Fractal-based image texture analysis of trabecular bone architecture

Fractal-based image analysis methods are investigated to extract textural features related to the anisotropic structure of trabecular bone from the X-ray images of cubic bone specimens. Three methods are used to quantify image textural features: power spectrum, Minkowski dimension and mean intercept length. The global fractal dimension is used to describe the overall roughness of the image texture. The anisotropic features formed by the trabeculae are characterised by a fabric ellipse, whose orientation and eccentricity reflect the textural anisotropy of the image. Tests of these methods with synthetic images of known fractal dimension show that the Minkowski dimension provides a more accurate and consistent estimation of global fractal dimension. Tests on bone x-ray (eccentricity range 0.25-0.80) images indicate that the Minkowski dimension is more sensitive to the changes in textural orientation. The results suggest that the Minkowski dimension is a better measure for characterising trabecular bone anisotropy in the x-ray images of thick specimens.

Use of in vitro gas production models in ruminal kinetics

Physiological systems models for ruminant animals are used to predict the extent of ruminal carbohydrate digestion, based on rates of intake, digestion, and passage to the lower tract. Digestion of feed carbohydrates is described in these models by a first-order rate constant. Recently, an in vitro gas production technique has been developed to determine the digestion kinetics in batch fermentation, and nonlinear mathematical models have been fitted to the cumulative gas production data from these experiments. In this paper, we present an analysis that converts these gas production models to an effective first-order rate constant that can be used directly in rumen systems models. The analysis considers the digestion of an incremental mass of substrate entering the rumen. The occurrence of passage is represented probabilistically, and integration through time gives the total mass of substrate and total rate of digestion in the rumen. To demonstrate the analysis, several gas production models are fitted to a sample data set for corn silage, and the effective first-order rate constants are calculated. The rate constants for digestion depend on ruminal passage rate, an interaction that arises from the nonlinearity of the gas production models.

Modeling ruminal pH fluctuations: interactions between meal frequency and digestion rate

A steady periodic analysis of ruminal carbohydrate digestion was developed to predict the effects of diet and frequency of eating on ruminal pH fluctuation. Tests of the model against previous data showed that pH fluctuations were too large when previously published rates of carbohydrate digestion were used but were improved using rates from an in vitro gas production system, which were lower. With the original digestion rates, the minimum meal frequency to maintain steady-state conditions in the rumen increased from 4 to 12 meals/d as dietary effective neutral detergent fiber (NDF) decreased from 34 to 6% of dry matter (DM); with the revised rates, the minimum frequency was 3 to 6 meals/d, respectively. The minimum effective NDF to maintain a pH value above 6.0 increased from 14 to 23% of DM as meal frequency decreased from steady state to 2 meals/d using the original rates; with the revised rates, the minimum effective NDF was slightly smaller, increasing from 13 to 21% of DM, respectively. Effects of DM intake and body weight on pH fluctuation were minor, and dietary buffers, when used at rates less than 1%, did not reduce fluctuation. Different methods of calculating mean ruminal pH yielded different results for the effect of meal frequency on mean pH.

Prediction of ruminal volatile fatty acids and pH within the net carbohydrate and protein system

A steady-state model of the production, absorption, passage, and concentration of ruminal VFA and pH is developed from published literature data and is structured to use the feed descriptions and inputs from the net carbohydrate and protein system. Included are the effects of pH on growth rate and yield of structural and non-structural carbohydrate-fermenting bacteria; production of acetate, propionate, butyrate, lactate, and methane; conversion of lactate to VFA; ruminal absorption of acids; and prediction of ruminal pH from dietary measures and from ruminal buffering and acidity. The root mean square error of predicted total VFA concentration was 12 mM. Individual VFA fractions were inadequately predicted. In a review of literature data, effective NDF (eNDF) provided a better correlation with ruminal pH than forage or NDF. Digestion rate of NDF remained at normal levels above pH 6.2, which corresponds to a minimum eNDF of 20% of dietary DM. Further research is needed to determine the individual VFA produced from carbohydrate fractions at various pH, the appropriateness of partitioning the starch and pectin carbohydrate pool into slowly and rapidly degraded fractions, and the effect on microbial yield, total tract digestibility, and predicted energy values of feeds.

Application of the Cornell Net Carbohydrate and Protein model for cattle consuming forages

Accurate prediction of forage biological values and performance with animals fed forages requires accurately accounting for factors that influence animal requirements and feedstuff utilization. The Cornell Net Carbohydrate and Protein System (CNCPS) is an application model that uses a combination of mechanistic and empirical approaches to account for the effects of variation in animal factors and feed carbohydrate and protein fractions on animal performance. Thus, accurate animal and environmental descriptions, DMI, feed carbohydrate, and protein fractions and their digestion rates are required inputs. In 25 growth periods with calves fed high-forage diets, the CNCPS accounted for 74, 81, and 83%, respectively, of the variation in ADG predicted to be supported by the ME, metabolizable protein, and essential amino acid intake, the first-limiting of all three accounting for 81% of the variation with a -1% bias. Thus, the CNCPS can be used to accurately describe forage quality and the effects of changes in forage composition on animal performance. The model was sensitive to variations in NDF, CP, protein solubility, NDF and starch digestion rates, feed and microbial amino acid composition, maintenance protein requirement, body protein amino acid content, and the coefficient of efficiency of use of absorbed protein. Analysis of several trials indicates an improved efficiency of ME use with improved amino acid balances. Uses of the CNCPS discussed include interpreting, planning and applying research, teaching, developing tables of requirements and biological values for feeds, complex nutritional accounting, and predicting performance and profits.

Kinetics of fiber digestion from in vitro gas production

In vitro gas production, measured by computer-interfaced pressure sensors, was used to follow the digestion of a crystalline processed cellulose, a bacterial cellulose, and mixtures of these substrates by mixed ruminal bacteria. A first-order, substrate limited model (simple exponential with lag) and two bacterial growth models (logistic, Gompertz) were tested to fit these data. No single pool model gave an optimal fit to all substrates, but dual pool versions of both the logistic and Gompertz models fitted the data extremely well. Derivations of these models in the context of gas production are presented. The dual pool version of the exponential model commonly used to analyze fiber digestion was not able to reproduce the slope variations seen with mixed substrates. A modified dual pool logistic equation, with a single lag value, was selected to model the in vitro digestion of these substrates. The model was able to predict adequately both the input composition and the kinetic parameters for a defined mixture and gave a good fit (r2 > .995) to data from all the single and mixed substrates tested. This model may be useful for interpreting gas accumulation from natural feedstuffs.

Osmometric behavior, hydraulic conductivity, and incidence of intracellular ice formation in bovine oocytes at different developmental stages

Bovine oocytes that were immature (IMM), matured in vitro (IVM) or in vivo (MAT), or matured and fertilized in vitro (IVF) were studied using a microscope diffusion chamber to estimate osmotic parameters and a cryomicroscope to characterize intracellular ice formation (IIF). Linear Boyle van't Hoff relationships were observed with all four types of oocytes between 0.265 and 0.799 osm NaCl. At 20 degrees C, estimates of hydraulic conductivity (Lp) were significantly higher for IVM oocytes than IMM and MAT oocytes (0.84 micron/(min.atm) vs 0.45 and 0.47, respectively). IVM oocytes also tended to have higher Lp values than IVF oocytes (0.55 micron/(min.atm)). At 5 degrees C, the Lp of IVM oocytes decreased to 0.36 micron/min.atm) corresponding to an Arrhenius activation energy of 7.84 kcal/mol. The incidence of IIF in MAT oocytes suspended in salt solution and subjected to linear cooling to -60 degrees C was 45% at 4 degrees C/min, 75% at 8 degrees C/min, and 93% at 16 degrees C/min; with IVF oocytes, the incidence of IIF was 40% at 4 degrees C/min, 92% at 8 degrees C/min, and 100% at 16 degrees C/min. Comparisons involving median IIF temperatures (TIIF50s) and the distributions of the observed IIF temperatures for IMM (Myers et al., Cryo-Lett. 8, 260), IVM (Chandrasekaran et al., Cryobiology 27, 676), MAT and IVF oocytes indicated that the IIF incidence in IMM oocytes cooled at 4 degrees C/min was greater than that of oocytes at the other developmental stages cooled at the same rate. The TIIF50s of IVM and IVF oocytes were lowered by equilibration in 1.5 M ethylene glycol (EG), glycerol, or propylene glycol (PG) prior to cooling, with EG tending to lower the TIIF50s more than glycerol or PG. For all three cryoprotectants, the TIIF50s and IFF temperature distributions were cooling-rate dependent. The Weibull probability distribution was fitted to the distributions of the IIF temperatures of oocytes suspended in salt solutions with and without cryoprotectants yielding R2 values ranging from 0.70 to 0.98.

A Descriptive Model of Mold Growth and Aflatoxin Formation as Affected by Environmental Conditions

A model is presented which integrates literature data on the effects of temperature, water activity, pH, and colony size on mold growth and aflatoxin formation. Mathematical forms for the rates of growth and toxin formation are based on assumptions about the biology of toxigenesis. The rate of toxin formation is assumed to be proportional to the rate of production of new cell mass, and the rate of toxin degradation is assumed to be proportional to the product of the concentrations of dead cell mass and aflatoxin; the latter assumption is an attempt to be consistent with the notion that toxin degradation is effected by enzymes released during mycelial lysis. Growth rate and toxin yield are represented by a maximum or reference value times a series of factors dependent on environmental conditions. Temperature and water activity have an interactive effect on growth and toxigenesis in the model. An Arrhenius-like function is postulated for the effects of temperature; shape parameters in the function are selected assuming that optimum temperature bears a fixed relationship to temperature limits for growth and toxigenesis, which vary with water activity. A linear function is postulated for the effect of water activity, with the lower limit dependent on temperature. Parabolic and Monod models are used to describe the effects of pH and colony size, respectively. Toxigenic parameters are estimated by comparing model simulations to the results of two published studies, with fair consistency in the two sets of parameters. In comparisons with other studies, the model did not correctly project the effects of spore load, but did correctly predict toxigenic behaviors relating to the effects of temperature and temperature cycling. The model provides a theoretical explanation for observed temporal shifts in the optimum temperature for toxigenesis, and for a hyperbolic relationship between heat units and time to toxigenesis with and without temperature cycling.

Dynamic model prediction of the value of reduced solubility of alfalfa silage protein for lactating dairy cows

A net carbohydrate and protein system was used to develop model diets for lactating dairy cattle with various protein solubilities in the alfalfa silage component of the diet. The objective was to determine the level to which alfalfa silage could be used to replace supplemental protein sources as the silage protein solubility decreased and to estimate the value of silage treatments needed to reduce protein solubility. Four cow groups were considered: early lactation multiparous cows, primiparous cows, midlactation cows, and late lactation cows. Diets were balanced for metabolizable protein, metabolizable energy, and ammonia and peptides for rumen bacteria; limits on DMI and effective NDF were enforced. Lower protein solubility was predicted to increase the yield of bacteria per unit of alfalfa silage DM and the yield of metabolizable protein per unit of alfalfa silage CP. Because of reduced protein supplements, diet costs were decreased. The savings per unit of silage in these rations increased as alfalfa silage protein solubility decreased. For example, with a reduction in solubility from 61 to 51% of CP, the savings ranged from $2.96 to $3.26/tonne of silage across the four cow groups. The value of acid treatment of silage needed to effect these reductions exhibited diminishing returns as application rate increased and appeared to be most cost effective when used on high quality alfalfa fed to high producing cows with application rates less than 2 kg/tonne. Management practices that reduce silage temperatures were predicted to save $.50 to $1.50/tonne of silage when the diets were balanced to account for protein degradability.

Performance of a kinetic model for intracellular ice formation based on the extent of supercooling

Cryomicroscopy was used to study the incidence of intracellular ice formation (IIF) in protoplasts isolated from rye (Secale cereale) leaves during subfreezing isothermal periods and in in vitro mature bovine oocytes during cooling at constant rates. IIF in protoplasts occurred at random times during isothermal periods, and the kinetics of IIF were faster as isothermal temperature decreased. Mean IIF times decreased from approximately 1700 s at -4.0 degrees C to less than 1 s at -18.5 degrees C. Total incidence of IIF after 200 s increased from 4% at -4.0 degrees C to near 100% at -15.5 degrees C. IIF behavior in protoplasts was qualitatively similar to that for Drosophila melanogaster embryos over the same temperature ranges (Myers et al., Cryobiology 26, 472-484, 1989), but the kinetics of IIF were about five times faster in protoplasts. IIF observations in linear cooling of bovine oocytes indicated a median IIF temperature of -11 degrees C at 16 degrees C/min and total incidences of 97%, 50%, and 19% at 16, 8, and 4 degrees C/min, respectively. A stochastic model of IIF was developed which preserved certain features of an earlier model (Pitt et al. Cryobiology 28, 72-86, 1991), namely Weibull behavior in IIF temperatures during rapid linear cooling, but with a departure from the concept of a supercooling tolerance. Instead, the new model uses the osmotic state of the cell, represented by the extent of supercooling, as the independent variable governing the kinetics of IIF. Two kinetic parameters are needed for the model: a scale factor tau 0 dictating the sensitivity to supercooling, and an exponent rho dictating the strength of time dependency. The model was fit to the data presented in this study as well as those from Myers et al. and Pitt et al. for D. melanogaster embryos with and without cryoprotectant, and from Toner et al. (Cryobiology 28, 55-71, 1991) for mouse oocytes. In protoplasts, D. melanogaster embryos, and mouse oocytes, the parameters were estimated from IIF times in the early stages of isothermal periods, while the osmotic state of the cell was relatively constant. In bovine oocytes, the parameters were estimated from linear cooling data. Without further calibration, the model was used to predict total IIF incidence under different cooling regimes. For protoplasts, D. melanogaster embryos, and bovine oocytes, the model's predictions were quite accurate compared to the actual data. In mouse oocytes, adjustment of the hydraulic permeability coefficient (Lp) at 0 degree C was required to yield realistic behavior.(ABSTRACT TRUNCATED AT 400 WORDS)

Subfreezing volumetric behavior and stochastic modeling of intracellular ice formation in Drosophila melanogaster embryos

Cryomicroscopic observations were made of the volumetric behavior and kinetics of intracellular ice formation (IIF) in Drosophila melanogaster embryos in a modified cell culture medium (BD.20) or BD.20 + 2 M ethylene glycol. After rapid cooling to a given temperature, transient volumetric contraction of the embryos during the isothermal period was quantified by computerized video image analysis. Fitting these data to the numerical solution of the volume flux equation yielded estimates of the hydraulic permeability coefficient (Lp) for individual embryos at various subfreezing temperatures. Lp approximately followed an Arrhenius relation between -2 and -9 degrees C, with a value of 0.168 microns/(min-atm) extrapolated to 0 degrees C and an apparent activation energy delta E of 38.9 kcal/mol. IIF during an isothermal period occurred at random times whose characteristic temperature range and kinetics were affected by the presence of ethylene glycol. A stochastic process model developed to fit these data indicated the influence of both time-dependent and instantaneous components of IIF, presumed to be the result of seeding and heterogeneous nucleation, respectively. The presence of 2 M ethylene glycol depressed the characteristic temperature of instantaneous IIF by about 12 degrees C and reduced the rate constant for time-dependent IIF. Comparison with observed incidences of IIF yielded an estimate of the supercooling tolerance of 3 to 5 degrees C.

A mechanics model of the compression of cells with finite initial contact area

The effect of intercellular bonding on the stress-strain behavior of soft plant tissue is considered. In our mechanical model, a conglomerate of identical cells is arranged in a regular array. Each cell is pressurized and bonded across flat contact areas with adjacent cells in the direction of the applied load. The cell wall is a finitely-deformed mechanical membrane bounding an incompressible fluid (the cytoplasm). A nonlinear elastic constitutive law is presented that describes data for apple parenchyma. Results show that intercellular bonding has a strong effect on the macroscopic properties of the whole tissue. A larger intercellular contact area increases tissue stiffness and magnifies the effect of initial turgor pressure on tissue stiffness.

Cryopreservation of Drosophila melanogaster embryos

There is an urgent need to preserve the ever-increasing number (greater than 30,000) of different genetic strains of D. melanogaster that are maintained in national and international stock centres and in the laboratories of individual investigators. In all cases, the stocks are maintained as adult populations and require transfer to fresh medium every two to four weeks. This is not only costly in terms of materials, labour and space, but unique strains are vulnerable to accidental loss, contamination, and changes in genotype that can occur during continuous culture through mutation, genetic drift or selection. Although cryopreservation of Drosophila germ-plasm would be an enormous advantage, many attempts using conventional procedures have been unsuccessful. D. melanogaster embryos are refractory to conventional cryopreservation procedures because of the contravening conditions required to minimize mortality resulting from both intracellular ice formation and chilling injury at subzero temperatures. To overcome these obstacles, we have developed a vitrification procedure that precludes intracellular ice formation so that the embryos can be cooled and warmed at ultra-rapid rates to minimize chilling injury, and have recovered viable embryos following storage in liquid nitrogen. In a series of 53 experiments, a total of 3,711 larvae emerged from 17,280 eggs that were cooled in liquid nitrogen (18.4 +/- 8.8%). Further, using a subset from this population, approximately 3% of the surviving larvae (24/800) developed into adults. These adults were fertile and produced an F1 generation.

Osmometric behavior of Drosophila melanogaster embryos

The osmometric behavior of Drosophila melanogaster embryos in permeabilized eggs was studied in a microscope diffusion chamber designed to impose a rapid change in osmotic environment at various temperatures. A numerical model of NaCl diffusion in the chamber predicted that radial variations in concentration arising from the presence of a thin film of solution at the top of the chamber were negligible. On the basis of transient electrical conductance measurements in the chamber, characteristic time constants for the change in concentration averaged over the chamber depth occupied by the eggs were 0.99, 0.77, and 0.60 min at 0, 10, and 20 degrees C, respectively. The chamber response was sufficiently rapid that the characteristic response of the embryo was not masked. Equilibrium volumetric behavior of the embryos indicated that they behaved as nearly ideal osmometers over the range of 0.256 to 2.000 osm, and followed the relation FVeq = 0.123C-1 + 0.541, where FVeq is equilibrium fractional volume and C is osmolality. Nonlinear regression of volumetric data during osmotic contraction yielded an average Lp of 0.722 micron/(min.atm) at 20 degrees C and an apparent activation energy delta E of 8.11 kcal/mol. The coefficients of variation in the Lp estimates among individual embryos were 38, 18, and 47% at 0, 10, and 20 degrees C, respectively. With the use of probability rules and a model for volumetric behavior during freezing, it was determined that the observed variability in Lp (assuming delta E is fixed) considerably broadens the transition range of cooling rates over which the predicted probability of intracellular ice formation goes from 0 to 1. However, experimental observations (21) show the actual transition range is even wider, indicating that there exist other important sources of variability which determine the event of ice formation in D. melanogaster embryos.

A two-step method for permeabilization of Drosophila eggs

As a first step in developing a procedure for the cryopreservation of Drosophila melanogaster embryos, we have established a method for permeabilization of the eggcase and have initiated studies of the hydraulic conductivity of permeabilized embryos and the permeation of selected cryoprotective agents. The eggcase of D. melanogaster embryos has a wax layer that precludes any flux of water. A two-step procedure employing organic solvents was developed to effect removal of the wax layer with minimal deleterious effects on the embryos. Dechorionated embryos (Oregon-R strain P2, 12 to 13 hr old) were rinsed sequentially in isopropanol and hexane. After removal of solvent, embryos were held in a modified cell culture medium for further manipulation. This procedure routinely yielded 80 to 95% of the eggs permeabilized (as determined by osmotic contraction in 1 M sucrose) and 75 to 90% survival (incidence of hatching). Hydraulic conductivity of permeabilized embryos and permeation of cryoprotectants were determined using a microdiffusion chamber and computerized video microscopy. Regression analysis of the volumetric data from individual embryos yielded the Boyle-van't Hoff function FVeq = 0.124 (osm-1) + 0.541 with the standard deviations of slope and intercept (Vb) being 0.010 and 0.040, respectively. Permeabilized embryos exhibited ideal osmotic behavior over the range of 0.265 to 2.00 osm. The mean hydraulic conductivity coefficient (Lp) was 0.722 +/- 0.366 micron/(min.atm) at 20 degrees C, based on observations of contraction following a step change in concentration of Ringer's solution.(ABSTRACT TRUNCATED AT 250 WORDS)

Characterization of intracellular ice formation in Drosophila melanogaster embryos

Cryomicroscopy and differential scanning calorimetry (DSC) were used to characterize the incidence of intracellular ice formation (IIF) in 12- to 13-hr-old embryos of Drosophila melanogaster (Oregon-R strain P2) as influenced by the state of the eggcase (untreated, dechorionated, or permeabilized), the composition of the suspending medium (with and without cryoprotectants), and the cooling rate. Untreated eggs underwent IIF over a very narrow temperature range when cooled at 4 or 16 degrees C/min with a median temperature of intracellular ice formation (TIIF50) of -28 degrees C. The freezable water volume of untreated eggs was approximately 5.4 nl as determined by DSC. IIF in dechorionated eggs occurred over a much broader temperature range (-13 to -31 degrees C), but the incidence of IIF increased sharply below -24 degrees C, and the cumulative incidence of IIF at -24 degrees C decreased with cooling rate. In permeabilized eggs without cryoprotectants (CPAs), IIF occurred at much warmer temperatures and over a much wider temperature range than in untreated eggs, and the TIIF50 was cooling rate dependent. At low cooling rates (1 to 2 degrees C/min), TIIF50 increased with cooling rate; at intermediate cooling rates (2 to 16 degrees C/min), TIIF50 decreased with cooling rate. The total incidence of IIF in permeabilized eggs was 54% at 1 degree C/min, and volumetric contraction almost always occurred during cooling. Decreasing the cooling rate to 0.5 degree C/min reduced the incidence of IIF to 43%. At a cooling rate of 4 degrees C/min, ethylene glycol reduced the TIIF50 by about 12 degrees C for each unit increase in molarity of CPA (up to 2.0 M) in the suspending medium. The TIIF50 was cooling rate dependent when embryos were preequilibrated with 1.0 M propylene glycol or ethylene glycol, but was not so in 1.0 M DMSO. For embryos equilibrated in 1.5 M ethylene glycol and then held at -5 degrees C for 1 min before further cooling at 1 degree C/min, the incidence of IIF was decreased to 31%. Increasing the duration of the isothermal hold to 10 min reduced the incidence of IIF to 22% and reduced the volume of freezable water in embryos when intracellular ice formation occurred. If the isothermal hold temperature was -7.5 or -10 degrees C, a 10- to 30-min holding time was required to achieve a comparable reduction in the incidence of IIF.

Quantitative analysis of the probability of intracellular ice formation during freezing of isolated protoplasts

(i) A quantitative prediction of the temperature and cooling-rate dependence of IIF requires information on the probability distribution for IIF temperature; the super-cooling tolerance; and membrane permeability, initial cell size, Boyle-van't Hoff relation, and other parameters associated with the thermodynamic description of cell volumetric behavior. (ii) A probabilistic analysis of IIF was developed on the basis that IIF occurs if the underlying potential IIF temperature T* falls within the range of temperatures over which the cell is supercooled beyond its tolerance delta T*. The "location" of the transition range of cooling rates, in which the Pr(IIF) increases from 0 to 1, depends on the mean of T* and delta T*. The breadth of the transition range increases strongly with variability in T*. (iii) Cryomicroscopic studies of IIF in rye protoplasts isolated from cold acclimated and nonacclimated leaves showed that the range of IIF temperatures and the incidence of IIF are strongly dependent on the solute used to manipulate osmolality in the suspending medium. The ionic solutes used in this study (NaCl + CaCl2, KCl + CaCl2, KNO3 + CaCl2) generally yielded median IIF temperatures lower than those of the nonionic solutes (sucrose, sorbitol, proline). Cold acclimation reduced the median IIF temperature for all suspending media and reduced the incidence of IIF for KCl + CaCl2, sorbitol, and proline. A Weibull distribution was found to describe adequately the distribution of IIF temperatures at the highest cooling rate. (iv) Estimates of the supercooling tolerance were generally from 1.0 to 1.5 degrees C based on the location of the transition range of cooling rates and on the estimates of Lp and delta E from (6). The breadth of the transition range of cooling rates could mostly be attributed to random variability in the underlying potential IIF temperature. The rise in median IIF temperature with higher cooling rates was correctly predicted by the model when the supercooling tolerance was also assumed to be random. For rye protoplasts, both the model and the data showed that cooling-rate dependence in median IIF temperatures occurs within the transition range of cooling rates.

Cell wall elastic constitutive laws and stress-strain behavior of plant vegetative tissue

The appropriateness of several elastic constitutive laws for apple and potato cell walls is tested using uniform cell inflation data. Whole-tissue stress-strain behavior under uniaxial loading is predicted from an analysis of the compression of a conglomerate of cells in a simple arrangement.

Elastic constitutive laws for cow teat tissue undergoing finite deformations

Five constitutive laws are investigated to model the effect of machine milking. A nonlinear least squares procedure is employed to estimate material constants from in vivo teat inflation data. An exponential form is found to be statistically adequate as a constitutive law, and is used to determine the mechanical stresses in teat tissue during finite deformations.