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### TECHNICAL PAPERS: Bone/Orthopedic

J Biomech Eng. 2005;127(5):729-735. doi:10.1115/1.1992527.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(5):736-741. doi:10.1115/1.1993663.

Background: Whole bone in vitro biomechanical compressive testing can be complicated by three factors: sample asymmetry, heterogeneous material properties, and unknown effective centroid location. Method of approach: The technique presented here facilitates the calculation of effective centroid position, modulus of elasticity and equivalent uniform strain magnitude for a cross section of bone from a simple whole bone compressive test. Simplification of section response to load is achieved through a combination of linear beam and simple planer geometry theory. The technique requires three longitudinal strain gauges be affixed around the test specimen cross section of interest, gauge position need not be determined. Sample loading is then accomplished using a simple four point loading jig. Results: Results of the technique are presented on an object with known elasticity and geometry, an aluminium tube, and seven pairs of equine third metacarpal whole bones. Conclusions: Average cross section modulus of elasticity, equivalent uniform cross section strain, and effective centroid locations were all predicted to within the range of published values. Employing the testing setup and analysis technique presented in this paper resulted in a significant savings in both implementation complexity and cost over previously available techniques.

Commentary by Dr. Valentin Fuster

### TECHNICAL PAPERS: Cell

J Biomech Eng. 2005;127(5):742-750. doi:10.1115/1.1992525.

An in vitro model system was developed to study structure-function relationships and the development of structural and mechanical anisotropy in collagenous tissues. Fibroblast-populated collagen gels were constrained either biaxially or uniaxially. Gel remodeling, biaxial mechanical properties, and collagen orientation were determined after $72h$ of culture. Collagen gels contracted spontaneously in the unconstrained direction, uniaxial mechanical constraints produced structural anisotropy, and this structural anisotropy was associated with mechanical anisotropy. Cardiac and tendon fibroblasts were compared to test the hypothesis that tendon fibroblasts should generate greater anisotropy in vitro. However, no differences were seen in either structure or mechanics of collagen gels populated with these two cell types, or between fibroblast populated gels and acellular gels. This study demonstrates our ability to control and measure the development of structural and mechanical anisotropy due to imposed mechanical constraints in a fibroblast-populated collagen gel model system. While imposed constraints were required for the development of anisotropy in this system, active remodeling of the gel by fibroblasts was not. This model system will provide a basis for investigating structure-function relationships in engineered constructs and for studying mechanisms underlying the development of anisotropy in collagenous tissues.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(5):751-757. doi:10.1115/1.1993661.

Thermal preconditioning protocols for cardiac cells were identified which produce elevated HSP70 levels while maintaining high cell viability. Bovine aortic endothelial cells were heated with a water bath at temperatures ranging from $44to50°C$ for periods of $1–30min$. Thermal stimulation protocols were determined which induce HSP70 expression levels ranging from 2.3 to 3.6 times the control while maintaining cell viabilities greater than 90%. An Arrhenius injury model fit to the cell damage data yielded values of $A=1.4×1066s−1$ and $Ea=4.1×105J∕mol$. Knowledge of the injury parameters and HSP70 kinetics will enhance dosimetry guideline development for thermal stimulation of heat shock proteins expression in cardiac tissue.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(5):758-766. doi:10.1115/1.1993664.

A combined experimental-numerical approach was adopted to characterize glucose and oxygen uptake and lactate production by bovine articular chondrocytes in a model system. For a wide range of cell concentrations, cells in agarose were supplemented with either low or high glucose medium. During an initial culture phase of $48h$, oxygen was monitored noninvasively using a biosensor system. Glucose and lactate were determined by medium sampling. In order to quantify glucose and oxygen uptake, a finite element approach was adopted to describe diffusion and uptake in the experimental model. Numerical predictions of lactate, based on simple relations for cell metabolism, were found to agree well for low glucose, but not for high glucose medium. Oxygen did not play a role in either case. Given the close association between chondrocyte energy metabolism and matrix synthesis, a quantifiable prediction of utilization can present a valuable contribution in the optimization of tissue engineering conditions.

Commentary by Dr. Valentin Fuster

### TECHNICAL PAPERS: Fluids/Heat/Transport

J Biomech Eng. 2005;127(5):767-775. doi:10.1115/1.1992521.

A Spiral Computerized Tomography (CT) scan of the aorta were obtained from a single subject and three model variations were examined. Computational fluid dynamics modeling of all three models showed variations in the velocity contours along the aortic arch with differences in the boundary layer growth and recirculation regions. Further downstream, all three models showed very similar velocity profiles during maximum velocity with differences occurring in the decelerating part of the pulse. Flow patterns obtained from transient 3-D computational fluid dynamics are influenced by different reconstruction methods and the pulsatility of the flow. Caution is required when analyzing models based on CT scans.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(5):776-781. doi:10.1115/1.1993662.

The Ahmed™ glaucoma valve (AGV) is a popular glaucoma drainage device, allowing maintenance of normal intraocular pressure in patients with reduced trabecular outflow facility. The uniquely attractive feature of the AGV, in contrast to other available drainage devices, is its variable resistance in response to changes in flow rate. As a result of this variable resistance, the AGV maintains a pressure drop between 7 and $12mmHg$ for a wide range of aqueous humor flow rates. In this paper, we demonstrate that the nonlinear behavior of the AGV is a direct result of the flexibility of the valve material. Due to the thin geometry of the system, the leaflets of the AGV were modeled using the von Kármán plate theory coupled to a Reynolds lubrication theory model of the aqueous humor flow through the valve. The resulting two-dimensional coupled steady-state partial differential equation system was solved by the finite element method. The Poisson’s ratio of the valve was set to 0.45, and the modulus was regressed to experimental data, giving a best-fit value $4.2MPa$. Simulation results compared favorably with previous experimental studies and our own pressure-drop∕flow-rate data. For an in vitro flow of $1.6μL∕min$, we calculated a pressure drop of $5.8mmHg$ and measured a pressure drop of $5.2±0.4mmHg$. As flow rate was increased, pressure drop rose in a strongly sublinear fashion, with a flow rate of $20μL∕min$ giving a predicted pressure drop of only $10.9mmHg$ and a measured pressure drop of $10.5±1.1mmHg$. The AGV model was then applied to simulate in vivo conditions. For an aqueous humor flow rate of $1.5–3.0μL∕min$, the calculated pressure drops were 5.3 and $6.3mmHg$.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(5):782-797. doi:10.1115/1.1993665.

Time-accurate, fully 3D numerical simulations and particle image velocity laboratory experiments are carried out for flow through a fully open bileaflet mechanical heart valve under steady (nonpulsatile) inflow conditions. Flows at two different Reynolds numbers, one in the laminar regime and the other turbulent (near-peak systole flow rate), are investigated. A direct numerical simulation is carried out for the laminar flow case while the turbulent flow is investigated with two different unsteady statistical turbulence modeling approaches, unsteady Reynolds-averaged Navier-Stokes (URANS) and detached-eddy simulation (DES) approach. For both the laminar and turbulent cases the computed mean velocity profiles are in good overall agreement with the measurements. For the turbulent simulations, however, the comparisons with the measurements demonstrate clearly the superiority of the DES approach and underscore its potential as a powerful modeling tool of cardiovascular flows at physiological conditions. The study reveals numerous previously unknown features of the flow.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(5):798-806. doi:10.1115/1.1992529.

Many medical therapies require liquid plugs to be instilled into and delivered throughout the pulmonary airways. Improving these treatments requires a better understanding of how liquid distributes throughout these airways. In this study, gravitational and surface mechanisms determining the distribution of instilled liquids are examined experimentally using a bench-top model of a symmetrically bifurcating airway. A liquid plug was instilled into the parent tube and driven through the bifurcation by a syringe pump. The effect of gravity was adjusted by changing the roll angle $(ϕ)$ and pitch angle $(γ)$ of the bifurcation ($ϕ=γ=0deg$ was isogravitational). $ϕ$ determines the relative gravitational orientation of the two daughter tubes: when $ϕ≠0deg$, one daughter tube was lower (gravitationally favored) compared to the other. $γ$ determines the component of gravity acting along the axial direction of the parent tube: when $γ≠0deg$, a nonzero component of gravity acts along the axial direction of the parent tube. A splitting ratio $Rs$, is defined as the ratio of the liquid volume in the upper daughter to the lower just after plug splitting. We measured the splitting ratio, $Rs$, as a function of: the parent-tube capillary number $(Cap)$; the Bond number (Bo); $ϕ$; $γ$; and the presence of pre-existing plugs initially blocking either daughter tube. A critical capillary number $(Cac)$ was found to exist below which no liquid entered the upper daughter $(Rs=0)$, and above which $Rs$ increased and leveled off with $Cap$. $Cac$ increased while $Rs$ decreased with increasing $ϕ$, $γ$, and Bo for blocked and unblocked cases at a given $Cap>Cac$. Compared to the nonblockage cases, $Rs$ decreased (increased) at a given $Cap$ while $Cac$ increased (decreased) with an upper (lower) liquid blockage. More liquid entered the unblocked daughter with a blockage in one daughter tube, and this effect was larger with larger gravity effect. A simple theoretical model that predicts $Rs$ and $Cac$ is in qualitative agreement with the experiments over a wide range of parameters.

Commentary by Dr. Valentin Fuster

### TECHNICAL PAPERS: Joint/Whole Body

J Biomech Eng. 2005;127(5):807-812. doi:10.1115/1.1992520.

In previous biomechanical studies of the human spine, we implemented a hybrid controller to investigate load-displacement characteristics. We found that measurement errors in both position and force caused the controller to be less accurate than predicted. As an alternative to hybrid control, a fuzzy logic controller (FLC) has been developed and implemented in a robotic testing system for the human spine. An FLC is a real-time expert system that can emulate part of a human operator’s knowledge by using a set of action rules. The FLC provides simple but robust solutions that cover a wide range of system parameters and can cope with significant disturbances. It can be viewed as a heuristic and modular way of defining a nonlinear, table-based control system. In this study, an FLC is developed which uses the force difference and the change in force difference as the input parameters, and the displacement as the output parameter. A rule-table based on these parameters is designed for the controller. Experiments on a physical model composed of springs demonstrate the improved performance of the proposed method.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(5):813-818. doi:10.1115/1.1992522.

Rigid body total knee replacement (TKR) models with tibiofemoral contact based on elastic foundation (EF) theory utilize simple contact pressure-surface overclosure relationships to estimate joint mechanics, and require significantly less computational time than corresponding deformable finite element (FE) methods. However, potential differences in predicted kinematics between these representations are currently not well understood, and it is unclear if the estimates of contact area and pressure are acceptable. Therefore, the objectives of the current study were to develop rigid EF and deformable FE models of tibiofemoral contact, and to compare predicted kinematics and contact mechanics from both representations during gait loading conditions with three different implant designs. Linear and nonlinear contact pressure-surface overclosure relationships based on polyethylene material properties were developed using EF theory. All other variables being equal, rigid body FE models accurately estimated kinematics predicted by fully deformable FE models and required only 2% of the analysis time. As expected, the linear EF contact model sufficiently approximated trends for peak contact pressures, but overestimated the deformable results by up to 30%. The nonlinear EF contact model more accurately reproduced trends and magnitudes of the deformable analysis, with maximum differences of approximately 15% at the peak pressures during the gait cycle. All contact area predictions agreed in trend and magnitude. Using rigid models, edge-loading conditions resulted in substantial overestimation of peak pressure. Optimal nonlinear EF contact relationships were developed for specific TKR designs for use in parametric or repetitive analyses where computational time is paramount. The explicit FE analysis method utilized here provides a unique approach in that both rigid and deformable analyses can be run from the same input file, thus enabling simple selection of the most appropriate representation for the analysis of interest.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(5):819-828. doi:10.1115/1.1992523.

Background: Myofascial force transmission occurs between muscles (intermuscular myofascial force transmission) and from muscles to surrounding nonmuscular structures such as neurovascular tracts and bone (extramuscular myofascial force transmission). The purpose was to investigate the mechanical role of the epimuscular connections (the integral system of inter- and extramuscular connections) as well as the isolated role of extramuscular connections on myofascial force transmission and to test the hypothesis, if such connections are prestrained. Method of approach: Length-force characteristics of extensor hallucis longus (EHL) muscle of the rat were measured in two conditions: (I) with the neighboring EDL muscle and epimuscular connections of the muscles intact: EDL was kept at a constant muscle tendon complex length. (II) After removing EDL, leaving EHL with intact extramuscular connections exclusively. Results: (I) Epimuscular connections of the tested muscles proved to be prestrained significantly. (1) Passive EHL force was nonzero for all isometric EHL lengths including very low lengths, increasing with length to approximately 13% of optimum force at high length. (2) Significant proximodistal EDL force differences were found at all EHL lengths: Initially, proximal EDL force $=1.18±0.11N$, where as distal EDL force $=1.50±0.08N$ (mean $±$ SE). EHL lengthening decreased the proximo-distal EDL force difference significantly (by 18.4%) but the dominance of EDL distal force remained. This shows that EHL lengthening reduces the prestrain on epimuscular connections via intermuscular connections; however; the prestrain on the extramuscular connections of EDL remains effective. (II) Removing EDL muscle affected EHL forces significantly. (1) Passive EHL forces decreased at all muscle lengths by approximately 17%. However, EHL passive force was still nonzero for the entire isometric EHL length range, indicating pre-strain of extramuscular connections of EHL. This indicates that a substantial part of the effects originates solely from the extramuscular connections of EHL. However, a role for intermuscular connections between EHL and EDL, when present, cannot be excluded. (2) Total EHL forces included significant shape changes in the length-force curve (e.g., optimal EHL force decreased significantly by 6%) showing that due to myofascial force transmission muscle length-force characteristics are not specific properties of individual muscles. Conclusions: The pre-strain in the epimuscular connections of EDL and EHL indicate that these myofascial pathways are sufficiently stiff to transmit force even after small changes in relative position of a muscle with respect to its neighboring muscular and nonmuscular tissues. This suggests the likelihood of such effects also in vivo.

Topics: Force , Muscle
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(5):829-837. doi:10.1115/1.1992524.

A new method is presented for measuring joint kinematics by optimally matching modeled trajectories of geometric surface models of bones with cine phase contrast (cine-PC) magnetic resonance imaging data. The incorporation of the geometric bone models (GBMs) allows computation of kinematics based on coordinate systems placed relative to full 3-D anatomy, as well as quantification of changes in articular contact locations and relative velocities during dynamic motion. These capabilities are additional to those of cine-PC based techniques that have been used previously to measure joint kinematics during activity. Cine-PC magnitude and velocity data are collected on a fixed image plane prescribed through a repetitively moved skeletal joint. The intersection of each GBM with a simulated image plane is calculated as the model moves along a computed trajectory, and cine-PC velocity data are sampled from the regions of the velocity images within the area of this intersection. From the sampled velocity data, the instantaneous linear and angular velocities of a coordinate system fixed to the GBM are estimated, and integration of the linear and angular velocities is used to predict updated trajectories. A moving validation phantom that produces motions and velocity data similar to those observed in an experiment on human knee kinematics was designed. This phantom was used to assess cine-PC rigid body tracking performance by comparing the kinematics of the phantom measured by this method to similar measurements made using a magnetic tracking system. Average differences between the two methods were measured as 2.82 mm rms for anterior∕posterior tibial position, and 2.63 deg rms for axial rotation. An inter-trial repeatability study of human knee kinematics using the new method produced rms differences in anterior∕posterior tibial position and axial rotation of 1.44 mm and 2.35 deg. The performance of the method is concluded to be sufficient for the effective study of kinematic changes caused to knees by soft tissue injuries.

Commentary by Dr. Valentin Fuster

### TECHNICAL PAPERS: Soft Tissue

J Biomech Eng. 2005;127(5):838-848. doi:10.1115/1.1992528.

An experimental study has been conducted on the penetration of silicone rubbers and human skin in vivo by sharp-tipped and flat-bottomed cylindrical punches. A penetrometer was developed to measure the penetration of human skin in vivo, while a conventional screw-driven testing machine was used to penetrate the silicone rubbers. The experiments reveal that the penetration mechanism of a soft solid depends upon the punch tip geometry: a sharp tipped punch penetrates by the formation and wedging open of a mode I planar crack, while a flat-bottomed punch penetrates by the growth of a mode II ring crack. The planar crack advances with the punch, and friction along the flanks of the punch leads to a rising load versus displacement response. In contrast, the flat-bottomed punch penetrates by jerky crack advance and the load on the punch is unsteady. The average penetration pressure on the shank cross section of a flat-bottomed punch exceeds that for a sharp-tipped punch of the same diameter. In addition, the penetration pressure decreases as the diameter of the sharp-tipped punch increases. These findings are in broad agreement with the predictions of Shergold and Fleck [Proc. R. Soc. London, Ser. A (in press)] who proposed models for the penetration of a soft solid by a sharp-tipped and flat-bottomed punch.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(5):849-856. doi:10.1115/1.1992526.

The absorption of hand-transmitted vibration energy may be an etiological factor in vibration-induced disorders. The vibration power absorption density (VPAD) may be a better measure of energy than the total power absorption of the hand-arm system. The objectives of the present study are to develop a method to estimate the average absorption density in the fingers and to investigate its basic characteristics. Ten healthy male subjects were used in this study. The biodynamic response of the fingers in a power grip subjected to a broad-band random excitation was measured under three grip forces (15, 30, $50N$) and three push forces (35, 45, $50N$). The response was used to estimate the total finger energy absorption. The response, together with the finger volume, was also used to estimate the amount of tissue effectively involved in the absorption. Then, the average VPAD under constant-acceleration, constant-power density, constant-velocity vibration spectra, and 20 tool vibration spectra were calculated. The correlations between the VPAD and the unweighted and weighted accelerations (ISO 5349-1, 2001) were also examined. The VPAD depends on both the characteristics of the vibration spectrum and the biodynamic response of the finger-hand-arm system. The biodynamic response generally plays a more important role in determining the VPAD in the middle frequency range $(31.5–400Hz)$ than those at the low and high ends. The applied force significantly affected the VPAD. The finger VPAD was highly correlated to the unweighted acceleration. The average VPAD can be determined using the proposed experimental method. It can serve as an alternative tool to quantify the severity of the vibration exposure for studying vibration-induced finger disorders.

Commentary by Dr. Valentin Fuster

### TECHNICAL PAPERS: Other

J Biomech Eng. 2005;127(5):857-861. doi:10.1115/1.1992535.

The biological response of valves to mechanical forces is not well understood. The aim of this study was to design a pulsatile system to enable the ex vivo study of aortic valves when subjected to various hemodynamic conditions. A bioreactor was designed to subject porcine aortic valves to physiological and pathophysiological pressure and flow conditions, while maintaining viability and sterility. Pressure and flow rate could be independently controlled to produce clinically relevant mechanical conditions. The oxygen transfer rate was characterized and sterile operation was achieved over $96hours$. The oxygenation capabilities ensure sufficient oxygen transport to valves, allowing operation for extended periods.

Commentary by Dr. Valentin Fuster

### TECHNICAL BRIEFS

J Biomech Eng. 2005;127(5):862-867. doi:10.1115/1.1992534.

Wave intensity analysis (WIA) is a powerful technique to study pressure and flow velocity waves in the time domain in vascular networks. The method is based on the analysis of energy transported by the wave through computation of the wave intensity $dI=dPdU$, where $dP$ and $dU$ denote pressure and flow velocity changes per time interval, respectively. In this study we propose an analytical modification to the WIA so that it can be used to study waves in conditions of time varying elastic properties, such as the left ventricle (LV) during diastole. The approach is first analytically elaborated for a one-dimensional elastic tube-model of the left ventricle with a time-dependent pressure-area relationship. Data obtained with a validated quasi-three dimensional axisymmetrical model of the left ventricle are employed to demonstrate this new approach. Along the base-apex axis close to the base wave intensity curves are obtained, both using the standard method and the newly proposed modified method. The main difference between the standard and modified wave intensity pattern occurs immediately after the opening of the mitral valve. Where the standard WIA shows a backward expansion wave, the modified analysis shows a forward compression wave. The proposed modification needs to be taken into account when studying left ventricular relaxation, as it affects the wave type.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(5):868-871. doi:10.1115/1.1992530.

Knowledge of impending abdominal aortic aneurysm (AAA) rupture can help in surgical planning. Typically, aneurysm diameter is used as the indicator of rupture, but recent studies have hypothesized that pressure-induced biomechanical stress may be a better predictor. Verification of this hypothesis on a large study population with ruptured and unruptured AAA is vital if stress is to be reliably used as a clinical prognosticator for AAA rupture risk. We have developed an automated algorithm to calculate the peak stress in patient-specific AAA models. The algorithm contains a mesh refinement module, finite element analysis module, and a postprocessing visualization module. Several aspects of the methodology used are an improvement over past reported approaches. The entire analysis may be run from a single command and is completed in less than $1h$ with the peak wall stress recorded for statistical analysis. We have used our algorithm for stress analysis of numerous ruptured and unruptured AAA models and report some of our results here. By current estimates, peak stress in the aortic wall appears to be a better predictor of rupture than AAA diameter. Further use of our algorithm is ongoing on larger study populations to convincingly verify these findings.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(5):872-880. doi:10.1115/1.1992531.

Existing standards for the preclinical testing of femoral hip implants have been successful in the objective of guaranteeing the implant’s fatigue strength. There is a need for an experimental test which could ensure prostheses were not susceptible to aseptic loosening. In this study we measure the relative movement between the prosthesis and the bone of four different cemented femoral component designs in in vitro tests. The aim is to determine if differences can be distinguished and whether the differences correlate with clinical performance. The four designs are the Charnley (DePuy International Ltd., UK), the Exeter (Stryker Osteonics Howmedica Corp., USA), the Lubinus SPII (Waldemar-Link GmbH, Germany), and the Müller Curved (JRI Ltd, UK). Five tests were carried out for each femoral component type, giving a total of 20 tests, and their permanent relative displacement (termed migration) and recoverable (i.e., elastic) relative displacement (termed inducible displacement) monitored over one million loading cycles. Considerable variation occurred in the tests. Nonetheless, most femoral components migrated medially, posteriorly, and distally. Most also rotated into varus. Translations of the Charnley $(64microns)$ and Lubinus $(67microns)$ implants were less than the Müller $(72microns)$ and Exeter $(94microns)$ implants, but this difference is not statistically significant. Most of the femoral components had rapid early migration followed by slower steady-state migration. With regard to the steady state inducible displacements of the prostheses, those of the Charnley, Exeter, and Lubinus decreased or were stable with respect to time, whilst those of the Müller typically increased with respect to time. It is concluded that migration is not a suitable basis for in vitro comparison of prosthesis designs. However, inducible displacement trends provide a clinically comparable performance ranking.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(5):881-886. doi:10.1115/1.1992532.

The long term patency of end-to-side peripheral artery bypasses are low due to failure of the graft generally at the distal end of the bypass. Both material mismatch between the graft and the host artery and junction hemodynamics are cited as being major factors in disease formation at the junction. This study uses experimental methods to investigate the major differences in fluid dynamics and wall mechanics at the proximal and distal ends for rigid and compliant bypass grafts. Injection moulding was used to produce idealized transparent and compliant models of the graft/artery junction configuration. An ePTFE graft was then used to stiffen one of the models. These models were then investigated using two-dimensional video extensometry and one-dimensional laser Doppler anemometry to determine the junction deformations and fluid velocity profiles for the rigid and complaint graft anastomotic junctions. Junction strains were evaluated and generally found to be under 5% with a peak stain measured in the stiff graft model junction of 8.3% at $100mmHg$ applied pressure. Hemodynamic results were found to yield up to 40% difference in fluid velocities for the stiff/compliant comparison but up to 80% for the proximal/distal end comparisons. Similar strain conditions were assumed for the proximal and distal models while significant differences were noted in their associated hemodynamic changes. In contrasting the fluid dynamics and wall mechanics for the proximal and distal anastomoses, it is evident from the results of this study, that junction hemodynamics are the more variable factor.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(5):887-890. doi:10.1115/1.1992533.

An increase in anterior laxity following reconstruction of the anterior cruciate ligament (ACL) can result from lengthening of the graft construct either at the sites of fixation and/or between the sites of fixation (i.e., graft substance). Roentgen stereophotogrammetric analysis (RSA), which requires that radio-opaque markers be attached to the graft, has been shown to be a useful technique in determining lengthening in these regions. Previous methods have been used for attaching radio-opaque markers to the graft, but they all have limitations particularly for single-loop grafts. Therefore, the objective of this study was to evaluate injecting markers directly into the substance of a tendon as a viable method for measuring lengthening of single-loop graft constructs by determining the maximum amount of migration after cyclic loading. Tantalum spheres of 0.8 mm diameter were used as tendon markers. Ten single-loop tendon grafts were passed through tibial tunnels drilled in calf tibias and fixed with a tibial fixation device. Two tendon markers were inserted in one tendon bundle of each graft and the grafts were cyclically loaded for 225,000 cycles from 20 N to 170 N. At specified intervals, simultaneous radiographs were obtained of the tendon markers. Marker migration was computed as the change in distance between the two tendon markers parallel to the axis of the tibial tunnel. Marker migration had a root mean square (RMS) value of less than 0.1 mm. Because the RMS value indicates the error introduced into measurements of lengthening and because this error is negligible, the method described for attaching markers to single-loop ACL grafts has the potential to be useful for determining lengthening of single-loop ACL graft constructs in in vivo studies in humans.

Commentary by Dr. Valentin Fuster

### ERRATUM

J Biomech Eng. 2005;127(5):891. doi:10.1115/1.2054587.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster