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F262. The rheology of developing embryonic epithelial tissue mathematical model
372
Vol. 32, Nos. 2-3
Free Communications
the obvious anatomical difference between the right coronary leaflet and the other two leaflets, no difference in their theological properties were observed.
F261. BIORHEOLOGICAL FEATURES OF NERVES AND TISSUE EXPANSION
AND BLOOD
BIOMECHANICAL VESSELS
UNDER
G. FU AND Y.J. ZENG Biomechanics Laboratory, Department of Basic Science, Beijing Polytechnic University, Beijing 100022, P. R. China Soft tissue expansion as a reconstructive maneuver is now a well-accepted co n cep t and skin expansion is a widely used technique for Plastic Surgery today. However, u n d e r some circumstances, it is essential to expand the muscles as well as nerves and blood vessels at the same time. Thus, the effect of tissue expansion on biomechanical features of nerves and blood vessels is a prerequisite subject, and so far has scarcely been studied. In our experiments, expanders were placed beneath the sartorius of one of the dog's hind legs to expand the saphenous neurovascular bundle, the o t h e r hind leg acted as control. The expanders were filled to different volumes and u n d e r w e n t different periods of expansion. Specimens of expanded saphenous nerves, arteries, veins and their opposite controls were tested on an Instron material testing machine. The stress relaxation curves and stress-strain curves showed that the biomechanical features of expanded specimens were changed when c o mp ar ed with their opposite controls. Within the same expanding period (nearly 2 weeks), the difference between expanded and control specimens increases with the e xt e nt of e x p a n d e r ' s inflation. However, when the expanding period is long enough, which is 15 weeks longer, the biomechanical features of expanded specimens began to approach that of their opposite controls again. We observed the same law for saphenous nerves, arteries and veins. Th e parameters of continuous relaxation spectrum and stress-strain relation function were also obtained.
F262.
THE
EPITHELIAL
RHEOLOGY TISSUE
OF
DEVELOPING
MATHEMATICAL
EMBRYONIC
MODEl.
A. A. STEIN Institute o f Mechanics, Moscow University, Michurinsky Props. 1, Moscow 119899, Russia The continual model of embryonic tissue, consisting of cells and extracellular structures, is presented. This model allows one to analyze self-organization and formation processes in epithelial sheets. The stress tensor is supposed to be the sum o f elastic and active components, the rate of active stress development depending on the total stress tensor. The averaged equations that take into account inhomogeneity of passive and active characteristics along the sheet width are obtained for the thin sheet. The closed circular sheet is considered. The active properties of tissue in this case are reduced to two parameters: active tensile force and active bending moment. T he averaged theological relations represent the time derivatives of active force and m o m e n t
Vol. 32, Nos. 2-3
373
Free Comnmnicatiom
as function of total tensile force and bending moment among other arguments. Linear analysis and numerical simulation show that instability of the system and formation of active moment regions which provide bending are possible. F263. T H E TISSUE
MATHEMATICAL
MODEI. OF GROWING
PLANT
A. A. STEIN Institute of Mechanics, Moscow University, Moscow 119899, Russia The tissue of axial plant organ (root or stem) consists mainly of cell walls that form a solid deformable framework and a multitude of closed intracellular volumes containing fluid under pressure. At the stage of primary growth, the relatively distinct partitioning of axially and transversely oriented walls allows one to separately introduce representative averaged parameters characterizing stresses and strains in cell walls of both sorts. The generalization of the Lockhart law for cell wall deformation, which takes into account growth rate dependence on mechanical stresses, leads to a model of growing material of a viscoelastic type for the tissue as a whole. The expression of tissue rheological parameters in terms of averaged microscopic variables is given. The model enables one to analyze growth problems with external mechanical restrictions and regulatory processes involved. The root tip growth in the soil or in the presence of an obstacle give examples of such problems. F264. A THEORETICAL ANALYSIS OF PULMONARY CAPHJARY FIIJ.ING ON LUNG
EFFECT OF EIASTICITY
A. D'YACHENKO Institute of Biomedical Problems, Moscow, Russia Lung elastic recoil is produced mainly by alveolar walls and ducts. Alveolar wall consists of a pair of alveolar-capillary membranes and is stretched due to lung inflation and pulmonary capillary filing. The objective of this study was a theoretical analysis of the effect of pulmonary capillary blood volume and pressure on lung elastic recoil and compliance. The effect was analyzed on the basis of the alveolar sheet model and models of the alveolar structure. Assuming a dominant role of alveolar walls in tissue elasticity, a stress-strain relation for alveolar-capillary membranes was deduced for some lung pressurevolume relationships. A dependence of lung elastic recoil upon lung volume and capillary blood volume was obtained. Simulated decrease of lung compliance due to increase of capillary blood filling accounts for some experimental findings. The effect of pulmonary capillary pressure on compliance strongly depends upon elastic recoil. In lungs with big recoil, this effect is small. Conclusion: The model predicts that lung compliance depends very much upon the change in pulmonary capillary blood volume during the maneuver of measurement of complicance.
Vol. 32, Nos. 2-3
Free Communications
the obvious anatomical difference between the right coronary leaflet and the other two leaflets, no difference in their theological properties were observed.
F261. BIORHEOLOGICAL FEATURES OF NERVES AND TISSUE EXPANSION
AND BLOOD
BIOMECHANICAL VESSELS
UNDER
G. FU AND Y.J. ZENG Biomechanics Laboratory, Department of Basic Science, Beijing Polytechnic University, Beijing 100022, P. R. China Soft tissue expansion as a reconstructive maneuver is now a well-accepted co n cep t and skin expansion is a widely used technique for Plastic Surgery today. However, u n d e r some circumstances, it is essential to expand the muscles as well as nerves and blood vessels at the same time. Thus, the effect of tissue expansion on biomechanical features of nerves and blood vessels is a prerequisite subject, and so far has scarcely been studied. In our experiments, expanders were placed beneath the sartorius of one of the dog's hind legs to expand the saphenous neurovascular bundle, the o t h e r hind leg acted as control. The expanders were filled to different volumes and u n d e r w e n t different periods of expansion. Specimens of expanded saphenous nerves, arteries, veins and their opposite controls were tested on an Instron material testing machine. The stress relaxation curves and stress-strain curves showed that the biomechanical features of expanded specimens were changed when c o mp ar ed with their opposite controls. Within the same expanding period (nearly 2 weeks), the difference between expanded and control specimens increases with the e xt e nt of e x p a n d e r ' s inflation. However, when the expanding period is long enough, which is 15 weeks longer, the biomechanical features of expanded specimens began to approach that of their opposite controls again. We observed the same law for saphenous nerves, arteries and veins. Th e parameters of continuous relaxation spectrum and stress-strain relation function were also obtained.
F262.
THE
EPITHELIAL
RHEOLOGY TISSUE
OF
DEVELOPING
MATHEMATICAL
EMBRYONIC
MODEl.
A. A. STEIN Institute o f Mechanics, Moscow University, Michurinsky Props. 1, Moscow 119899, Russia The continual model of embryonic tissue, consisting of cells and extracellular structures, is presented. This model allows one to analyze self-organization and formation processes in epithelial sheets. The stress tensor is supposed to be the sum o f elastic and active components, the rate of active stress development depending on the total stress tensor. The averaged equations that take into account inhomogeneity of passive and active characteristics along the sheet width are obtained for the thin sheet. The closed circular sheet is considered. The active properties of tissue in this case are reduced to two parameters: active tensile force and active bending moment. T he averaged theological relations represent the time derivatives of active force and m o m e n t
Vol. 32, Nos. 2-3
373
Free Comnmnicatiom
as function of total tensile force and bending moment among other arguments. Linear analysis and numerical simulation show that instability of the system and formation of active moment regions which provide bending are possible. F263. T H E TISSUE
MATHEMATICAL
MODEI. OF GROWING
PLANT
A. A. STEIN Institute of Mechanics, Moscow University, Moscow 119899, Russia The tissue of axial plant organ (root or stem) consists mainly of cell walls that form a solid deformable framework and a multitude of closed intracellular volumes containing fluid under pressure. At the stage of primary growth, the relatively distinct partitioning of axially and transversely oriented walls allows one to separately introduce representative averaged parameters characterizing stresses and strains in cell walls of both sorts. The generalization of the Lockhart law for cell wall deformation, which takes into account growth rate dependence on mechanical stresses, leads to a model of growing material of a viscoelastic type for the tissue as a whole. The expression of tissue rheological parameters in terms of averaged microscopic variables is given. The model enables one to analyze growth problems with external mechanical restrictions and regulatory processes involved. The root tip growth in the soil or in the presence of an obstacle give examples of such problems. F264. A THEORETICAL ANALYSIS OF PULMONARY CAPHJARY FIIJ.ING ON LUNG
EFFECT OF EIASTICITY
A. D'YACHENKO Institute of Biomedical Problems, Moscow, Russia Lung elastic recoil is produced mainly by alveolar walls and ducts. Alveolar wall consists of a pair of alveolar-capillary membranes and is stretched due to lung inflation and pulmonary capillary filing. The objective of this study was a theoretical analysis of the effect of pulmonary capillary blood volume and pressure on lung elastic recoil and compliance. The effect was analyzed on the basis of the alveolar sheet model and models of the alveolar structure. Assuming a dominant role of alveolar walls in tissue elasticity, a stress-strain relation for alveolar-capillary membranes was deduced for some lung pressurevolume relationships. A dependence of lung elastic recoil upon lung volume and capillary blood volume was obtained. Simulated decrease of lung compliance due to increase of capillary blood filling accounts for some experimental findings. The effect of pulmonary capillary pressure on compliance strongly depends upon elastic recoil. In lungs with big recoil, this effect is small. Conclusion: The model predicts that lung compliance depends very much upon the change in pulmonary capillary blood volume during the maneuver of measurement of complicance.