Morphodynamics of phyllotaxis

A morphodynamic model for phyllotaxis based upon an axiomatic approach is presented. We show that the helical forms of alternate phyllotaxis can be derived from the assumption of the rudiment's growth and movement on the cylindrical embryo surface in the absence of a longitudinal displacement. This leads to the repeating transition of tetragonal packaging of the rudiments into hexagonal packaging and vice versa. Under these conditions, sequences of rudiments produce either left-handed or right-handed helices, the number of which at the circumference of the cylinder corresponds to adjacent numbers of the Fibonacci series. Cross-opposite phyllotaxis forms are defined as superior with respect to the alternate ones, and verticillate phyllotaxis forms as superior with respect to the cross-opposite ones. Different phyllotaxis forms can be interpreted as a result of stretching of crystalline structures of the embryo formed by dense packing of rudiments. The superior phyllotaxis forms can be considered as the additive summation of lower forms. Morphodynamic mechanisms underlying the formation of multiple forms of helical phyllotaxis are discussed.     

A causal analysis of the heart curvatures in the chicken embryo

Summary By means of grafts of the heart tube of the chicken embryo (before incurvation), we tried to clear up those factors which determine the curvatures. The heart tube, cultivated or grafted, possesses in itself the property of incurvation but it is manifested only if it is developed in a medium or a cavity similar to the pericardiac cavity. This property cannot manifest itself in the thickening of the tissues such as the embryonic mesenchyme. The curvatures which are formed, that is to say the morphogenesis (in the coelomic grafts) is always imperfect and cannot be compared to those of a normal heart in the same stage of development. The ventricle and the heart bulb can be recognized many times, but not the atrium or the venous sinus. The retrocardiac tissue and the endoderm of the anterior intestinal portal are factors necessary for a normal morphogenesis, as the grafts accompanied by these tissues give rise to better morphogenesis and one can recognize all the fundamental portions of the heart. In these cases a liver is almost always differentiated, originating with the graft. The blood flow has no influence for some time in the heart morphogenesis but it does in the structure of the heart. Only in those cases in which circulation exists are the endocardium and the myoepicardium formed, with their typical structure. The morphogenesis and the heart structure are, to a certain point, independent processes during these stages of development and are due to different factors.This investigation was supported in part, by a grant from the Pfizer, s. A.     

CFD simulation of flow through heart: a perspective review

The heart is an organ which pumps blood around the body by contraction of muscular wall. There is a coupled system in the heart containing the motion of wall and the motion of blood fluid; both motions must be computed simultaneously, which make biological computational fluid dynamics (CFD) difficult. The wall of the heart is not rigid and hence proper boundary conditions are essential for CFD modelling. Fluid-wall interaction is very important for real CFD modelling. There are many assumptions for CFD simulation of the heart that make it far from a real model. A realistic fluid-structure interaction modelling the structure by the finite element method and the fluid flow by CFD use more realistic coupling algorithms. This type of method is very powerful to solve the complex properties of the cardiac structure and the sensitive interaction of fluid and structure. The final goal of heart modelling is to simulate the total heart function by integrating cardiac anatomy, electrical activation, mechanics, metabolism and fluid mechanics together, as in the computational framework.     

Study of the velocity and strain fields in the flow through prosthetic heart valves

A comparative experimental study of the velocity field and the strain field produced down-stream of biological and mechanical artificial valves is presented. In order to determine the spatial and temporal distributions of these fields, a phase-locked stereoscopic particle image velocimetry (or 3D-PIV) technique was implemented. Emphasis was placed on the identification of the fundamental differences between the extensional and the shear components of the strain tensor. The analysis of the characteristic flows reveal that the strains in every direction may reach high values at different times during the cardiac cycle. It was found that elevated strain levels persist throughout the cardiac cycle as a result of all these contributions. Finally, it is suggested that the frequency with which the strain variations occur at particular instants and locations could be associated to the cumulative damage process of the blood constituents and should be taken into account in the overall assessment of existing valve types, as well as in future design efforts.     

Glucose Controls Morphodynamics of LPS-Stimulated Macrophages

Macrophages constantly undergo morphological changes when quiescently surveying the tissue milieu for signs of microbial infection or damage, or after activation when they are phagocytosing cellular debris or foreign material. These morphofunctional alterations require active actin cytoskeleton remodeling and metabolic adaptation. Here we analyzed RAW 264.7 and Maf-DKO macrophages as models to study whether there is a specific association between aspects of carbohydrate metabolism and actin-based processes in LPS-stimulated macrophages. We demonstrate that the capacity to undergo LPS-induced cell shape changes and to phagocytose complement-opsonized zymosan (COZ) particles does not depend on oxidative phosphorylation activity but is fueled by glycolysis. Different macrophage activities like spreading, formation of cell protrusions, as well as phagocytosis of COZ, were thereby strongly reliant on the presence of low levels of extracellular glucose. Since global ATP production was not affected by rewiring of glucose catabolism and inhibition of glycolysis by 2-deoxy-D-glucose and glucose deprivation had differential effects, our observations suggest a non-metabolic role for glucose in actin cytoskeletal remodeling in macrophages, e.g. via posttranslational modification of receptors or signaling molecules, or other effects on the machinery that drives actin cytoskeletal changes. Our findings impute a decisive role for the nutrient state of the tissue microenvironment in macrophage morphodynamics.     

A comparative computational study of blood flow through prosthetic heart valves using the finite element method

The steady flow of blood through three common types of prosthetic heart valves was simulated numerically using the finite element method. The velocity, pressure and stress fields were obtained for the disk-type, tilting-disk and ball-type prosthetic heart valves in aortic position, for increasing Reynolds numbers up to 900, 1500 and 2000 respectively. Computer graphics of calculated velocities are presented, showing in detail the accelerated flow, recirculation and stagnation areas developed in the prosthesis. Maximum wall shear stresses were found at 0.5, 1.4, and 1.2 diameters from the sewing ring downstream for the disk, tilting-disk and ball valves being the values of 55, 18 and 33 dyn cm-2 respectively. In the vicinity of the occluder, maximum shear stresses of 38, 30 and 47 dyn cm-2 respectively were computed. The flow characteristics and performance for each valve are compared, the results are presented in terms of energy loss and maximum shear stress. The velocity and stress fields are compared with in vitro evaluations found in the literature.     

Computational simulations of flow dynamics and blood damage through a bileaflet mechanical heart valve scaled to pediatric size and flow

Despite pressing needs, there are currently no FDA approved prosthetic valves available for use in the pediatric population. This study is performed for predictive assessment of blood damage in bileaflet mechanical heart valves (BMHVs) with pediatric sizing and flow conditions. A model of an adult-sized 23 mm St. Jude Medical (SJM) Regent^™ valve is selected for use in simulations, which is scaled in size for a 5-year old child and 6-month old infant. A previously validated lattice-Boltzmann method (LBM) is used to simulate pulsatile flow with thousands of suspended platelets for cases of adult, child, and infant BMHV flows. Adult BMHV flows demonstrate more disorganized small-scale flow features, but pediatric flows are associated with higher fluid shear stresses. Platelet damage in the pediatric cases is higher than in adult flow, highlighting thrombus complication dangers of pediatric BMHV flows. This does not necessarily suggest clinically important differences in thromboembolic potential. Highly damaged platelets in pediatric flows are primarily found far downstream of the valve, as there is less flow recirculation in pediatric flows. In addition, damage levels are well below expected thresholds for platelet activation. The extent of differences here documented between the pediatric and adult cases is of concern, demanding particular attention when pediatric valves are designed and manufactured. However, the differences between the pediatric and adult cases are not such that development of pediatric sized valves is untenable. This study may push for eventual approval of prosthetic valves resized for the pediatric population. Further studies will be necessary to determine the validity and potential thrombotic and clinical implications of these findings.     

Numerical and experimental investigations of pulsatile blood flow pattern through a dysfunctional mechanical heart valve

Around 250,000 heart valve replacements are performed every year around the world. Due their higher durability, approximately 2/3 of these replacements use mechanical prosthetic heart valves (mainly bileaflet valves). Although very efficient, these valves can be subject to valve leaflet malfunctions. These malfunctions are usually the consequence of pannus ingrowth and/or thrombus formation and represent serious and potentially fatal complications. Hence, it is important to investigate the flow field downstream of a dysfunctional mechanical heart valve to better understand its impact on blood components (red blood cells, platelets and coagulation factors) and to improve the current diagnosis techniques. Therefore, the objective of this study will be to numerically and experimentally investigate the pulsatile turbulent flow downstream of a dysfunctional bileaflet mechanical heart valve in terms of velocity field, vortex formation and potential negative effect on blood components. The results show that the flow downstream of a dysfunctional valve was characterized by abnormally elevated velocities and shear stresses as well as large scale vortices. These characteristics can predispose to blood components damage. Furthermore, valve malfunction led to an underestimation of maximal transvalvular pressure gradient, using Doppler echocardiography, when compared to numerical results. This could be explained by the shifting of the maximal velocity towards the normally functioning leaflet. As a consequence, clinicians should try, when possible, to check the maximal velocity position not only at the central orifice but also through the lateral orifices. Finding the maximal velocity in the lateral orifice could be an indication of valve dysfunction.     

Ion flow through biomembranes

Numerous biomembranes exhibit a sensitivity to changes in electrical potential greater than predicted as possible from the classical application of the Boltzmann relation, a phenomenon which has long defied explanation, the actual sensitivity of some Na⁺ channels being many times greater than the classical limit. This paper explains, using a minimum of mathematics, how the very rapid gating effect of adsorbed Ca²⁺ (or other impermeable divalent cations) can directly affect the conductance of channels, and thus interact with the electric field within the channel to produce a change in the potential across the channel’s gate much greater than the change in the membrane potential, with a corresponding change in the fraction of open conformational gates and change in conductance. These results are not in conflict with the Boltzmann relation, the necessary energy being made available from the total potential difference across the membrane by a long unrecognized stochastic process; the full mathematical theory is given in cited references.     

Electron flow through metalloproteins

Electron transfers in photosynthesis and respiration commonly occur between metal-containing cofactors that are separated by large molecular distances. Understanding the underlying physics and chemistry of these biological electron transfer processes is the goal of much of the work in our laboratories. Employing laser flash-quench triggering methods, we have shown that 20 Å, coupling-limited Fe(II) to Ru(III) and Cu(I) to Ru(III) electron tunneling in Ru-modified cytochromes and blue copper proteins can occur on the microsecond timescale both in solutions and crystals; and, further, that analysis of these rates suggests that distant donor-acceptor electronic couplings are mediated by a combination of sigma and hydrogen bonds in folded polypeptide structures. Redox equivalents can be transferred even longer distances by multistep tunneling, often called hopping, through intervening amino acid side chains. In recent work, we have found that 20 Å hole hopping through an intervening tryptophan is several hundred-fold faster than single-step electron tunneling in a Re-modified blue copper protein.     

Morphodynamics of the thoracic lymphatic vessels in the dog in experimental pericarditis

The changes in the veins of a lymph node in experimental pericarditis appear together with those in the organ tissues and characterize the morphodynamic process.     

Morphodynamics of the nervous system in the regenerative processes of Convoluta convoluta (Turbellaria, Acoela)]

By means of the method for revealing cholinesterases the alterations in the nervous system of Convoluta convoluta after mechanical lesion were studied. After a transversal transection of the animal into two pieces the anterior part of the body acquired the normal form within 3-4 days; the nervous system underwent inconsiderable transformations associated with a formation of a plexus in the injured area. The posterior parts of the body regenerated slowly. During the first days disintegration of the resting parts of the nervous system was observed. Later on the diffuse cholinesterase activity suggesting the beginning of the brain formation was manifested in the wound field. Plexus strands "grow" in the caudal direction from the brain in parallel with its development. Within three weeks the nervous system of the animals which had restored their mouth opening, body shape and normal behaviour consists of the brain and plexus not arranged in nervous trunks. The reaction of the nervous system to the ablation of a part of the brain and to a continuous mechanical injury were studied. The data obtained show a high morphological lability of the nervous system of Convoluta convoluta, its ability to radical structural rearrangements.     

Mathematical model of flow through the patent ductus arteriosus

The ductus arteriosus is one of several shunts in the cardiovascular system. It is a small vessel connecting the aortic arch and pulmonary artery that allows blood to bypass the pulmonary circulation. It is open during foetal development because the foetal lungs cannot function and oxygenation of the blood occurs by exchange with the maternal blood in the placenta. Normally it closes a few days after birth; however, in a small number of people closure does not occur, leading to a condition known as patent ductus arteriosus. In this paper our aim is to investigate the resulting cardiovascular effects. We develop a mathematical model of the haemodynamics in three different idealised geometries by assuming that the entry flow is irrotational and remains so in the core until at least the shunt position. We argue that separation or diffusion of vorticity into the core flow is delayed due to the high frequency associated with the pulsatile component of the flow profile. The analysis uses complex potential theory, Schwarz–Christoffel transformations, conformal mappings and Fourier series. The main results are based on the assumption that the flow in patients with patent ductus arteriosus is similar to the flow in healthy adults, and we apply this assumption using boundary conditions that are representative of physiological values in healthy adults. The model suggests that the pressures in the aorta and pulmonary artery are likely to equalise, that the shear stress increases near the edges of the shunt and that backflow of large volumes may occur from the pulmonary artery into the aorta or towards the ventricles due to the presence of the patent shunt. Our results strongly suggest that an abnormal compensatory physiology develops in patients with patent ductus arteriosus.     

Numerical simulations of the blood flow through vertebral arteries

Vertebral arteries are two arteries whose structure and location in human body result in development of special flow conditions. For some of the arteries, one can observe a significant difference between flow rates in the left and the right arteries during ultrasonography diagnosis. Usually the reason of such a difference was connected with pathology of the artery in which a smaller flow rate was detected. Simulations of the flow through the selected type of the vertebral artery geometry for twenty five cases of artery diameters have been carried out. The main aim of the presented experiment was to visualize the flow in the region of vertebral arteries junction in the origin of the basilar artery. It is extremely difficult to examine this part of human circulation system, thus numerical experiments may be helpful in understanding the phenomena occurring when two relatively large arteries join together to form one vessel. The obtained results have shown that an individual configuration and diameters of particular arteries can exert an influence on the flow in them and affect a significant difference between flow rates for vertebral arteries. It has been assumed in the investigations that modelled arteries were absolutely normal, without any pathology. In the numerical experiment, the non-Newtonian model of blood was employed.     

Measurement of spinal sagittal curvatures using the laser triangulation method

The purpose of the first part of the study was to establish the variability of repeated measurements in different measuring conditions. In the second part, we performed in a large number of patients, a measurement of thoracic kyphosis and lumbar lordosis and compared them to age, gender, and level of nourishment. In the first part, measurements were performed on a plastic model of the back of a patient with a rigid and a normal spine. In the second part, 250 patients participated in the study (126 men and 124 women). For measuring spinal curvatures we used an apparatus for laser triangulation constructed at the Faculty of Mechanical Engineering, University of Ljubljana. A comparison of 30 repeated measurements was shown as the average value +/- 2 SD which included 95% of the results. Thirty repeated readings of one 3D measurement: thoracic kyphosis 41.2 degrees +/- 0.6 degrees, lumbar lordosis 4.4 degrees +/- 1.2 degrees; 30 measurements on a plastic model: thoracic kyphosis 36.8 degrees +/- 1.2 degrees, lumbar lordosis 30.9 degrees +/- 2.0 degrees; 30 measurements on a patient with a rigid spine: thoracic kyphosis 41.5 degrees +/- 2.4 degrees, lumbar lordosis 4.0 degrees +/- 1.8 degrees; 30 measurements on a patient with a normal spine: thoracic kyphosis 48.8 degrees +/- 7.4 degrees, lumbar lordosis 21.1 degrees +/- 4.4 degrees. The average size of thoracic kyphosis in 250 patients was 46.8 degrees (SD 10.1 degrees) and lumbar lordosis 31.7 degrees (SD 12.5 degrees). The angle size was statistically significantly correlated to gender (increased thoracic kyphosis and lumbar lordosis in women) and body mass index (increased thoracic kyphosis and lumbar lordosis in more nourished patients). Age was not significantly correlated to the observed angles. During measurements of the spinal angles it was important to pay attention to relaxation and the patient's position as well as to perform more measurements providing the average value. The age and the level of nourishment influence the size of the sagittal spinal angles. In the observed sample the effect of age was not confirmed.