Mechanisms of anterior-posterior stability of the knee joint under load-bearing

The anterior-posterior (AP) stability of the knee is an important aspect of functional performance. Studies have shown that the stability increases when compressive loads are applied, as indicated by reduced laxity, but the mechanism has not been fully explained. A test rig was designed which applied combinations of AP shear and compressive forces, and measured the AP displacements relative to the neutral position. Five knees were evaluated at compressive loads of 0, 250, 500, and 750 N, with the knee at 15° flexion. At each load, three cycles of shear force at ±100 N were applied. For the intact knee under load, the posterior tibial displacement was close to zero, due to the upward slope of the anterior medial tibial surface. The soft tissues were then resected in sequence to determine their role in AP laxity. After anterior cruciate ligament (ACL) resection, the anterior tibial displacement increased significantly even under load, highlighting its importance in stability. Meniscal resection further increased displacement but also the vertical displacement increased, implying the meniscus was providing a buffering effect. The PCL had no effect on any of the displacements under load. Plowing cartilage deformation and surface friction were negligible. This work highlighted the particular importance of the upward slope of the anterior medial tibial surface and the ACL to AP knee stability under load. The results are relevant to the design of total knees which reproduce anatomic knee stability behavior.     

Meniscofemoral ligaments--structural and material properties

The meniscofemoral ligaments (MFLs) of 28 human cadaveric knees were studied to determine their incidence, structural and material properties. Using the Race–Amis casting method for measurement, the mean cross-sectional area for the anterior MFL (aMFL) was 14.7 mm² (±14.8 mm²) whilst that of the posterior MFL (pMFL) was 20.9 mm² (±11.6 mm²). The ligaments were isolated and tensile tested in a materials testing machine. The mean loads to failure were 300.5 N (±155.0 N) for the aMFL and 302.5 N (±157.9 N) for the pMFL, with elastic moduli of 281 (±239 MPa) and 227 MPa (±128 MPa), respectively. These significant anatomical and material properties suggest a function for the MFL in the biomechanics of the knee, and should be borne in mind when considering hypotheses on MFL function. Such hypotheses include roles for the ligaments in knee stability and guiding meniscal motion.     

Effect of knee musculature on anterior cruciate ligament strain in vivo

Squatting is a commonly prescribed exercise following reconstruction of the anterior cruciate ligament (ACL). The objective of this paper was to measure the in vivo strain patterns of the normal ACL and the load at the knee for the simple squat and for squatting with a “sport cord”. A sport cord is a large elastic rubber tube used for added resistance. Strain patterns were deduced using displacement data from a Hall Effect Strain Transducer (HEST), while joint loads were determined by a mathematical model with inputs from a force plate and electrogoniometers. ACL strain for the free squat in one subject had a maximum of 2% at a knee angle of 10° and was slack for knee angles >17°. In squatting with a sport cord, peak strain was 1% at 10° and was slack at knee angles >14°. Since these peak strains are low, squatting appears to be a safe exercise for conservative rehabilitation of ACL reconstruction patients. In addition, the sport cord is a recommended augmentation to the activity. We believe that the decrease in strain with the sport cord results from added joint stiffness due to greater compressive forces at the tibiofemoral joint. This greater compressive force results from the approximately 10% increase in quadriceps activity. From shear force data predicted by the mathematical model, the maximum anterior drawer force for free squatting (50 N) was considerably less than for sport cord squatting (430 N). Therefore, the value of shear force at the tibiofemoral joint only partially determines the load placed on the ACL.     

The relationships between active extensibility, and passive and active stiffness of the knee flexors

Insufficient active knee flexor stiffness may predispose the anterior cruciate ligament to injury. Insufficient passive stiffness may result in insufficient active stiffness. Similarly, higher levels of musculotendinous extensibility may inhibit active and passive muscle stiffness, potentially contributing to an increased risk of injury. The literature is both limited and inconsistent concerning relationships between extensibility, passive stiffness, and active stiffness. Extensibility was measured as the maximal active knee extension angle from a supine position with the hip flexed to 90°. Passive stiffness was calculated as the slope of the moment–angle curve resulting from passive knee extension. Active stiffness was assessed via acceleration associated with damped oscillatory motion about the knee. Stepwise multiple regression indicated that passive stiffness accounted for 25% of active muscle stiffness variance. The linear combination of extensibility and passive stiffness explained only 2% more variance compared to passive stiffness alone. Musculotendinous extensibility was moderately related to passive muscle stiffness, and weakly related to active muscle stiffness. The moderate relationship observed between active and passive stiffness emphasizes the dependence of active muscle stiffness on cross-bridge formation, and the relatively smaller contribution from parallel elastic tissues. Additionally, heightened extensibility does not appear to be a predisposing factor for reduced muscle stiffness.     

Material properties and effect of preconditioning of human sclera,optic nerve,and optic nerve sheath

The optic nerve (ON) is a recently recognized tractional load on the eye during larger horizontal eye rotations. In order to understand the mechanical behavior of the eye during adduction, it is necessary to characterize material properties of the sclera, ON, and in particular its sheath. We performed tensile loading of specimens taken from fresh postmortem human eyes to characterize the range of variation in their biomechanical properties and determine the effect of preconditioning. We fitted reduced polynomial hyperelastic models to represent the nonlinear tensile behavior of the anterior, equatorial, posterior, and peripapillary sclera, as well as the ON and its sheath. For comparison, we analyzed tangent moduli in low and high strain regions to represent stiffness. Scleral stiffness generally decreased from anterior to posterior ocular regions. The ON had the lowest tangent modulus, but was surrounded by a much stiffer sheath. The low-strain hyperelastic behaviors of adjacent anatomical regions of the ON, ON sheath, and posterior sclera were similar as appropriate to avoid discontinuities at their boundaries. Regional stiffnesses within individual eyes were moderately correlated, implying that mechanical properties in one region of an eye do not reliably reflect properties of another region of that eye, and that potentially pathological combinations could occur in an eye if regional properties are discrepant. Preconditioning modestly stiffened ocular tissues, except peripapillary sclera that softened. The nonlinear mechanical behavior of posterior ocular tissues permits their stresses to match closely at low strains, although progressively increasing strain causes particularly great stress in the peripapillary region.

     

The effects of flexion and rotation on the length patterns of the ligaments of the knee

Measurements have been made of the lengths of the ligaments in human knee joint specimens. The ligaments considered were the lateral collateral, medial collateral, anterior cruciate and posterior cruciate. The ligament length patterns were determined for twelve specimens at flexions of 0, 30, 60, 90 and 120°, in neutral, internal rotation and external rotation at each angle. The collateral ligaments steadily diminished by about 20 per cent in length from 0 to 120° flexion, rotation having little effect. The anterior cruciate gradually increased 10 per cent from 0 to 120° flexion and the posterior cruciate, was 10 per cent longer at 0° flexion than at all other angles for which length was constant. The action of the cruciates was therefore somewhat reciprocal. Rotation had a significant effect on cruciate lengths, affecting the anterior more than the posterior cruciate. Computations were made of the change in length of the anterior and posterior fibres of each cruciate ligament, in relation to the central fibres. Reciprocal functions between fibres were demonstrated.     

Direct contribution of axial impact compressive load to anterior tibial load during simulated ski landing impact

Anterior tibial loading is a major factor involved in the anterior cruciate ligament (ACL) injury mechanism during ski impact landing. We sought to investigate the direct contribution of axial impact compressive load to anterior tibial load during simulated ski landing impact of intact knee joints without quadriceps activation. Twelve porcine knee specimens were procured. Four specimens were used as non-impact control while the remaining eight were mounted onto a material-testing system at 70° flexion and subjected to simulated landing impact, which was successively repeated with incremental actuator displacement. Four specimens from the impacted group underwent pre-impact MRI for tibial plateau angle measurements while the other four were subjected to histology and microCT for cartilage morphology and volume assessment. The tibial plateau angles ranged from 29.4 to 38.8°. There was a moderate linear relationship (Y=0.16X; R²=0.64; p<0.001) between peak axial impact compressive load (Y) and peak anterior tibial load (X). The anterior and posterior regions in the impacted group sustained surface cartilage fraying, superficial clefts and tidemark disruption, compared to the control group. MicroCT scans displayed visible cartilage deformation for both anterior and posterior regions in the impacted group. Due to the tibial plateau angle, increased axial impact compressive load can directly elevate anterior tibial load and hence contribute to ACL failure during simulated landing impact. Axial impact compressive load resulted in shear cartilage damage along anterior–posterior tibial plateau regions, due to its contribution to anterior tibial loading. This mechanism plays an important role in elevating ACL stress and cartilage deformation during impact landing.     

New parameters describing how knee ligaments carry force in situ predict interspecimen variations in laxity during simulated clinical exams

Knee laxity, defined as the net translation or rotation of the tibia relative to the femur in a given direction in response to an applied load, is highly variable from person to person. High levels of knee laxity as assessed during routine clinical exams are associated with first-time ligament injury and graft reinjury following reconstruction. During laxity exams, ligaments carry force to resist the applied load; however, relationships between intersubject variations in knee laxity and variations in how ligaments carry force as the knee moves through its passive envelope of motion, which we refer to as ligament engagement, are not well established. Thus, the objectives of this study were, first, to define parameters describing ligament engagement and, then, to link variations in ligament engagement and variations in laxity across a group of knees. We used a robotic manipulator in a cadaveric knee model (n = 20) to quantify how important knee stabilizers, namely the anterior and posterior cruciate ligaments (ACL and PCL, respectively), as well as the medial collateral ligament (MCL) engage during respective tests of anterior, posterior, and valgus laxity. Ligament engagement was quantified using three parameters: (1) in situ slack, defined as the relative tibiofemoral motion from the neutral position of the joint to the position where the ligament began to carry force; (2) in situ stiffness, defined as the slope of the linear portion of the ligament force–tibial motion response; and (3) ligament force at the peak applied load. Knee laxity was related to parameters of ligament engagement using univariate and multivariate regression models. Variations in the in situ slack of the ACL and PCL predicted anterior and posterior laxity, while variations in both in situ slack and in situ stiffness of the MCL predicted valgus laxity. Parameters of ligament engagement may be useful to further characterize the in situ biomechanical function of ligaments and ligament grafts.     

An instrumented,dynamic test for anterior laxity of the ankle joint complex

Evaluation of anterior laxity of the ankle joint complex is a difficult clinical problem. Currently, the prime determinant for anterolateral ligament function is the subjective manual examination of anterior laxity of the ankle joint complex. An instrumented dynamic test was developed for objective measurement of anterior laxity of the ankle joint complex. The principle of the test was to apply a force-impulse to the calcaneus, within the muscle reflex time, and to measure anterior–posterior and mediolateral rotation. The test was performed on a cadaver specimen and on 15 volunteers of which five subjects suffered from chronic one-sided lateral ankle ligament instability.

In the cadaver test, anterior translation values increased from 5 to 11 mm, after cutting the anterior talofibular ligament and subsequently cutting the calcaneofibular ligament. In the 10 normal subjects, the mean anterior translation value was 6.7 mm (±1.9 mm). The relative variation of the test result within a measurement session was 2.5% (±1.6%). Between the sessions the relative laxity variation was 2.6% (±2.6%). In the ten normal subjects the mean right–left difference was not significantly different from zero. In four out of the five patients it was more than 2 mm. As in the cadaver test in all measurements, the mediolateral rotations were small (<2.5°). The volunteers complained about same pain at the heel after multiple test sessions.

In conclusion the dynamic, functional test appears to be capable of objectively measuring a value for anterior laxity of the ankle joint complex reflecting the functional status of the anterolateral ankle ligaments.     

Evaluation of a cruciate ligament model: sensitivity to the parameters during drawer test simulation

The knowledge of how cruciate ligaments stabilize the knee joint could be very useful during the execution of daily living activities for the development of clinical procedures. The objective of this study was to evaluate a cruciate ligament model that could achieve this knowledge while avoiding any destructive measurements in living healthy subjects. Subject-specific geometries and kinematic data, acquired from a living subject, were the foundations of the devised model. Each cruciate ligament was modeled with 25 linear-elastic elements and their geometrical properties were subject specific. The anteroposterior drawer test was simulated, and the sensitivity to the reference length and the elastic modulus was performed. Laxity, anterior, and posterior stiffness were calculated and compared with the literature. The laxity was most sensitive to reference length but fitted the literature well considering the reference length estimated from the subject. Both stiffnesses were most sensitive to elastic modulus variations. At full extension, anterior stiffness overestimated the literature, but at 90 degrees good comparisons with the literature were obtained. Posterior stiffness showed smaller overestimations. The devised model, when properly improved, could evaluate the role of the cruciate ligaments of a living subject during the execution of daily living activities.     

Effects of radiograph projection parameter uncertainty on TKA kinematics from model-image registration

Model-image registration techniques have been used extensively for the measurement of joint kinematics in vivo. These techniques typically utilize an explicit measurement of X-ray projection parameters (principal distance, principal point), which is easily done for prospective studies. However, there is vast opportunity to derive useful information from previously collected clinical radiographic films where the projection parameters are unknown. The purpose of this study was to determine variation in measured knee arthroplasty kinematics when the X-ray projection parameters were unknown, but bounded. Based on the clinical radiographic protocol, a nominal principal point was chosen and eight additional points ±2 and ±5 cm in the horizontal and vertical directions were defined. Tibiofemoral kinematics were determined for all nine projection parameter sets for a series of 10 lateral radiographs. In addition, the principal distance was varied ±15 cm and tibiofemoral kinematics were determined for these two projection sets. Measured joint kinematics varied less than 0.6° and 0.4 mm for ±2 cm variations in principal point location, and 0.7° and 0.6 mm for ±5 cm variations in principal point location. Measured joint kinematics varied less than 0.6° and 0.7 mm for ±15 cm variations in principal distance. Variation in X-ray principal point and principal distance over clinically bounded ranges has a small effect on knee arthroplasty kinematics computed from model-image registration with high-quality clinical radiographs.     

A dynamic multibody model of the physiological knee to predict internal loads during movement in gravitational field

Obtaining tibio-femoral (TF) contact forces, ligament deformations and loads during daily life motor tasks would be useful to better understand the aetiopathogenesis of knee joint diseases or the effects of ligament reconstruction and knee arthroplasty. However, methods to obtain this information are either too simplified or too computationally demanding to be used for clinical application. A multibody dynamic model of the lower limb reproducing knee joint contact surfaces and ligaments was developed on the basis of magnetic resonance imaging. Several clinically relevant conditions were simulated, including resistance to hyperextension, varus–valgus stability, anterior–posterior drawer, loaded squat movement. Quadriceps force, ligament deformations and loads, and TF contact forces were computed. During anterior drawer test the anterior cruciate ligament (ACL) was maximally loaded when the knee was extended (392 N) while the posterior cruciate ligament (PCL) was much more stressed during posterior drawer when the knee was flexed (319 N). The simulated loaded squat revealed that the anterior fibres of ACL become inactive after 60° of flexion in conjunction with PCL anterior bundle activation, while most components of the collateral ligaments exhibit limited length changes. Maximum quadriceps and TF forces achieved 3.2 and 4.2 body weight, respectively. The possibility to easily manage model parameters and the low computational cost of each simulation represent key points of the present project. The obtained results are consistent with in vivo measurements, suggesting that the model can be used to simulate complex and clinically relevant exercises.     

Influence of patella alta on knee extensor mechanics

The purpose of this study was to compare the knee extensor mechanics in persons with and without patella alta. Thirteen subjects with patella alta and 14 subjects with normal patellar position participated in the study. Sagittal and axial MR images of the knee were acquired at 0°, 20°, 40°, and 60° of knee flexion. Measurements of actual moment arm, patellar ligament/quadriceps tendon force ratio, quadriceps effective moment arm, and joint reaction force/quadriceps force ratio were obtained. There were no differences between groups in terms of actual moment arm. However, subjects with patella alta had significantly larger patellar ligament/quadriceps tendon force ratios (1.04±0.02 vs. 0.92±0.02) and quadriceps effective moment arms (4.40±0.09 vs. 4.00±0.09 cm) when averaged across the range of knee flexion angles tested. There was no difference in the joint reaction force/quadriceps force ratio between groups. The observed differences in knee extensor mechanics suggest that individuals with patella alta have a more efficient knee extensor mechanism and would be expected to generate similar joint reaction forces per unit quadriceps force compared to subjects with normal patellar position. Therefore, persons with patella alta may experience less patellofemoral joint reaction force to overcome the same knee flexion moment in the range of 0°–60° of knee flexion.     

In vitro response of the natural cadaver knee to the loading profiles specified in a standard for knee implant wear testing

The purpose of this study was to examine how a natural knee responds to the inputs of a total knee replacement testing standard developed by the International Organization for Standardization (ISO). This load control standard prescribes forces to be used for wear testing of knee replacements independent of implant size or design. A parallel ISO standard provides wear testing inputs that are displacement based instead of force based. Eight fresh frozen cadaveric knees were potted and tested in a 6 degree of freedom knee simulator using the load-control standard. The resulting displacements during load-control testing were compared to the prescribed displacements of the ISO displacement standard. At half the tibial torque prescribed by the load standard there was three times more average internal tibial rotation (20.3°) than is prescribed by the displacement standard (5.7°). The AP motion resulting from load testing was much different than is specified by the displacement standard. All eight knees had anterior tibial translation with respect to the femur during swing phase while the displacement standard specifies posterior tibial displacement. The variation in these motions among knees and their difference from the ISO displacement standard may be one factor that explains why wear results of total knee replacements based on ISO load or displacement testing frequently do not agree with each other or with clinical retrievals.     

Thermal stabilization of collagen molecules in bone tissue

Differential thermal calorimetry (DSC) analysis of partially dehydrated bovine bone, demineralized bone and bovine tendon collagen was performed up to 300 °C to determine factors influencing stability of mineralized collagen in bone tissue. Two endothermal regions were recognized. The first, attributed to denaturation of collagen triple helix, was hydration dependent and had a peak at 155–165 °C in bone, 118–137 °C in tendon and 131–136 °C in demineralized bone. The second region extended from 245 to 290 °C in bone and from 200 to 280 °C in tendon and was connected with melting and decomposition of collagen. Differences in thermodynamic parameters between cortical and trabecular bone tissue were stated. Activation energy of collagen unfolding in native bone tissue increased with dehydration of the bone. From the results of the present study we conclude that dehydrated bone collagen is thermally very stable both in native and in demineralized bone. Presence of mineral additionally stabilizes bone tissue.     

A modeling study of partial ACL injury: simulated KT-2000 arthrometer tests

A partial ACL injury may involve different levels of fiber disruption, orfibers may sustain microscopic changes in their structure without gross disruption, resulting in a change in ligament function. The effect of partial ACL tears on the mechanical and functional stability of the knee has not been well documented, in part because of diagnostic difficulties. A computer model of the knee in the sagittal plane was used in this study to simulate tests using the KT-2000 Knee Arthrometer, which quantifies Lachman's test for ACL injury. A variety of partial ACL anterior and posterior bundle injuries were simulated. Anterior and posterior bundle injuries were subdivided into four different simulated injury levels: mild (one-half tear of the bundle), moderate (complete tear of the bundle), severe (complete tear of the bundle and tear of one-half of the other bundle), and more severe (severe injury plus an additional elongation of the other bundle represented by 5% increases of its initial strain). Force-displacement results obtained from simulated KT-2000 knee arthrometer tests depended on the level of injury. Mild and moderate injuries produced only small change in the anterior tibial translation--at different force levels. Severe injury produced increased anterior tibial translation depending on which bundle was completely ruptured. The compliance index defined as the ratio of the displacement and the force within 68 N and 90 N anterior drawer forces, the stiffness, and the rate of change of stiffness of the anterior force-displacement were found to be better at predicting partial ACL ruptures than simple differences in anterior tibial translation. It was possible in the model results to discriminate knees with various levels of partial ACL injuries using the first and second derivatives of the force-displacement curve.     

Thermoregulatory use of heat increment of feeding in the tawny owl (Strix aluco)

The heat increment of feeding (HIF) was investigated in the tawny owl (Strix aluco) in central Norway (63°N, 10°E), close to the northern limit of its distribution. HIF was measured as the increase in heat production (measured as oxygen consumption) after force-feeding the owls with laboratory mice at thermoneutral conditions (20 °C) and during cold-exposure (5 °C and −5 °C). The basal metabolic rate of the owls (mean mass 419 g) was 4.39 kJ h⁻¹ and the lower critical temperature was approximately 16 °C. During cold conditions, HIF substituted for thermogenesis, and at an ambient temperature of −5 °C the substitution was complete. Calculations indicate that the substitution by HIF may save the owls as much as 60% of their daily thermoregulatory costs. This corresponds to about 10% of their total daily energy budget.     

The Effect of Graft Strength on Knee Laxity and Graft In-Situ Forces after Posterior Cruciate Ligament Reconstruction

Surgical reconstruction is generally recommended for posterior cruciate ligament (PCL) injuries; however, the use of grafts is still a controversial problem. In this study, a three-dimensional finite element model of the human tibiofemoral joint with articular cartilage layers, menisci, and four main ligaments was constructed to investigate the effects of graft strengths on knee kinematics and in-situ forces of PCL grafts. Nine different graft strengths with stiffness ranging from 0% (PCL rupture) to 200%, in increments of 25%, of an intact PCL’s strength were used to simulate the PCL reconstruction. A 100 N posterior tibial drawer load was applied to the knee joint at full extension. Results revealed that the maximum posterior translation of the PCL rupture model (0% stiffness) was 6.77 mm in the medial compartment, which resulted in tibial internal rotation of about 3.01°. After PCL reconstruction with any graft strength, the laxity of the medial tibial compartment was noticeably improved. Tibial translation and rotation were similar to the intact knee after PCL reconstruction with graft strengths ranging from 75% to 125% of an intact PCL. When the graft’s strength surpassed 150%, the medial tibia moved forward and external tibial rotation greatly increased. The in-situ forces generated in the PCL grafts ranged from 13.15 N to 75.82 N, depending on the stiffness. In conclusion, the strength of PCL grafts have has a noticeable effect on anterior-posterior translation of the medial tibial compartment and its in-situ force. Similar kinematic response may happen in the models when the PCL graft’s strength lies between 75% and 125% of an intact PCL.     

A thermodynamic and crystallographic study of complexes of the highly preorganized ligand 8-hydroxyquinoline-2-carboxylic acid

The metal ion complexing properties of the ligand HQC (8-hydroxyquinoline-2-carboxylic acid) are reported. The structures of [Zn(HQCH)₂] · 3H₂O (1) and [Cd(HQCH)₂] · 3H₂O (2) were determined (HQCH = HQC with phenol protonated). Both 1 and 2 are triclinic, space group , with Z = 2. For 1 a = 7.152(3), b = 9.227(4), c = 15.629(7) Å,  = 103.978(7)°, β = 94.896(7)°, γ = 108.033(8)°, R = 0.0499. For 2 a = 7.0897(5), b = 9.1674(7), c = 16.0672(11) Å,  = 105.0240(10)°, β = 93.9910(10)°, γ = 107.1270(10)°, R = 0.0330. In 1 the Zn has a distorted octahedral coordination geometry, with Zn–N of 2.00 and 2.15 Å, and Zn–O to the protonated phenolic oxygens of 2.431 and 2.220 Å. The structure of 2 is similar, with Cd–N bonds of 2.220 and 2.228 Å, with Cd–O bonds to the protonated phenolate oxygens of 2.334 and 2.463 Å. The structures of 1 and 2, and isomorphous Ni(II) and Co(II) HQC complexes reported in the literature, show very interesting short (<2.5 Å) O–O distances in H-bonds involving the protons on the coordinated phenolates and lattice water molecules. These are discussed in relation to the possible role of short low-energy H-bonds in alcohol dehydrogenase in mediating the transfer of the hydroxyl proton of the alcohol to an adjacent serine oxygen.

The formation constants for HQC are determined by UV–Visible spectroscopy at 25 °C in 0.1 M NaClO₄ with Mg(II), Ca(II), Sr(II), Ba(II), La(III), Gd(III), Zn(II), Cd(II), Ni(II), Cu(II), and Pb(II). These show greatest stabilization with metal ions with an ionic radius above 1.0 Å. This is as would be expected from the fact that HQC forms two five-membered chelate rings on complex-formation, which favors larger metal ions. The ligand design concept of using rigid aromatic backbones in ligands to achieve high levels of preorganization, and hence the high log K values (for a tridentate ligand) and strong metal ion selectivities observed for HQC, is discussed.     

Circumferential variations of mechanical behavior of the porcine thoracic aorta during the inflation test

We developed an extension-inflation experimental apparatus with a stereo vision system and a stress-strain analysis method to determine the regional mechanical properties of a blood vessel. Seven proximal descending thoracic aortas were investigated during the inflation test at a fixed longitudinal stretch ratio of 1.35 over a transmural pressure range from 1.33 to 21.33 kPa. Four circumferential regions of each aorta were designated as the anterior (A), left lateral (L), posterior (P), and right lateral (R) regions, and the inflation test was repeated for each region of the aortas. We used continuous functions to approximate the surfaces of the regional aortic wall in the reference configuration and the deformed configuration. Circumferential stretch and stress at the four circumferential regions of the aorta were computed. Circumferential stiffness, defined as the tangent of the stress-stretch curve, and physiological aortic stiffness, named pressure-strain elastic modulus, were also computed for each region. In the low pressure range, the stress increased linearly with increased stretch, but the mechanical response became progressively stiffer in the high-pressure range above a transition point. At a transmural pressure of 12.00 kPa, mean values of stiffness were 416±104 kPa (A), 523±99 kPa (L), 634±91 kPa (P), and 489±82 kPa (R). The stiffness of the posterior region was significantly higher than that of the anterior region, but no significant difference was found in pressure-strain elastic modulus.