Tissue differentiation and bone regeneration in an osteotomized mandible: a computational analysis of the latency period.

Mandibular symphyseal distraction osteogenesis is a common clinical procedure to modify the geometrical shape of the mandible for correcting problems of dental overcrowding and arch shrinkage. In spite of consolidated clinical use, questions remain concerning the optimal latency period and the influence of mastication loading on osteogenesis within the callus prior to the first distraction of the mandible. This work utilized a mechano-regulation model to assess bone regeneration within the callus of an osteotomized mandible. A 3D model of the mandible was reconstructed from CT scan data and meshed using poroelastic finite elements (FE). The stimulus regulating tissue differentiation within the callus was hypothesized to be a function of the strain and fluid flow computed by the FE model. This model was then used to analyse tissue differentiation during a 15-day latency period, defined as the time between the day of the osteotomy and the day when the first distraction is given to the device. The following predictions are made: (1) the mastication forces generated during the latency period support osteogenesis in certain regions of the callus, and that during the latency period the percentage of progenitor cells differentiating into osteoblasts increases; (2) reducing the mastication load by 70% during the latency period increases the number of progenitor cells differentiating into osteoblasts; (3) the stiffness of new tissue increases at a slower rate on the side of bone callus next to the occlusion of the mandibular ramus which could cause asymmetries in the bone tissue formation with respect to the middle sagittal plane. Although the model predicts that the mastication loading generates such asymmetries, their effects on the spatial distribution of callus mechanical properties are insignificant for typical latency periods used clinically. It is also predicted that a latency period of longer than a week will increase the risk of premature bone union across the callus.

Cement-in-cement revision hip arthroplasty: an analysis of clinical and biomechanical literature.

INTRODUCTION: The number of revision hip arthroplasties is increasing but several aspects of this procedure could be improved. One method of reducing intra-operative complications is the cement-in-cement technique. This procedure entails cementing a smaller femoral prosthesis into the existing stable cement mantle. The aim of this systematic review is to provide a concise overview of the existing historical, operative, biomechanical and clinical literature on the cement-in-cement construct. RESULTS: Four biomechanical publications exist in authoritative journals and these were reviewed. Simple specimens were produced and these were tested by static means. Although these published tests support the cement-in-cement technique, they cannot be regarded as conclusive. Areas which could be subject to further research are identified. Five clinical publications on patients undergoing cement-in-cement revisions were also reviewed. Patient numbers were generally low (7-53) apart from one study containing 354 patients. Long-term patient follow-up was not available except in Hubble's study (41 patients followed for 8 years). Outcomes of these patients were very satisfactory for the period of follow-up. Three expert reviews of cemented femoral revisions outline the cement in cement procedure. If other Orthopaedic Centres can emulate the results of the clinical research presented, complication rates, operative times and financial costs may be decreased. CONCLUSION: The analysis presented in this paper consolidates the latest biomechanical and clinical information on cement-in-cement revision hip arthroplasty. Although we find evidence to support the use of the method clinically, we do note that the scientific basis needs further investigation.

Bone ingrowth simulation for a concept glenoid component design.

Glenoid component loosening is the major problem of total shoulder arthroplasty. It is possible that uncemented component may be able to achieve superior fixation relative to cemented component. One option for uncemented glenoid is to use porous tantalum backing. Bone ingrowth into the porous backing requires a degree of stability to be achieved directly post-operatively. This paper investigates the feasibility of bone ingrowth with respect to the influence of primary fixation, elastic properties of the backing and friction at the bone prosthesis interface. Finite element models of three glenoid components with different primary fixation configurations are created. Bone ingrowth into the porous backing is modelled based on the magnitude of the relative interface micromotions and mechanoregulation of the mesenchymal stem cells that migrated via the bonded part of the interface. Primary fixation had the most influence on bone ingrowth. The simulation showed that its major role was not to firmly interlock the prosthesis, but rather provide such a distribution of load, that would result in reduction of the peak interface micromotions. Should primary fixation be provided, friction has a secondary importance with respect to bone ingrowth while the influence of stiffness was counter intuitive: a less stiff backing material inhibits bone ingrowth by higher interface micromotions and stimulation of fibrous tissue formation within the backing.

Microdamage accumulation in the cement layer of hip replacements under flexural loading.

Mechanical fatigue of bone cement leading to damage accumulation is implicated in the loosening of cemented hip components. Even though cracks have been identified in autopsy-retrieved mantles, damage accumulation by continuous growth and increase in number of microcracks has not yet been demonstrated experimentally. To determine just how damage accumulation occurs in the cement layer of a hip replacement, a physical model of the joint was used in an experimental study. The model regenerates the stress pattern found in the cement layers whilst at the same time allowing visualisation of microcrack initiation and growth. In this way the gradual process of damage accumulation can be determined. Six specimens were tested to 5 million cycles and a total of 1373 cracks were observed. It was found that, under the flexural loading allowed by the model, the majority of cracks come from pores in the bulk cement and not from the interfaces. Furthermore, the lateral and medial sides have statistically different damage accumulation behaviours, and pre-load cracks significantly accelerate the damage accumulation process. The experimental results confirm that damage accumulation commences early on in the loading history and that it is continuously increasing with load in the form of crack initiation and crack propagation. The results highlight the importance of replicating the loading and restraint conditions of clinical cement mantles when endeavouring to accurately model the damage accumulation process.

Discriminating the loosening behaviour of cemented hip prostheses using measurements of migration and inducible displacement.

In vitro pre-clinical tests of hip prostheses have not yet been developed to the extent that inferior prostheses can be 'screened-out' prior to animal or clinical trials. This paper reports the experimental part of a project to develop a pre-clinical testing platform for cemented femoral hip implants. It is based on the clinical observation (Kärrholm et al. JBJS, 76B (1994) 912-916) that higher subsidence (distal migration) correlates with early revision of hip prostheses. A protocol to measure the relative movement between implant and bone was designed to test whether or not such a measurement, if made in a laboratory, could discriminate between hip prostheses. The protocol was applied to the Lubinus SPII prosthesis (W. Link, Germany) and a Müller Curved Stem (JRI Ltd., UK)-these prostheses were chosen because they are known to have different loosening rates in vivo. Five prostheses of each design were tested. The migration, the rate-of-migration, and the inducible displacement of each prosthesis was recorded over two million cycles of loading. For each implant, rapid initial migration was found, followed by a period of steady-state migration. In the majority of cases, the prostheses migrated medially, distally and posteriorly. On average, the Lubinus migrated less than the Müller in all directions. The average Lubinus migration was less than half that of the Müller, and this difference was significant at a level of p=0.05. Inducible displacement was greater for the Müller compared to the Lubinus. Furthermore, the inducible displacement decreased over time for the majority of Lubinus prostheses whereas it increased over time for the majority of the Müller prostheses leading to the conclusion that a rapid pre-clinical test based on measurement of inducible displacement may be possible.

Residual stress due to curing can initiate damage in porous bone cement: experimental and theoretical evidence.

Residual stress due to shrinkage of polymethylmethacrylate bone cement after polymerisation is possibly one factor capable of initiating cracks in the mantle of cemented hip replacements. No relationship between residual stress and observed cracking of cement has yet been demonstrated. To investigate if any relationship exists, a physical model has been developed which allows direct observation of damage in the cement layer on the femoral side of total hip replacement. The model contains medial and lateral cement layers between a bony surface and a metal stem; the tubular nature of the cement mantle is ignored. Five specimens were prepared and examined for cracking using manual tracing of stained cracks, observed by transmission microscopy; cracks were located and measured using image analysis. A mathematical approach for the prediction of residual stress due to shrinkage was developed which uses the thermal history of the material to predict when stress-locking occurs, and estimates subsequent thermal stress. The residual stress distribution of the cement layer in the physical model was then calculated using finite element analysis. Results show maximum tensile stresses normal to the observed crack directions, suggesting a link between residual stress and pre-load cracking. The residual stress predicted depends strongly on the definition of the reference temperature for stress-locking. The highest residual stresses (4-7 MPa) are predicted for shrinkage from maximum temperature; in this case, magnitudes are sufficiently high to initiate cracks when the influence of stress raisers such as pores or interdigitation at the bone/cement interface are taken into account (up to 24 MPa when calculating stress around a pore according to the method of Harrigan and Harris (J. Biomech. 24(11) (1991) 1047-1058). We conclude that the damage accumulation failure scenario begins before weight-bearing due to cracking induced by residual stress around pores or stress raisers.

Computer prediction of adaptive bone remodelling around noncemented femoral prostheses: the relationship between damage-based and strain-based algorithms.

Several mathematical models to predict tissue adaptation have been derived since Julius Wolff proposed a function-form relationship for bone. These can be formulated as computational procedures (algorithms) to predict bone adaptation around implants. The objective of this paper was to further develop the damage-adaptive algorithm, to test its validity, and to determine the relationship between it and algorithms based on strain energy. This was achieved using finite element models of the proximal femur, one for the intact case and another for the case where a noncemented hip prosthesis is implanted. The finite models were generated using CT scan data. Initial bone resorption patterns around a femoral prosthesis following total hip arthroplasty were computed for both damage-adaptive and strain-adaptive adaptation rules. It is found that the damage-adaptive algorithm can successfully predict the bone's adaptive behaviour in response to altered mechanical loading provided that account is taken of the nonlinear nature of damage accumulation. Predictions are made using a strain energy stimulus for comparison with the damage stimulus, and a theoretical relationship between the two is proposed. It is shown that an advantage of the damage approach over the strain-based approach is that the nonlinearity required to replicate clinically observed resorption patterns can be derived theoretically, whereas for strain-adaptive remodelling, empirical relationships are assumed.

The relationship between cement fatigue damage and implant surface finish in proximal femoral prostheses.

The majority of cemented femoral hip replacements fail as a consequence of loosening. One design feature that may affect loosening rates is implant surface finish. To determine whether or not surface finish effects fatigue damage accumulation in a bone cement mantle, we developed an experimental model of the implanted proximal femur that allows visualisation of damage growth in the cement layer. Five matte surface and five polished surface stems were tested. Pre-load damage and damage after two million cycles was measured. Levels of pre-load (shrinkage) damage were the same for both matte and polished stems; furthermore damage for matte vs. polished stems was not significantly different after two million cycles. This was due to the large variability in damage accumulation rates. Finite element analysis showed that the stress is higher for the polished (assumed debonded) stem, and therefore we must conclude that either the magnitude of the stress increase is not enough to appreciably increase the damage accumulation rate or, alternatively, the polished stem does not debond immediately from the cement. Significantly (P=0.05) more damage was initiated in the lateral cement compared to the medial cement for both kinds of surface finish. It was concluded that, despite the higher cement stresses with debonded stems, polished prostheses do not provoke the damage accumulation failure scenario.

Measurement of the migration of a cemented hip prosthesis in an in vitro test.

OBJECTIVE: To develop a method to measure the migration of a cemented hip prosthesis in an in vitro experimental test. DESIGN: A device to measure prosthesis movement relative to bone was designed and fabricated. It was tested using a Lubinus prosthesis (W. Link, Germany) implanted in a composite femur. BACKGROUND: Clinical studies using radiostereophotogrammetry have shown that those cemented hip prosthesis that migrate rapidly in the first two post-operative years are the ones that require early revision. If migration be used as a basis for a pre-clinical test, then it should be possible to screen-out inferior designs before implantation in animal or clinical trials. METHODS: The micromotion measurement device consisted of a 'target' of three spheres arranged in a cruciform structure. Six linear variable displacement transducers were aligned with the spheres so that motion of the prosthesis relative to the bone could be measured. RESULTS: The displacement and rotation of the prosthesis relative to the composite femur was recorded for two million cycles. Relative rapid initial migration was found, followed by a period of steady-state migration. Distal migration (called 'subsidence' in this paper) of up to 0.1 mm was measured; however the variability in absolute prosthesis migration was very high despite efforts to ensure that all extraneous factors were minimised. In the majority of cases, the prostheses migrated medially, distally and anteriorly. The absolute subsidence, and its variability, were similar to that recorded clinically. CONCLUSIONS: A method has been designed and tested which measures prosthesis migration in an experimental test. It provides a basis for a pre-clinical testing standard. Relevance. Hip prostheses need to be tested experimentally before implantation. However, no reliable test exists for such experimental tests. Rapid migration of a cemented prosthesis relative to bone has been shown in vivo to correlate with early failure, and in this paper a method to make such migration measurements in vitro is described and tested.

Mechanical simulation of muscle loading on the proximal femur: analysis of cemented femoral component migration with and without muscle loading.

OBJECTIVE: This study examines the effect of including muscle forces in fatigue tests of cemented total hip arthroplasty reconstructions. DESIGN: An experimental device capable of applying the joint reaction force, the abductor force, the vastus lateralis force, and the tensor fasciae latae force to the implanted femur is described. BACKGROUND: Current in vitro fatigue tests of cemented total hip arthroplasty reconstructions do not apply physiological muscle loads. Experimental and numerical studies report significant differences in stresses obtained in the cement mantle depending on the loads applied. The differing stresses may alter the outcome of an in vitro test. METHODS: Ten femoral components were reproducibly implanted into proximal composite femurs. Five of these femoral components were tested using a loadprofile which included muscle loading, five were tested without muscle loading. The migration of each femoral component was monitored continuously during dynamic fatigue tests. RESULTS: Clinically comparable migration amounts were found for both sets of femoral components, with the femoral components tested with muscle loading experiencing lower mean migration, lower mean inducible displacement, and less experimental scatter. CONCLUSIONS: The inclusion of muscle forces seems to stabilise the femoral component during the test. In vitro fatigue tests of cemented total hip arthroplasty reconstructions should include muscle loading to provide increased confidence in the results obtained. RELEVANCE: This study examines how the migration of cemented femoral hip prostheses is influenced by muscle forces. Hip prostheses are one of the few medical devices for which pre-clinical testing protocols have emerged, and this study ascertains whether or not the inclusion of muscle forces is necessary for pre-clinical tests. The conclusion that muscle loading should be included, and that it is important for the development of a new generation of standardised tests to provide enhanced patient protection against functionally poor prostheses.

Stress analysis of glenoid component designs for shoulder arthroplasty.

Secure and lasting fixation of the glenoid component in total shoulder arthroplasty is difficult because there is an insufficient volume of strong bone in the scapula. Consequently, radiolucencies of the glenoid component are common (much more common than radiolucencies of the humeral component). Early glenoid component designs were fabricated wholly from polyethylene, were fixated with PMMA cement, and had various degrees of constraint and conformity between the glenoid surface and the ball of the humeral component. More recent design variations include metal backing and non-cemented anchorage systems. In this study, various designs of cemented glenoid component are analysed using the finite element method. These are examined for (a) two different abduction angles; 60 degrees and 90 degrees; (b) high and low conformity and (c) high and low constraint. Stress distributions are compared with the failure strengths of the components and the influence of the various design factors can be observed.

Contact stresses in the glenoid component in total shoulder arthroplasty.

Several studies of retrieved glenoid components from total shoulder arthroplasty show an erosion of the rim, surface irregularities, component fracture and wear resulting from polyethylene deformation in vivo. Particles resulting from polyethylene wear might be one of the reasons for the very high rate of glenoid component loosening found clinically. Because wear can be the result of high contact stresses, the aim of this study is to find out whether or not contact stresses are high enough to cause wear of the glenoid component and what influence the component type and geometry have on polyethylene contact stresses for different humerus abduction angles. Elasticity theory is used in a parametric study of contact stresses in several glenoid component designs. A finite element method is used to confirm the accuracy of the analytical solution. The analysis shows that the peak stress generated in glenoid components under conditions of normal living can be as high as 25 MPa; since this exceeds the polyethylene yield strength, wear and also cold flow of the components can be expected. It is predicted that more conforming components have lower contact stresses, which might result in lower wear rate and less cold flow. It is also found that a metal-backed component promotes higher contact stresses than an all-polyethylene component with the same total thickness, therefore it can be expected that metal-backed components have inferior wear properties.

An investigation of the performance of Biostop G and Hardinge bone plugs.

Although distal plugging is a common procedure to prevent distal flow of polymethyl-methacrylate (PMMA) cement during cementing of femoral prostheses, there is little biomechanical testing to confirm that (a) the plugs do not displace under cementing pressure, and (b) they do in fact occlude cement flow. Two designs of femoral intramedullary plugs, the Biostop G (Bioland, France) and Hardinge (De Puy, Leeds, UK) were examined to determine their performance under cement pressurization in a biomechanical test. A testing rig was fabricated in which distal migration could be measured as a function of cement pressurization. Sectioning of the samples after polymerization of the cement revealed the extent of cement flow. The results show that, even in this well controlled test, there is significant variability in plug performance. It is shown that the Biostop G displaces less than the Hardinge for similar cement pressures. Sectioning reveals that cement can escape around the Hardinge plug at high pressures. Furthermore, a pore forming effect of the Biostop G plug was occasionally observed indicating that design improvements may be possible for this plug.

Modelling medical devices: the application of bioengineering in surgery.

Medical device technology has an increasingly important role in surgical procedures. In this article, five case studies of bioengineering in surgery are described as follows: computer-aided design of vascular grafts; middle-ear prostheses; hip prosthesis stems for optimal cement pressurisation; prototype development of a device for measurement of abdominal sounds for monitoring digestive tract activity and a hand-access device for laparoscopic surgery. In each case, new bioengineering design methodologies are demonstrated. The general principles underlying the application of bioengineering in surgery are discussed.

Biomechanics and mechanobiology in osteochondral tissues.

Osteochondral tissues are those that form the synovial joints, namely cartilage and bone, including sub-chondral bone. The biomechanical purpose of synovial joints is to provide lubricated contact between the moving surfaces with as little frictional forces as possible. This is achieved by separating the cartilage layers by a thin film of fluid and supporting the cartilage layers by a bony trabecular network that becomes dense and more calcified immediately underneath the cartilage layer. Each tissue's biomechanical behavior is well understood after several decades of research and this behavior is briefly reviewed here, as are the concepts relating to the mechanical induction of cartilage degradation (osteoarthritis) with a discussion of clinical strategies for repair. Focusing on tissue-engineering strategies, the following concepts are reviewed: scaffolds, bioreactors and computational simulations, with an analysis of how these elements may be combined in future.

An analysis of crack propagation paths at implant/bone-cement interfaces.

Clinical follow-up studies of joint replacements indicate that debonding of the implant from the bone-cement is the first mechanical event of loosening. Debonding can occur due to unsustainable interface stresses, usually initiated from defects along the interface. Such defects, or flaws, are inevitably introduced during the surgical procedure and from polymerisation shrinkage. Debonding leads to increased stresses within the cement mantle. This study is concerned with modelling the propagation of a crack from the debonded region on the cement/implant interface under physiological loading conditions for different implant materials and prosthesis designs. Using the theory of linear fracture mechanics for bimaterial interfaces, the behaviour of a crack along an interface between implant materials, under various states of stress, is studied. Specifically, a model is developed to determine the conditions under which a debonded region, along an otherwise bonded interface, will either propagate along the interface or will "kink" into the cement mantle. The relationship between the stress state and the crack propagation direction at the interface is then predicted for different interface materials, and it is shown that different crack directions exist for different materials, even when the stress state is the same. Furthermore, the crack behavior is shown to be dependent on the ratio of normal stress to shear stress at the interface and this may be important for the design optimisation of load-bearing cemented prostheses. Finally, the likelihood that an interface crack will propagate into the cement mantle is explored using a suitable fracture criterion.

The relationship between stress, porosity, and nonlinear damage accumulation in acrylic bone cement.

The long-term survival of cemented hip replacements depends on the ability of the cemented fixation to resist fatigue damage. Damage has been assumed to accumulate linearly (Miner's law) even though it is unlikely to be the case in such a porous brittle material. This study addresses the nonlinear stress-dependent nature of fatigue damage accumulation in acrylic bone cement. Specimens were subjected to a zero-to-tension fatigue load in water at 37 degrees C. A total of 15 specimens were tested, i.e., five specimens at each of three stress levels. The specimens were cyclically loaded to a certain fraction of their fatigue lives and the amount of microcracking present at that time was quantified by counting each crack and measuring its length. This procedure was repeated until the specimen failed. A total of 801 cracks formed in the 15 specimens. All cracks were found to initiate at pores. Crack propagation directions were distributed normally about the direction perpendicular to the applied load at the lower stress levels, but at higher stress, the distribution tended to be broader. At higher stresses, more cracks were produced per pore. The damage accumulation process in acrylic bone cement was found to be nonlinear with the degree of nonlinearity increasing with stress. Furthermore, great variability was found which was attributed to the differences in porosity between specimens. A power law equation is given which describes the predicted relationship between damage accumulation and number of loading cycles as a function of the stress level.

Evaluation of cement stresses in finite element analyses of cemented orthopaedic implants.

Stress analysis of the cement fixation of orthopaedic implants to bone is frequently carried out using finite element analysis. However the stress distribution in the cement layer is usually intricate, and it is difficult to report it in a way that facilitates comparison of implants for pre-clinical testing. To study this problem, and make recommendations for stress reporting, a finite element analysis of a hip prosthesis implanted into a synthetic composite femur is developed. Three cases are analyzed: a fully bonded implant, a debonded implant, and a debonded implant where the cement is removed distal to the stem tip. In addition to peak stresses, and contour and vector plots, a stressed volume and probability-of-failure analysis is reported. It is predicted that the peak stress is highest for the debonded stem, and that removal of the distal cement more than halves this peak stress. This would suggest that omission of the distal cement is good for polished prostheses (as practiced for the Exeter design). However, if the percentage of cement stressed above a certain threshold (say 3 MPa) is considered, then the removal of distal cement is shown to be disadvantageous because a higher volume of cement is stressed to above the threshold. Vector plots clearly demonstrate the different load transfer for bonded and debonded prostheses: A bonded stem generates maximum tensile stresses in the longitudinal direction, whereas a debonded stem generates most tensile stresses in the hoop direction, except near the tip where tensile longitudinal stresses occur due to subsidence of the stem. Removal of the cement distal to the tip allows greater subsidence but alleviates these large stresses at the tip, albeit at the expense of increased hoop stresses throughout the mantle. It is concluded that a thorough analysis of cemented implants should not report peak stress, which can be misleading, but rather stressed volume, and that vector plots should be reported if a precise analysis of the load transfer mechanism is required.

Three-dimensional finite element analysis of glenoid replacement prostheses: a comparison of keeled and pegged anchorage systems.

Glenoid component loosening is the dominant cause of failure in total shoulder arthroplasty. It is presumed that loosening in the glenoid is caused by high stresses in the cement layer. Several anchorage systems have been designed with the aim of reducing the loosening rate, the two major categories being "keeled" fixation and "pegged" fixation. However, no three-dimensional finite element analysis has been performed to quantify the stresses in the cement or to compare the different glenoid prosthesis anchorage systems. The objective of this study was to determine the stresses in the cement layer and surrounding bone for glenoid replacement components. A three-dimensional model of the scapula was generated using CT data for geometry and material property definition. Keeled and pegged designs were inserted into the glenoid, surrounded by a 1-mm layer of bone cement. A 90 deg arm abduction load with a full muscle and joint load was applied, following van der Helm (1994). Deformations of the prosthesis, stresses in the cement, and stresses in the bone were calculated. Stresses were also calculated for a simulated case of rheumatoid arthritis (RA) in which bone properties were modified to reflect that condition. A maximum principal stress-based failure model was used to predict what quantity of the cement is at risk of failure at the levels of stress computed. The prediction is that 94 percent (pegged prosthesis) and 68 percent (keeled prosthesis) of the cement has a greater than 95 percent probability of survival in normal bone. In RA bone, however, the situation is reversed where 86 percent (pegged prosthesis) and 99 percent (keeled prosthesis) of the cement has a greater than 95 percent probability of survival. Bone stresses are shown to be not much affected by the prosthesis design, except at the tip of the central peg or keel. It is concluded that a "pegged" anchorage system is superior for normal bone, whereas a "keeled" anchorage system is superior for RA bone.

Fatigue failure in the cement mantle of an artificial hip joint.

The cement mantle of an artificial hip joint was retrieved, largely intact, during a revision operation, and subjected to detailed failure analysis. The results reveal a number of features which are important to our understanding of the failure of bone cement in situ and its consequences for prosthesis loosening. Microscopic examination showed clear evidence of fatigue cracking in the mantle prior to removal. This took the form of worn areas in certain regions of the fracture surfaces, which elsewhere showed evidence of rapid, brittle fracture. The mantle contained two large defects which had been introduced during insertion; fatigue was shown to have originated both from these defects and from the proximal surface. Results from a finite element analysis were used, together with the techniques of fracture mechanics, in an attempt to explain the magnitude and direction of fatigue cracking. Fracture mechanics calculations, though subject to some uncertainty in this case, indicate that the local stress intensity in the region of the principal defect would have been sufficient to exceed the threshold for fatigue crack propagation in this material. This approach demonstrates the advantages of this 'defect-tolerance' analysis.