Mechanical behavior of bovine nasal cartilage under static and dynamic loading

Abnormal mechanical loading may trigger cartilage degeneration associated with osteoarthritis. Tissue response to load has been the subject of several in vitro studies. However, simple stimuli were often applied, not fully mimicking the complex in vivo conditions. Therefore, a rolling/plowing explant test system (RPETS) was developed to replicate the combined in vivo loading patterns. In this work we investigated the mechanical behavior of bovine nasal septum (BNS) cartilage, selected as tissue approximation for experiments with RPETS, under static and dynamic loading. Biphasic material properties were determined and compared with those of other cartilaginous tissues. Furthermore, dynamic loading in plowing modality was performed to determine dynamic response and experimental results were compared with analytical models and Finite Elements (FE) computations. Results showed that BNS cartilage can be modeled as a biphasic material with Young's modulus E=2.03±0.7 MPa, aggregate modulus H_A=2.35±0.7 MPa, Poisson's ratio ν=0.24±0.07, and constant hydraulic permeability k₀=3.0±1.3×10⁻¹⁵ m⁴ (N s)⁻¹. Furthermore, dynamic analysis showed that plowing induces macroscopic reactions in the tissue, proportionally to the applied loading force. The comparison among analytical, FE analysis and experimental results showed that predicted tangential forces and sample deformation lay in the range of variation of experimental results for one specific experimental condition. In conclusion, mechanical properties of BNS cartilage under both static and dynamic compression were assessed, showing that this tissue behave as a biphasic material and has a viscoelastic response to dynamic forces.     

The role of particle softness in determining the value of Poisson's ratio for soft sphere solids

The influence of particle softness on the Poisson's ratio of model solids has been investigated. We have used the repulsive inverse power potential (～r ^? n for particle separations, r) between the particles, which is conveniently characterised by one adjustable parameter, ? = 1/n. For large ?, the interaction is soft whereas in the ? → 0 limit the particles approach hard spheres. The pressure and elastic constants of the solid phase have been calculated at various densities with constant temperature molecular dynamics (MD) simulation for a range of the softness parameter in the range, n>12. Density-softness surfaces of these quantities were determined which revealed hitherto unrecorded trends in the behaviour of the elastic moduli and Poisson's ratio. It was found that the pressure and some elastic properties, e.g. the C₁₂ elastic constant and the bulk modulus, manifest a maximum value or ‘ridge’ on this surface. The height of the maximum increases with density and interaction steepness (small ?). The Poisson's ratio varies essentially linearly with softness and is relatively insensitive to density. However, at higher densities and for larger steepness a considerable lowering of the Poisson's ratio is observed. In order to identify possible mechanisms for reducing the value of Poisson's ratio, ν, the fluctuation and Born-Green contributions were analysed. Changes in the Poisson's ratio are mainly determined by the fluctuation contribution which can cause a considerable decrease as well as increase of its value.     

Time and depth dependent poisson’s ratio of cartilage explained by an inhomogeneous orthotropic fiber embedded biphasic model

A time- and depth-dependent Poisson’s ratio has been observed during unconfined compression experiments on articular cartilage, but existing cartilage models have not fully addressed these phenomena. The goal of this study was to develop a model which is able to predict and explain these phenomena, while also being able to fit other experimental scenarios on full depth cartilage specimens such as confined and unconfined compressions. A biphasic (poroelastic), fiber-embedded cartilage model was developed. The heterogeneous material properties of the cartilage (aggregate modulus, void ratio tensile modulus) were extracted from reported experiments on individual layers of bovine articular cartilage. The nonlinear permeability material constants were found by fitting the overall response to published experimental data from confined compression. The matrix of the cartilage was modelled as an inhomogeneous isotropic biphasic material with nonlinear strain dependent permeability. Orthotropic layers were added as embedded elements to represent collagen fibers. Material parameters for these layers were derived from tensile tests of different layers of cartilage. With these predefined tensile parameters, the model showed a good fit with multi-step confined and unconfined compression experiments (R²=0.984 and 0.977, respectively) and could also predict the depth-dependent Poisson’s ratio (R²=0.981). The highlight of the model is the ability to explain the time-depth dependent Poisson's ratio and, by association, the strong effect of material inhomogeneity on local stress and strain patterns within the cartilage layer. This material model’s response may provide valuable new insight into potential initiation of cartilage fibrillation or delamination in whole-joint simulations.     

Surface elastic modulus of barnacle adhesive and release characteristics from silicone surfaces

The properties of barnacle adhesive on silicone surfaces were studied by AFM indentation, imaging, and other tests and compared to the barnacle shear adhesion strength. A multilayered structure of barnacle adhesive plaque is proposed based on layered modulus regions measured by AFM indentation. The fracture of barnacles from PDMS surfaces was found to include both interfacial and cohesive failure of barnacle adhesive plaque, as determined by protein staining of the substratum after forced barnacle release from the substrate. Data for freshly released barnacles showed that there was a strong correlation between the mean Young's modulus of the outermost (softest) adhesive layer (E< 0.3 MPa) and the shear strength of adhesion, but no correlation for other higher modulus regions. Linear, quadratic, and Griffith's failure criterion (based on rough estimate of crack length) regressions were used in the fit, and showed significance.     

Hydraulic permeability and compressive properties of porcine and human synovium

The synovium is a multilayer connective tissue separating the intra-articular spaces of the diarthrodial joint from the extra-synovial vascular and lymphatic supply. Synovium regulates drug transport into and out of the joint, yet its material properties remain poorly characterized. Here, we measured the compressive properties (aggregate modulus, Young's modulus, and Poisson's ratio) and hydraulic permeability of synovium with a combined experimental-computational approach. A compressive aggregate modulus and Young's modulus for the solid phase of synovium were quantified from linear regression of the equilibrium confined and unconfined compressive stress upon strain, respectively (H_A = 4.3 ± 2.0 kPa, E_s = 2.1 ± 0.75, porcine; H_A = 3.1 ± 2.0 kPa, E_s = 2.8 ± 1.7, human). Poisson's ratio was estimated to be 0.39 and 0.40 for porcine and human tissue, respectively, from moduli values in a Monte Carlo simulation. To calculate hydraulic permeability, a biphasic finite element model's predictions were numerically matched to experimental data for the time-varying ramp and hold phase of a single increment of applied strain (k = 7.4 ± 4.1 × 10^?15 m⁴/N.s, porcine; k = 7.4 ± 4.3 × 10^?15 m⁴/N.s, human). We can use these newly measured properties to predict fluid flow gradients across the tissue in response to previously reported intra-articular pressures. These values for material constants are to our knowledge the first available measurements in synovium that are necessary to better understand drug transport in both healthy and pathological joints.     

Micromechanical models of helical superstructures in ligament and tendon fibers predict large Poisson's ratios

Experimental measurements of the Poisson's ratio in tendon and ligament tissue greatly exceed the isotropic limit of 0.5. This is indicative of volume loss during tensile loading. The microstructural origin of the large Poisson's ratios is unknown. It was hypothesized that a helical organization of fibrils within a fiber would result in a large Poisson's ratio in ligaments and tendons, and that this helical organization would be compatible with the crimped nature of these tissues, thus modeling their classic nonlinear stress–strain behavior. Micromechanical finite element models were constructed to represent crimped fibers with a super-helical organization, composed of fibrils embedded within a matrix material. A homogenization procedure was performed to determine both the effective Poisson's ratio and the Poisson function. The results showed that helical fibril organization within a crimped fiber was capable of simultaneously predicting large Poisson's ratios and the nonlinear stress–strain behavior seen experimentally. Parametric studies revealed that the predicted Poisson's ratio was strongly dependent on the helical pitch, crimp angle and the material coefficients. The results indicated that, for physiologically relevant parameters, the models were capable of predicting the large Poisson's ratios seen experimentally. It was concluded that helical organization within a crimped fiber can produce both the characteristic nonlinear stress–strain behavior and large Poisson's ratios, while fiber crimp alone could only account for the nonlinear stress–strain behavior.     

Indentation with atomic force microscope,Saccharomyces cerevisiae cell gains elasticity under ethanol stress

During bioethanol fermentation process, Saccharomyces cerevisiae cell membrane is the first target to be attacked by the accumulated ethanol. In such a prominent position, S. cerevisiae cell membrane could reversely provide protection through changing fluidity or elasticity secondary to remodeled membrane components or structure during the fermentation process. However, there is yet to be a direct observation of the real effect of the membrane compositional change. In this study, atomic force microscope-based strategy was performed to determine Young's modulus of S. cerevisiae to directly clarify ethanol stress-associated changes and roles of S. cerevisiae cell membrane fluidity and elasticity. Cell survival rate decreased while the cell swelling rate and membrane permeability increased as ethanol concentration increased from 0% to 20% v/v. Young's modulus decreased continuously from 3.76 MPa to 1.53 MPa while ethanol stress increased from 0% to 20% v/v, indicating that ethanol stress induced the S. cerevisiae membrane fluidity and elasticity changes. Combined with the fact that membrane composition varies under ethanol stress, to some extent, this could be considered as a forced defensive act to the ethanol stress by S. cerevisiae cells. On the other hand, the ethanol stress induced loosening of cell membrane also caused S. cerevisiae cell to proactively remodel membrane to make cell membrane more agreeable to the increase of environmental threat. Increased ethanol stress made S. cerevisiae cell membrane more fluidized and elastic, and eventually further facilitated yeast cell’s survival.     

Elastic properties of human supraorbital and mandibular bone

Elastic constants, including the elastic modulus, the shear modulus, and Poisson's ratio, were measured on human craniofacial bone specimens obtained from the supraorbital region and the buccal surfaces of the mandibles of unembalmed cadavers. Constants were determined using an ultrasonic wave technique in three directions relative to the surface of each sample: 1) normal, 2) tangential, and 3) longitudinal. Statistical analysis of these elastic constants indicated that significant differences in the relative proportions of elastic properties existed between the regions. Bone from the mandible along its longitudinal axis was stiffer than bone from the supraorbital region. Directional differences in both locations demonstrated that cranial bone was not elastically isotropic. It is suggested that differences in elastic properties correspond to regional differences in function. © 1993 Wiley-Liss, Inc.     

Biomechanical characterisation of ovine spinal facet joint cartilage

The spinal facet joints are known to be an important component in the kinematics and the load transmission of the spine. The articular cartilage in the facet joint is prone to degenerative changes which lead to back pain and treatments for the condition have had limited long term success. There is currently a lack of information on the basic biomechanical properties of the facet joint cartilage which is needed to develop tissue substitution or regenerative interventions. In the present study, the thickness and biphasic properties of ovine facet cartilage were determined using a combination of indentation tests and computational modelling. The equilibrium biphasic Young's modulus and permeability were derived to be 0.76±0.35 MPa and 1.61±1.10×10^?15 m⁴/(Ns) respectively, which were within the range of cartilage properties characterised from the human synovial joints. The average thickness of the ovine facet cartilage was 0.52±0.10 mm, which was measured using a needle indentation test. These properties could potentially be used for the development of substitution or tissue engineering interventions and for computational modelling of the facet joint. Furthermore, the developed method to characterise the facet cartilage could be used for other animals or human donors.     

Numerical analysis of the influence of nucleus pulposus removal on the biomechanical behavior of a lumbar motion segment

Nucleus replacement was deemed to have therapeutic potential for patients with intervertebral disc herniation. However, whether a patient would benefit from nucleus replacement is technically unclear. This study aimed to investigate the influence of nucleus pulposus (NP) removal on the biomechanical behavior of a lumbar motion segment and to further explore a computational method of biomechanical characteristics of NP removal, which can evaluate the mechanical stability of pulposus replacement. We, respectively, reconstructed three types of models for a mildly herniated disc and three types of models for a severely herniated disc based on a L4–L5 segment finite element model with computed tomography image data from a healthy adult. First, the NP was removed from the herniated disc models, and the biomechanical behavior of NP removal was simulated. Second, the NP cavities were filled with an experimental material (Poisson's ratio = 0.3; elastic modulus = 3 MPa), and the biomechanical behavior of pulposus replacement was simulated. The simulations were carried out under the five loadings of axial compression, flexion, lateral bending, extension, and axial rotation. The changes of the four biomechanical characteristics, i.e. the rotation degree, the maximum stress in the annulus fibrosus (AF), joint facet contact forces, and the maximum disc deformation, were computed for all models. Experimental results showed that the rotation range, the maximum AF stress, and joint facet contact forces increased, and the maximum disc deformation decreased after NP removal, while they changed in the opposite way after the nucleus cavities were filled with the experimental material.     

Mechanical effects of load speed on the human colon

The aim of this study was to examine the mechanical behavior of the colon using tensile tests under different loading speeds.Specimens were taken from different locations of the colonic frame from refrigerated cadavers. The specimens were submitted to uniaxial tensile tests after preconditioning using a dynamic load (1 m/s), intermediate load (10 cm/s), and quasi-static load (1 cm/s).A total of 336 specimens taken from 28 colons were tested. The stress-strain analysis for longitudinal specimens indicated a Young’s modulus of 3.17 ± 2.05 MPa under dynamic loading (1 m/s), 1.74 ± 1.15 MPa under intermediate loading (10 cm/s), and 1.76 ± 1.21 MPa under quasi-static loading (1 cm/s) with p < 0.001. For the circumferential specimen, the stress-strain curves indicated a Young’s modulus of 3.15 ± 1.73 MPa under dynamic loading (1 m/s), 2.14 ± 1.3 MPa under intermediate loading (10 cm/s), and 0.63 ± 1.25 MPa under quasi-static loading (1 cm/s) with p < 0.001. The curves reveal two types of behaviors of the colon: fast break behavior at high speed traction (1 m/s) and a lower break behavior for lower speeds (10 cm/s and 1 cm/s). The circumferential orientation required greater levels of stress and strain to obtain lesions than the longitudinal orientation. The presence of taeniae coli changed the mechanical response during low-speed loading.Colonic mechanical behavior varies with loading speeds with two different types of mechanical behavior: more fragile behavior under dynamic load and more elastic behavior for quasi-static load.     

Mechanical properties of the porcine growth plate and its three zones from unconfined compression tests

The aim of the study was to determine intrinsic mechanical properties of the complete growth plate and its reserve, proliferative and hypertrophic zones. Growth plate disk samples from newborn swine's ulnae were tested using stress relaxation tests under unconfined compression. The Transversely Isotropic Biphasic Model (TIBPE) derived by [Cohen, B., Lai, W. M., Mow, V. C., 1998. A transversely isotropic biphasic model for unconfined compression of growth plate and chondroepiphysis. Journal of Biomechanical Engineering, 120, pp. 491–496] was used to extract intrinsic mechanical properties using a four-parameter optimization procedure. Significant differences were found for the transverse permeability k₁, the Poisson's ratio in the transverse plane ν₂₁, the out-of-plane Poisson's ratio ν₃₁ and the out-of-plane Young's modulus E₃ between the reserve zone and the proliferative zone as well as between the reserve zone and the hypertrophic zone. The same trends were obtained for the Young's modulus in the transverse plane E₁, but significant differences were also found between the reserve zone and the complete growth plate. The proliferative and hypertrophic zones are half as stiff as the reserve zone along the compression axis and about three times less stiff than the reserve zone in the transverse plane. These two zones are also three times as permeable as the reserve zone in the radial direction. The mechanical behavior of the newborn porcine distal ulna growth plate is non-uniform along its thickness. The reserve zone, with its greater zonal component at that development stage, has noteworthy effects on the complete growth plate intrinsic mechanical properties. This study provides, for the very first time, an investigation of the intrinsic mechanical properties of the reserve, proliferative and hypertrophic zones of the growth plate.     

Simulation of muscle and adipose tissue deformation in the passive human pharynx

Quantifying the contribution of passive mechanical deformation in the human pharynx to upper airway collapse is fundamental to understanding the competing biomechanical processes that maintain airway patency. This study uses finite element analysis to examine deformation in the passive human pharynx using an intricate 3D anatomical model based on computed tomography scan images. Linear elastic properties are assigned to bone, cartilage, ligament, tendon, and membrane structures based on a survey of values reported in the literature. Velopharyngeal and oropharyngeal cross-sectional area versus airway pressure slopes are determined as functions of Young's moduli of muscle and adipose tissue. In vivo pharyngeal mechanics for small deformations near atmospheric pressure are matched by altering Young's moduli of muscle and adipose tissue. The results indicate that Young's moduli ranging from 0.33 to 14 kPa for muscle and adipose tissue matched the in vivo range of area versus pressure slopes. The developed anatomical model and determined Young's moduli range are expected to be useful as a starting point for more complex simulations of human upper airway collapse and obstructive sleep apnea therapy.     

Modelling of the mechanical and mass transport properties of auxetic molecular sieves: an idealised inorganic (zeolitic) host–guest system

Force field based simulations have been employed to model the structure, and mechanical and mass transport properties of the all-silica zeolite MFI (ZSM5—Si₉₆O₁₉₂). Undeformed and deformed MFI subject to uniaxial loading in each of the three principal directions were investigated. The mechanical properties are predicted to include negative on-axis Poisson's ratios (auxetic behaviour) in the x ₁–x ₃ plane of the undeformed structure, and are strain-dependent. Transformation from positive-to-negative Poisson's ratio behaviour, and vice versa, is predicted for most on-axis Poisson's ratios at critical loading strains. Simulations of the simultaneous sorption of neopentane and benzene guest molecules onto the undeformed host MFI framework indicate a low neopentane-to-benzene loading ratio, consistent with experimental observation. The sorption of these two molecular species onto deformed MFI is Poisson's ratio- and strain-dependent. Uniaxial tensile loading along a direction containing a negative on-axis Poisson's ratio leads to an increase in the loading of the larger neopentane molecules with respect to benzene, strongly correlated with the increase in volume associated with auxetic behaviour.     

New resource for the computation of cartilage biphasic material properties with the interpolant response surface method

Cartilage material properties are important for understanding joint function and diseases, but can be challenging to obtain. Three biphasic material properties (aggregate modulus, Poisson's ratio and permeability) can be determined using an analytical or finite element model combined with optimisation to find the material properties values that best reproduce an experimental creep curve. The purpose of this study was to develop an easy-to-use resource to determine biphasic cartilage material properties. A Cartilage Interpolant Response Surface was generated from interpolation of finite element simulations of creep indentation tests. Creep indentation tests were performed on five sites across a tibial plateau. A least-squares residual search of the Cartilage Interpolant Response Surface resulted in a best-fit curve for each experimental condition with corresponding material properties. These sites provided a representative range of aggregate moduli (0.48–1.58 MPa), Poisson's ratio (0.00–0.05) and permeability (1.7 × 10^? 15–5.4 × 10^? 15 m⁴/N s) values found in human cartilage. The resource is freely available from https://simtk.org/home/va-squish.     

Characterization of bone-implant fixation using modal analysis: Application to a press-fit implant model

Orthopaedic implant fixation is strongly dependant upon the effective mechanical properties of newly formed tissue. In this study, we evaluated the potential of modal analysis to derive viscoelastic properties of periprosthetic tissue. We hypothesized that Young's modulus and loss factor could be obtained by a combined theoretical, computational and experimental modal analysis approach. This procedure was applied to ex vivo specimens from a cylindrical experimental implant placed in cancellous bone in an unloaded press-fit configuration, obtained after a four week observation period. Four sections each from seven textured titanium implants were investigated. The first resonant frequency and loss factor were measured. Average experimentally determined loss factor was 2% (SD 0.4%) and average first resonant frequency was 2.1 KHz (SD: 50). A 2D axisymmetric finite element (FE) model identified effective Young's modulus of tissue using experimental resonant frequencies as input. Average value was 42 MPa (SD: 2.4) and no significant difference between specimens was observed.In this pilot study, the non-destructive method allowed accurate measure of dynamic loss factor and resonant frequency and derivation of effective Young's modulus. Prior to implementing this dynamic protocol for broader mechanical evaluation of experimental implant fixation, further work is needed to determine if this affects results from subsequent destructive shear push-out tests.     

Effects of co‐cultures of meniscus cells and articular chondrocytes on PLLA scaffolds

The knee meniscus, a fibrocartilaginous tissue located in the knee joint, is characterized by heterogeneity in extracellular matrix and biomechanical properties. To recreate these properties using a tissue engineering approach, co‐cultures of meniscus cells (MCs) and articular chondrocytes (ACs) were seeded in varying ratios (100:0, 75:25, 50:50, 25:75, and 0:100) on poly‐L ‐lactic acid (PLLA) scaffolds and cultured in serum‐free medium for 4 weeks. Histological, biochemical, and biomechanical tests were used to assess constructs at the end time point. Strong staining for collagen and glycosaminoglycan (GAG) was observed in all groups. Constructs with 100% MCs were positive for collagen I and constructs cultured with 100% ACs were positive for collagen II, while a mixture of collagen I and II was observed in other co‐culture groups. Total collagen and GAG per construct increased as the percentage of ACs increased (27 ± 8 µg, 0% AC to 45 ± 8 µg, 100% ACs for collagen and 12 ± 4 µg, 0% ACs to 40 ± 5 µg, 100% ACs for GAG). Compressive modulus (instantaneous and relaxation modulus) of the constructs was significantly higher in the 100% ACs group (63 ± 12 and 22 ± 9 kPa, respectively) when compared to groups with higher percentage of MCs. No differences in tensile properties were noted among groups. Specific co‐culture ratios were identified mimicking the GAG/DW of the inner (0:100, 25:75, and 50:50) and outer regions (100:0) of the meniscus. Overall, it was demonstrated that co‐culturing MCs and ACs on PLLA scaffolds results in functional tissue engineered meniscus constructs with a spectrum of biochemical and biomechanical properties. Biotechnol. Bioeng. 2009;103: 808–816. © 2009 Wiley Periodicals, Inc.     

Mechanical properties of the patellar tendon in adults and children

It is not currently known how the mechanical properties of human tendons change with maturation in the two sexes. To address this, the stiffness and Young's modulus of the patellar tendon were measured in men, women, boys and girls (each group, n=10). Patellar tendon force (F_pt) was calculated from the measured joint moment during a ramped voluntary isometric knee extension contraction, the antagonist knee extensor muscle co-activation quantified from its electromyographical activity, and the patellar tendon moment arm measured from magnetic resonance images. Tendon elongation was imaged using the sagittal-plane ultrasound scans throughout the contraction. Tendon cross-sectional area was measured at rest from ultrasound scans in the transverse plane. Maximal F_pt and tendon elongation were (mean±SE) 5453±307 N and 5±0.5 mm for men, 3877±307 N and 4.9±0.6 mm for women, 2017±170 N and 6.2±0.5 mm for boys and 2169±182 N and 5.9±0.7 mm for girls. In all groups, tendon stiffness and Young's modulus were examined at the level that corresponded to the maximal 30% of the weakest participant's F_pt and stress, respectively; these were 925–1321 N and 11.5–16.5 MPa, respectively. Stiffness was 94% greater in men than boys and 84% greater in women than girls (p<0.01), with no differences between men and women, or boys and girls (men 1076±87 N/mm; women 1030±139 N/mm; boys 555±71 N/mm and girls 561.5±57.4 N/mm). Young's modulus was 99% greater in men than boys (p<0.01), and 66% greater in women than girls (p<0.05). There were no differences in modulus between men and women, or boys and girls (men 597±49 MPa; women 549±70 MPa; boys 255±42 MPa and girls 302±33 MPa). These findings indicate that the mechanical stiffness of tendon increases with maturation due to an increased Young's modulus and, in females due to a greater increase in tendon cross-sectional area than tendon length.     

Influence of material properties on the mechanical behaviour of the L5-S1 intervertebral disc in compression: a nonlinear finite element study

A simple finite element model of the L₅-S₁ intervertebral disc body has been constructed; it is circular and symmetrical about the sagittal plane. The annulus fibrosus of the model was idealized as an inhomogeneous composite of an isotropic ground substance, reinforced by helically oriented collagen fibres so that the model has six different structural components namely: cortical bone, cancellous bone, cartilaginous endplates, nucleus pulposus, ground substance and collagen fibres. A sensitivity analysis of the material properties of each structural component was carried out by varying those properties for one structural component at a time and evaluating the changes in the biomechanical response to compressive displacements. Experimentally available relations between the applied compressive force and the vertical displacements, the nucleus pulposus pressure increase and the disc lateral bulge were used to evaluate the biomechanical responses for each set of material properties. Results showed that both the Poisson's ratio and the Young's modulus of the ground substance play an important role in the prediction of the biomechanical response.     

Deformation analysis of microcapsules compressed by two rigid parallel plates

Alginate-poly(l)lysine-alginate microcapsules with a diameter of 200–300 μm were produced and subjected to compression experiments using two rigid parallel plates. The deformed shape was observed, and the relationship between the applied force and the displacement of the plate was measured. A practical analysis method is proposed for the prediction of mechanical properties of microcapsules, namely, the changes in force, transmural pressure, and deformed shape due to the change in the displacement of the plate. The analysis is based on a microcapsule model comprising an axi-symmetric elastic membrane with a constant capsule volume during deformation. Young’s modulus of the membrane, which is used in the analysis, was determined by applying the Hertz contact theory to the experimental results obtained by using an atomic force microscope. The bending stiffness and permeability of the membrane as well as the frictional force between the membrane and the plate were neglected in the analysis. A non-dimensional relationship between the applied force and the displacement of the plate was shown. The theoretically predicted compression force was smaller than the experimentally measured force in the small displacement region, whereas both forces were in good agreement in the large displacement region. The effects of change in Poisson’s ratio, which varied from 0 to 0.5, on the force, transmural pressure, and deformed shape were shown. Under the same displacement conditions, it was observed that the calculated deformed shape was almost coincident with the shape observed in the experiment.