A cellular model of lung elasticity

The mechanics of the lung parenchyma is studied using models comprised of line members interconnected to form 3-D cellular structures. The mechanical properties are represented as elastic constants of a continuum. These are determined by perturbing each individual cell from a reference state by an increment in stress which is superimposed upon the uniform stretching forces initially present in the members due to the transpulmonary pressure. A force balance on the distorted structure, together with a force-deformation law for the members, leads to a calculation of the strain increments of the members. Predictions based on the analysis of the 3-D isotropic dodecahedron are in good agreement with experimental values for the Young's, shear, and bulk moduli reported in the literature. The model provides an explanation for the dependence of the elastic moduli on transpulmonary pressure, the geometrical details of the structure, and the stress-strain law of the tissue.     

A macroscopic formulation of electromagnetophoresis

A macroscopic conservation equation is derived for electromagnetophoresis of a dilute suspension. The governing equation and auxiliary conditions are formulated for transport in a rectangular cell, these being reduced to standard form by dimensional methods.     

A generalization of hooke's law in muscle elasticity

Experimental data concerning stress-strain relations of biological substances, including single muscle fibers, are reviewed in the literature. A reconsideration of the conclusions reached from these data is made. Thus, the experiments indicate that prima facie a linear theory of elasticity such as Hooke's law does not obtain because of the complicated form of the stress-strain curves. It is then shown that from a consideration oftrue stress at a point, where true stress is the force per unitactual area at the point, Hooke's law may be so generalized as to predict qualitatively and semi-quantitatively the complicated experimental curves. This complication arises from the long range “elasticity” of biological substances in general and muscle fibers in particular. Thus, substitutingtrue stress for stress, the stress-strain relation of muscle fibers remains linear. In the case of “small” strains, the true stress reduces to the usual stress concept in which the force is considered per unitinitial area at the point.     

A distributed nonlinear model of lung tissue elasticity

Maksym, Geoffrey N., and Jason H. T. Bates. Adistributed nonlinear model of lung tissue elasticity.J. Appl. Physiol. 82(1): 32-41, 1997.- We present a theory relating the static stress-strainproperties of lung tissue strips to the stress-bearing constituents,collagen and elastin. The fiber pair is modeled as a Hookean spring(elastin) in parallel with a nonlinear string element (collagen), whichextends to a maximum stop length. Based on a series of fiber pairs, wedevelop both analytical and numerical models with distributedconstituent properties that account for nonlinear tissue elasticity.The models were fit to measured stretched stress-strain curves of fiveuniaxially stretched tissue strips, each from a different dog lung. Wefound that the distributions of stop length and spring stiffness followinverse power laws, and we hypothesize that this results from thecomplex fractal-like structure of the constituent fiber matrices inlung tissue. We applied the models to representative pressure-volume(PV) curves from patients with normal, emphysematous,and fibrotic lungs. The PV curves were fit to theequation V = A  Bexp(KP),where V is volume, P is transpulmonary pressure, andA, B, andK are constants. Our models lead to apossible mechanistic explanation of the shape factorK in terms of the structuralorganization of collagen and elastin fibers.

     

Warmest Congratulations to Dr. Yuan-Cheng Fung at His Centennial Celebration

Professor Y.C. Fung has made tremendous impacts on science, engineering and humanity through his research and its applications, by setting the highest standards, through educating many students and their students, and providing his exemplary leadership. He has applied his profound knowledge and elegant analytical methods to the study of biomedical problems with rigor and excellence. He established the foundations of biomechanics in living tissues and organs. Through his vision of the power of “making models” to explain and predict biological phenomena, Dr. Fung opened up new vista for bioengineering, from organs-systems to molecules-genes, and has provided the foundation of research activities in many institutions in the United States and the world. He has made outstanding contributions to education in bioengineering, service to professional organizations, and translation to industry and clinical medicine. He is widely recognized as the Father of Biomechanics and the leading Bioengineer in the world. His extraordinary achievements and commands in science, engineering and the arts make him a Renaissance Man for the world.     

A quantitative formulation of biology's first law

The zero‐force evolutionary law (ZFEL) states that in evolutionary systems, in the absence of forces or constraints, diversity and complexity tend to increase. The reason is that diversity and complexity are both variance measures, and variances tend to increase spontaneously as random events accumulate. Here, we use random‐walk models to quantify the ZFEL expectation, producing equations that give the probabilities of diversity or complexity increasing as a function of time, and that give the expected magnitude of the increase. We produce two sets of equations, one for the case in which variation occurs in discrete steps, the other for the case in which variation is continuous. The equations provide a way to decompose actual trajectories of diversity or complexity into two components, the portion due to the ZFEL and a remainder due to selection and constraint. Application of the equations is demonstrated using real and hypothetical data.     

A generalized formulation of dual radiation action

Dual radiation action is a process in which cellular lesions are produced as a result of the interaction of pairs of sublesions that are molecular alterations produced by ionizing radiation. Previous formulations of this process have employed a number of simplifying assumptions that limit the accuracy and the range of application of theoretical analysis. The formulation presented here removes some of these restrictions by introducing three functions that describe the geometry of the sensitive material in the cell, the geometry of the pattern of energy deposition, and the interaction probability of sublesions as a function of their separation. The relation derived is similar to that obtained previously, in that lesion production is found to depend on two terms that are proportional to the first and the second power of the absorbed dose. However, the coefficients of these terms are now derived on the basis of a more realistic treatment.     

A quantitative model of cellular elasticity based on tensegrity

A tensegrity structure composed of six struts interconnected with 24 elastic cables is used as a quantitative model of the steady-state elastic response of cells, with the struts and cables representing microtubules and actin filaments, respectively. The model is stretched uniaxially and the Young's modulus (E0) is obtained from the initial slope of the stress versus strain curve of an equivalent continuum. It is found that E0 is directly proportional to the pre-existing tension in the cables (or compression in the struts) and inversely proportional to the cable (or strut) length square. This relationship is used to predict the upper and lower bounds of E0 of cells, assuming that the cable tension equals the yield force of actin (approximately 400 pN) for the upper bound, and that the strut compression equals the critical buckling force of microtubules for the lower bound. The cable (or strut) length is determined from the assumption that model dimensions match the diameter of probes used in standard mechanical tests on cells. Predicted values are compared to reported data for the Young's modulus of various cells. If the probe diameter is greater than or equal to 3 microns, these data are closer to the lower bound than to the upper bound. This, in turn, suggests that microtubules of the CSK carry initial compression that exceeds their critical buckling force (order of 10(0)-10(1) pN), but is much smaller than the yield force of actin. If the probe diameter is less than or equal to 2 microns, experimental data fall outside the region defined by the upper and lower bounds.     

A physical basis for red cell membrane elasticity

An estimate is made of the effect of lipid-water interactions at the membrane surface on observed membrane elasticity in the red blood cell. It is shown that elastic effects are expected to result from these interactions even in a completely fluid membrane. A simple statistical model is described and used to estimate the magnitude of the resultant elasticity. The estimate thus derived is compared with results of experiments during which a biaxial stress is applied to the membrane. The derived elasticity is sufficient to account for the results of these studies. Other properties of the red cell membrane are discussed in the light of this result.     

Centromere elasticity

In addition to the role in the spindle apparatus and associated motors, the chromosome themselves play an important role in facilitating chromosome segregation. Sister chromatids are joined at the centromere through a protein complex called cohesin. Chromatids separation requires the degradation by separase of specific proteins acting as a glue to form the cohesin complex. This evolutionally complex is required for the establishment and maintenance of sister chromatids in a ring like structure. It is therefore a key question whether cohesin is indeed a main component of active centromere. Cohesin is insufficient to resist the splitting force exerted by microtubules until anaphase and must be renforced by cohesion provided by flanking DNA. The ring model suggests that cohesine might possess a considerable mobility when associated with chromatin. Observations demonstrate that the interior region of the centromere behaves as an elastic element. Chromosomes display remarkable elasticity, returning to their initial shape after being extended by up to 10 times. For larger deformations the thick filament is converted in thin filament which can be stretched six times before breaking. This article suggests an additional and novel role for the protein titin on chromosome structure and dynamic. Titine was identified as a chromosomal component and it was hypothesised that titin may provide elasticity to chromosome and resistance to chromosome breakages during mitosis. The elastic properties of purified titin correspond well to the elastic properties of chromosome in living cells. The deformability and bending rigidity are consistent with a model developed for titin elasticity. The association of the presence of cohesine ring and the activity of titin could be necessary for segregation.     

The dialectics of socialization: A tentative formulation

Conclusion A cognitive anthropological approach helps us to understand that children's conceptions are antithetical to adult conceptions. Furthermore, socialization is a dialectical process involving an interplay of these antithetical child conceptions and adult conceptions. As indicated in the field observations, change in the child is internal but the transition from one stage of growth to another occurs only through interaction with the environment. One sees elements of adult conceptions created in the child but they are and remain child conceptions until such time as the Leap has occurred. Babs' teacher, for example, misunderstood this antithetical quality in Babs and assumed her mature behavior indicated she was really mature, really an adult. Qualitatively and quantitatively Babs was still a child and had to initiate action on her own part to prove that. She exhibited behavior that was misconstrued as adult-like, but because she was still a child, her conceptions of herself, her environment and correlatively, of her behavior remained child-like.Carol was obviously quite resourceful and adept at moving in and out of various behavioral patterns appropriate to social situations in which she found herself. This was necessary for survival, particularly when she was forced into situations where prejudicial people controlled her life and her future. The antithetical qualities of her conceptual framework and that of her teacher are overshadowed by the real historical circumstances of race relations in this society. But those antithetical conceptual qualities are still clearly evident. Adult conceptions from the outside intrude on Carol's life and her thinking. And, elements of adult conceptions are being created within her. Yet these autonomous creations will remain child conceptions as long as she remains a child. She responds to her environment, but she responds as a child, subjectified/objectified. She is still qualitatively and quantitatively a childClearly much of what children learn from the environment — from school — is harmful to their autonomy. Through current socialization processes, the dialectics of learning remain incomplete. The interaction whereby children's categories antithetical to adult categories are transformed into a new synthesis of adult categories is missing. Instead, the adult conceptions created in and by the children merely replicate the adult categories of their socializers. Therefore, the current socialization process is a reactionary one. Children are increasingly objectified as their adult categories are less and less new categories, but merely replications of already formalized adult categories. Because the dialectical process of socialization is left incomplete, incomplete adults reach physical maturity. Such people are incapable of governing their own lives, of living out the complexities and inconsistencies of adulthood.Reformists are correct in calling for change in educational methods but not with the methods they suggest. Children should be educated for democracy, but the methods utilized should not result in chaos and disorder because they lack discipline.In fact, although ideologically at odds with each other, methodologically conventional and emancipated teachers differ only in locus of control. Conventional teachers see socialization as a unidirectional process in which they provide the stimulus and the students provide the response. Emancipated teachers see socialization as a dialectical process and deploy that process to educate children for greater autonomy, social and self-understanding. But, in rejecting conventional modes of thought, unconventional teachers do not necessarily reject sensible pedagogical methods. The processes and methods of education are more complex than a simple liberal (soft)/conservative (strict) theoretical dichotomy of education would suggest. Children can still be respected even as their teachers realize their conceptual categories are incomplete and inferior. Relativists who insist, for example, that all speech patterns, because they exhibit internal consistency and structural regularity are inherently equal, fail to recognize or to uncover the true source of social inequality. Relativistic revelations only mystify that inequality and contribute nothing to social liberation.Education for liberation is a slow, arduous task and will not occur by using short-cuts, or pop-psych approaches. It will come from strict adherence to exacting and demanding methods. It will be facilitated through a recognition of the dialectical nature of the socialization process and a cognitive anthropological investigation into the nature of conceptual categories of children. And it will have to be part of a general transformation of this society, while, at the same time, remaining an index of the succes of any such transformation. This means, among other things, that children must be taught to govern their own lives and to govern others. It does not mean, of course, that every person would govern; only that every person should understand the mechanics of governing — that every person, as Gramsci held, could govern.Maribeth Durst is Assistant Professor of Sociology, at St. John's University, Staten Island, New York.

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A model for formulation of protein assay.

The principle of the protein assay using the reaction of an alkaline copper-protein complex with the Folin-Ciocalteu phenol reagent has been investigated. In contrast to the long-established Lowry method, a stable and rapid protein assay is developed without a buffering agent in alkaline copper solution. In the absence of a buffering agent, the reaction pH drops relatively rapidly and moves the reaction toward a more stable pH. When the reaction of alkaline copper-protein complex with Folin-Ciocalteu reagent is started at around pH 11.7, the reaction color absorbance reaches a plateau in approximately 10 min and remains stable to allow a reliable measurement of the absorbance. In the absence of the buffering agent sodium carbonate, the alkaline copper solution is also stable for months. The principle of the protein assay is presented as a model that can be used to formulate protein assays of desired specification.     

A voxel-based formulation for contact finite element analysis

To date, voxel-based finite element models have not been feasible for contact problems, owing to the inherent stair-step boundary discontinuities. New preprocessing techniques are reported herein to mesh these boundaries smoothly, for purposes of contact stress analysis. Further, new techniques are reported to concentrate the mesh resolution automatically near the articular surface, thus reducing the problem size to levels compatible with executing nonlinear problems on contemporary engineering workstations. Close approximations to Hertzian analytical solutions were obtained for spherical and cylindrical geometries meshed in this manner, and an illustrative anatomical contact problem of the human hip joint is presented.