, a measured sample is described by TM time series detected on a particular patient, while the regression is determined by a set of samples obtained from a group of patients following periodontal therapy. The influence of surgical access therapy and systemic administration of metronidazole as an adjunct to the mechanical treatment is demonstrated. For this purpose the average changes of tooth mobility are determined on variously treated subgroups. A new method of healing process prediction is demonstrated and its performance is described by a prediction quality.     

Detection and prediction of tooth mobility during the periodontitis healing process

The focus of the article is on a generic approach to prediction of a healing process based on automatic measurement and modelling of mechanical disease indicators. As a specific example the healing process after treatment of advanced periodontitis is characterised and predicted based on measurement of tooth mobility (TM). For the measurement a new mechatronic instrument was developed that includes a pneumatically driven probe with incorporated sensors of tooth displacement and loading force. TM is measured by a computer controlled data acquisition system and predicted by a non-parametric regression. Similarly as in the characterisation of technical processes, a measured sample is described by TM time series detected on a particular patient, while the regression is determined by a set of samples obtained from a group of patients following periodontal therapy. The influence of surgical access therapy and systemic administration of metronidazole as an adjunct to the mechanical treatment is demonstrated. For this purpose the average changes of tooth mobility are determined on variously treated subgroups. A new method of healing process prediction is demonstrated and its performance is described by a prediction quality.     

Study of thermal behavior of a biological tissue: An equivalence of Pennes bioheat equation and Wulff continuum model

Equivalence of Pennes bioheat equation (PBHE) and Wulff continuum model (WCM) is established for a 1-D planar tissue. The derived condition of equivalence is specific to tissue without metabolic heat generation. Mathematical analysis is carried out to relate blood perfusion rate and local mean blood velocity that are needed in the analysis of WCM. It is found that the local mean blood velocity in a tissue is a direct function of square root of blood perfusion rate. This functional dependence is also established numerically by having same solution obtained from PBHE and WCM. Analysis is also done to check how closely the derived relation can be used for practical cases of breast tissue with and without a tumor. Blood velocity is a very important physiological quantity. Its measurement is a difficult process and requires a state-of-the-art technique. The proposed relation allows its computation merely from the knowledge of blood perfusion rate.     

Translational-entropy gain of solvent upon protein folding

We show that even in the complete absence of potential energies among the atoms in a protein-aqueous solution system, there is a physical factor that favors the folded state of the protein. It is a gain in the translational entropy (TE) of water originating from the translational movement of water molecules. An elaborate statistical-mechanical theory is employed to analyze the TE of water in which a protein or peptide with a prescribed conformation is immersed. It is shown that if the number of residues is sufficiently large, the TE gain is powerful enough to compete with the conformational-entropy loss upon folding. For protein G we have tested over 100 compact conformations generated by a computer simulation with the all-atom potentials as well as the native structure. A significant finding is that the largest TE is attained in the native structure. The translational movement of water molecules is quite effective in achieving the tight packing in the interior of a natural protein. These results are true only when the solvent is water whose molecular size is the smallest among the ordinary liquids in nature.     

Determination of the maximum velocity and Michaelis constant of enzymes by a fixed-point method which avoids the necessity to measure initial rates

Measuring the initial velocity is difficult in some enzyme assays where a significant fraction of the substrate is consumed. Here a solution to this problem is proposed; the time to produce a fixed amount of reaction product is measured. This time is inversely proportional to the initial velocity, and is related to the maximum velocity and Michaelis constant by a simple equation and linear plot. The method is illustrated using the reaction catalysed by pyruvate kinase.     

A multiphysics approach for modeling early atherosclerosis

This work is devoted to the development of a mathematical model of the early stages of atherosclerosis incorporating processes of all time scales of the disease and to show their interactions. The cardiovascular mechanics is modeled by a fluid–structure interaction approach coupling a non-Newtonian fluid to a hyperelastic solid undergoing anisotropic growth and a change of its constitutive equation. Additionally, the transport of low-density lipoproteins and its penetration through the endothelium is considered by a coupled set of advection–diffusion-reaction equations. Thereby, the permeability of the endothelium is wall-shear stress modulated resulting in a locally varying accumulation of foam cells triggering a novel growth and remodeling formulation. The model is calibrated and applied to an murine-specific case study, and a qualitative validation of the computational results is performed. The model is utilized to further investigate the influence of the pulsatile blood flow and the compliance of the artery wall to the atherosclerotic process. The computational results imply that the pulsatile blood flow is crucial, whereas the compliance of the aorta has only a minor influence on atherosclerosis. Further, it is shown that the novel model is capable to produce a narrowing of the vessel lumen inducing an adaption of the endothelial permeability pattern.     

On religious ritual as deference and communicative excess

I shall argue that most religious ritual is a performance that not only invokes but also performs communication. The ethnographic material from which I derive this argument is from China, in particular the temple rituals of local festivals. My argument is that a deep obeisance of welcome and departure that is both like and not like the normal ritual of greeting marks a religious from a non-religious ritual occasion and place. It is a ritual doubling that makes the honoured guest also a host. Religious ritual is a medium, and as a medium it is double in another sense. It is deference and deferral, a repeated transmission of obeisance to authority that has the authority of repetition. As well as doubling, religious ritual is excessively communicative. The medium is a performance not only of invitation and departure but also of communicative response, and it repeats this communication as a test of communicative response over and over again. Religious ritual performs both the opening and closing of communication, both the seeking and the responsive reciprocation of gift offerings with bounteousness. It is shadowed by the possibility of no response, of giving offence, of being abandoned. This possibility is acknowledged by being prevented, while the possibility that the performers are their own responders is disavowed.