Advertisement for orthosearch.org.uk
Results 1 - 20 of 124
Results per page:
The Journal of Bone & Joint Surgery British Volume
Vol. 84-B, Issue 5 | Pages 748 - 752
1 Jul 2002
Berlemann U Ferguson SJ Nolte L Heini PF

Vertebroplasty, which is the percutaneous injection of bone cement into vertebral bodies has recently been used to treat painful osteoporotic compression fractures. Early clinical results have been encouraging, but very little is known about the consequences of augmentation with cement for the adjacent, non-augmented level. We therefore measured the overall failure, strength and structural stiffness of paired osteoporotic two-vertebra functional spine units (FSUs). One FSU of each pair was augmented with polymethyl-methacrylate bone cement in the caudal vertebra, while the other served as an untreated control. Compared with the controls, the ultimate failure load for FSUs treated by injection of cement was lower. The geometric mean treated/untreated ratio of failure load was 0.81, with 95% confidence limits from 0.70 to 0.92, (p < 0.01). There was no significant difference in overall FSU stiffness. For treated FSUs, there was a trend towards lower failure loads with increased filling with cement (r. 2. = 0.262, p = 0.13). The current practice of maximum filling with cement to restore the stiffness and strength of a vertebral body may provoke fractures in adjacent, non-augmented vertebrae. Further investigation is required to determine an optimal protocol for augmentation


The Journal of Bone & Joint Surgery British Volume
Vol. 87-B, Issue 11 | Pages 1561 - 1567
1 Nov 2005
Janssen D Aquarius R Stolk J Verdonschot N

The Capital Hip implant was a Charnley-based system which included a flanged and a roundback stem, both of which were available in stainless steel and titanium. The system was withdrawn from the market because of its inferior performance. However, all four of the designs did not produce poor rates of survival. Using a simulated-based, finite-element analysis, we have analysed the Capital Hip system. Our aim was to investigate whether our simulation was able to detect differences which could account for the varying survival between the Capital Hip designs, thereby further validating the simulation. We created finite-element models of reconstructions with the flanged and roundback Capital Hips. A loading history was applied representing normal walking and stair-climbing, while we monitored the formation of fatigue cracks in the cement. Corresponding to the clinical findings, our simulation was able to detect the negative effects of the titanium material and the flanged design in the Capital Hip system. Although improvements could be made by including the effect of the roughness of the surface of the stem, our study increased the value of the model as a predictive tool for determining failure of an implant


The Journal of Bone & Joint Surgery British Volume
Vol. 90-B, Issue 5 | Pages 680 - 684
1 May 2008
Simon DWN Clarkin CE Das-Gupta V Rawlinson SCF Emery RJ Pitsillides AA

We examined cultured osteoblasts derived from paired samples from the greater tuberosity and acromion from eight patients with large chronic tears of the rotator cuff. We found that osteoblasts from the tuberosity had no apparent response to mechanical stimulation, whereas those derived from the acromion showed an increase in alkaline phosphatase activity and nitric oxide release which is normally a response of bone cells to mechanical strain. By contrast, we found that cells from both regions were able to respond to dexamethasone, a well-established promoter of osteoblastic differentiation, with the expected increase in alkaline phosphatase activity. Our findings indicate that the failure of repair of the rotator cuff may be due, at least in part, to a compromised capacity for mechanoadaptation within the greater tuberosity. It remains to be seen whether this apparent decrease in the sensitivity of bone cells to mechanical stimulation is the specific consequence of the reduced load-bearing history of the greater tuberosity in these patients


The Journal of Bone & Joint Surgery British Volume
Vol. 90-B, Issue 1 | Pages 103 - 106
1 Jan 2008
Kettler M Tingart MJ Lunger J Kuhn V

Operative fixation is the treatment of choice for a rupture of the distal tendon of biceps. A variety of techniques have been described including transosseous sutures and suture anchors. The poor quality of the bone of the radial tuberosity might affect the load to failure of the tendon repair in early rehabilitation. The aim of this study was to determine the loads to failure of different techniques of fixation and to investigate their association with the bone mineral density of the radial tuberosity. Peripheral quantitative computed tomography was carried out to measure the trabecular and cortical bone mineral density of the radial tuberosity in 40 cadaver specimens. The loads to failure in four different techniques of fixation were determined. The Endobutton-based method showed the highest failure load at 270 N (. sd. 22) (p < 0.05). The mean failure load of the transosseous suture technique was 210 N (. sd. 66) and that of the TwinFix-QuickT 5.0 mm was 57 N (. sd. 22), significantly lower than those of all other repairs (p < 0.05). No significant correlation was seen between bone mineral density and loads to failure. The transosseous technique is an easy and cost-saving procedure for fixation of the distal biceps tendon. TwinFix-QuickT 5.0 mm had significantly lower failure loads, which might affect early rehabilitation, particularly in older patients


The Journal of Bone & Joint Surgery British Volume
Vol. 90-B, Issue 10 | Pages 1386 - 1391
1 Oct 2008
Ozbaydar M Elhassan B Esenyel C Atalar A Bozdag E Sunbuloglu E Kopuz N Demirhan M

We compared time-dependent changes in the biomechanical properties of single-and double-row repair of a simulated acute tear of the rotator cuff in rabbits to determine the effect of the fixation techniques on the healing process. A tear of the supraspinatus tendon was created in 80 rabbits which were separated into two equal groups. A single-row repair with two suture anchors was conducted in group 1 and a double-row repair with four suture anchors in group 2. A total of ten intact contralateral shoulder joints was used as a control group. Biomechanical testing was performed immediately post-operatively and at four and eight weeks, and histological analysis at four and eight weeks. The mean load to failure in group 2 animals was greater than in group 1, but both groups remained lower than the control group at all intervals. Histological analysis showed similar healing properties at four and eight weeks in both groups, but a significantly larger number of healed tendon-bone interfaces were identified in group 2 than in group 1 at eight weeks (p < 0.012). The ultimate load to failure increased with the number of suture anchors used immediately post-operatively, and at four and eight weeks. The increased load to failure at eight weeks seemed to be related to the increase in the surface area of healed tendon-to-bone in the double-row repair group


The Journal of Bone & Joint Surgery British Volume
Vol. 92-B, Issue 8 | Pages 1165 - 1170
1 Aug 2010
Hirpara KM Sullivan PJ O’Sullivan ME

We split 100 porcine flexor tendons into five groups of 20 tendons for repair. Three groups were repaired using the Pennington modified Kessler technique, the cruciate or the Savage technique, one using one new device per tendon and the other with two new devices per tendon. Half of the tendons received supplemental circumferential Silfverskiöld type B cross-stitch. The repairs were loaded to failure and a record made of their bulk, the force required to produce a 3 mm gap, the maximum force applied before failure and the stiffness. When only one device was used repairs were equivalent to the Pennington modified Kessler for all parameters except the force to produce a 3 mm gap when supplemented with a circumferential repair, which was equivalent to the cruciate. When two devices were used the repair strength was equivalent to the cruciate repair, and when the two-device repair was supplemented with a circumferential suture the force to produce a 3 mm gap was equivalent to that of the Savage six-strand technique


The Journal of Bone & Joint Surgery British Volume
Vol. 90-B, Issue 11 | Pages 1522 - 1527
1 Nov 2008
Davis ET Olsen M Zdero R Waddell JP Schemitsch EH

A total of 20 pairs of fresh-frozen cadaver femurs were assigned to four alignment groups consisting of relative varus (10° and 20°) and relative valgus (10° and 20°), 75 composite femurs of two neck geometries were also used. In both the cadaver and the composite femurs, placing the component in 20° of valgus resulted in a significant increase in load to failure. Placing the component in 10° of valgus had no appreciable effect on increasing the load to failure except in the composite femurs with varus native femoral necks. Specimens in 10° of varus were significantly weaker than the neutrally-aligned specimens. The results suggest that retention of the intact proximal femoral strength occurs at an implant angulation of ≥ 142°. However, the benefit of extreme valgus alignment may be outweighed in clinical practice by the risk of superior femoral neck notching, which was avoided in this study


The Journal of Bone & Joint Surgery British Volume
Vol. 89-B, Issue 10 | Pages 1396 - 1401
1 Oct 2007
Hirpara KM Sullivan PJ Raheem O O’Sullivan ME

We compared the bulking and tensile strength of the Pennington modified Kessler, Cruciate and the Savage repairs in an ex vivo model. A total of 60 porcine tendons were randomised to three groups, half repaired using a core suture alone and the remainder employing a core and peripheral technique. The tendons were distracted to failure. The force required to produce a 3 mm gap, the ultimate strength, the mode of failure and bulking for each repair were assessed. We found that there was a significant increase in strength without an increase in bulk as the number of strands increased. The Cruciate repair was significantly more likely to fail by suture pullout than the Pennington modified Kessler or Savage repairs. We advise the use of the Savage repair, especially in the thumb, and a Cruciate when a Savage is not possible. The Pennington modified Kessler repair should be reserved for multiple tendon injuries


The Journal of Bone & Joint Surgery British Volume
Vol. 88-B, Issue 9 | Pages 1245 - 1251
1 Sep 2006
Pendegrass CJ Oddy MJ Sundar S Cannon SR Goodship AE Blunn GW

We examined the mechanical properties of Vicryl (polyglactin 910) mesh in vitro and assessed its use in vivo as a novel biomaterial to attach tendon to a hydroxyapatite-coated metal implant, the interface of which was augmented with autogenous bone and marrow graft. This was compared with tendon re-attachment using a compressive clamp device in an identical animal model. Two- and four-ply sleeves of Vicryl mesh tested to failure under tension reached 5.13% and 28.35% of the normal ovine patellar tendon, respectively. Four-ply sleeves supported gait in an ovine model with 67.05% weight-bearing through the operated limb at 12 weeks, without evidence of mechanical failure. Mesh fibres were visible at six weeks but had been completely resorbed by 12 weeks, with no evidence of chronic inflammation. The tendon-implant neoenthesis was predominantly an indirect type, with tendon attached to the bone-hydroxyapatite surface by perforating collagen fibres


The Journal of Bone & Joint Surgery British Volume
Vol. 79-B, Issue 6 | Pages 995 - 1002
1 Nov 1997
Ding M Dalstra M Danielsen CC Kabel J Hvid I Linde F

We tested in compression specimens of human proximal tibial trabecular bone from 31 normal donors aged from 16 to 83 years and determined the mechanical properties, density and mineral and collagen content. Young’s modulus and ultimate stress were highest between 40 and 50 years, whereas ultimate strain and failure energy showed maxima at younger ages. These age-related variations (except for failure energy) were non-linear. Tissue density and mineral concentration were constant throughout life, whereas apparent density (the amount of bone) varied with ultimate stress. Collagen density (the amount of collagen) varied with failure energy. Collagen concentration was maximal at younger ages but varied little with age. Our results suggest that the decrease in mechanical properties of trabecular bone such as Young’s modulus and ultimate stress is mainly a consequence of the loss of trabecular bone substance, rather than a decrease in the quality of the substance itself. Linear regression analysis showed that collagen density was consistently the single best predictor of failure energy, and collagen concentration was the only predictor of ultimate strain


The Journal of Bone & Joint Surgery British Volume
Vol. 82-B, Issue 3 | Pages 450 - 456
1 Apr 2000
Azangwe G Mathias KJ Marshall D

In a study combining tissue mechanics and fracture morphology for the first time, we examined the ruptured surfaces of anterior cruciate ligaments of rabbits and related their appearance to the initial loading conditions. Sixteen specimens were stretched to failure at rates of displacement of 10 and 500 mm/min. We used video images to study the changes which occurred during the fracture process and SEM to examine the appearance of the ruptured surfaces. The surfaces of ligaments tested at 10 mm/min had more pulled-out collagen fibres and the fibres had more pronounced waviness compared with those tested at 500 mm/min. We have shown that the macroscopic appearance of ruptured ligaments can be related to their microscopic appearance and that it is possible to deduce whether failure was by gradual tearing of the fibres or catastrophic failure


The Journal of Bone & Joint Surgery British Volume
Vol. 87-B, Issue 5 | Pages 741 - 744
1 May 2005
Beaulé PE Krismer M Mayrhofer P Wanner S Le Duff M Mattesich M Stoeckl B Amstutz HC Biedermann R

Studies on the migration of an implant may be the only way of monitoring the early performance of metal-on-metal prostheses. The Ein Bild Roentgen Analyse - femoral component analysis (EBRA-FCA) method was adapted to measure migration of the femoral component in a metal-on-metal surface arthroplasty of the hip using standard antero-posterior radiographs. In order to determine the accuracy and precision of this method a prosthesis was implanted into cadaver bones. Eleven series of radiographs were used to perform a zero-migration study. After adjustment of the femoral component to simulate migration of 3 mm the radiographs were repeated. All were measured independently by three different observers. The accuracy of the method was found to be ± 1.6 mm for the x-direction and ± 2 mm for the y-direction (95% percentile). The method was validated using 28 hips with a minimum follow-up of 3.5 years after arthroplasty. Seventeen were sound, but 11 had failed because of loosening of the femoral component. The normal (control) group had a different pattern of migration compared with that of the loose group. At 29.2 months, the control group showed a mean migration of 1.62 mm and 1.05 mm compared with 4.39 mm and 4.05 mm in the failed group, for the centre of the head and the tip of the stem, respectively (p = 0.001). In the failed group, the mean time to migration greater than 2 mm was earlier than the onset of clinical symptoms or radiological evidence of failure, 19.1 versus 32.2 months (p = 0.001) and 24.8 months (p = 0.012), respectively. EBRA-FCA is a reliable and valid tool for measuring migration of the femoral component after surface arthroplasty and can be used to predict early failure of the implant. It may be of value in determining the long-term performance of surface arthroplasty


The Journal of Bone & Joint Surgery British Volume
Vol. 89-B, Issue 11 | Pages 1545 - 1550
1 Nov 2007
Koslowsky TC Mader K Dargel J Koebke J Hellmich M Pennig D

We have evaluated four different fixation techniques for the reconstruction of a standard Mason type-III fracture of the radial head in a sawbone model. The outcome measurements were the quality of the reduction, and stability. A total of 96 fractures was created. Six surgeons were involved in the study and each reconstructed 16 fractures with 1.6 mm fine-threaded wires (Fragment Fixation System (FFS)), T-miniplates, 2 mm miniscrews and 2 mm Kirschner (K-) wires; four fractures being allocated to each method using a standard reconstruction procedure. The quality of the reduction was measured after definitive fixation. Biomechanical testing was performed using a transverse plane shear load in two directions to the implants (parallel and perpendicular) with respect to ultimate failure load and displacement at 50 N. A significantly better quality of reduction was achieved using the FFS wires (Tukey’s post hoc tests, p < 0.001) than with the other devices with a mean step in the articular surface and the radial neck of 1.04 mm (. sd. 0.96) for the FFS, 4.25 mm (. sd. 1.29) for the miniplates, 2.21 mm (. sd. 1.06) for the miniscrews and 2.54 mm (. sd. 0.98) for the K-wires. The quality of reduction was similar for K-wires and miniscrews, but poor for miniplates. The ultimate failure load was similar for the FFS wires (parallel, 196.8 N (. sd. 46.8), perpendicular, 212.5 N (. sd. 25.6)), miniscrews (parallel, 211.8 N (. sd. 47.9), perpendicular, 208.0 N (. sd. 65.9)) and K-wires (parallel, 200.4 N (. sd. 54.5), perpendicular, 165.2 N (. sd. 37.9)), but significantly worse (Tukey’s post hoc tests, p < 0.001) for the miniplates (parallel, 101.6 N (. sd. 43.1), perpendicular, 122.7 N (. sd. 40.7)). There was a significant difference in the displacement at 50 N for the miniplate (parallel, 4.8 mm (. sd. 2.8), perpendicular, 4.8 mm (. sd. 1.7)) vs FFS (parallel, 2.1 mm (. sd. 0.8), perpendicular, 1.9 mm (. sd. 0.7)), miniscrews (parallel, 1.8 mm (. sd. 0.5), perpendicular, 2.3 mm (. sd. 0.8)) and K-wires (parallel, 2.2 mm (. sd. 1.8), perpendicular, 2.4 mm (. sd. 0.7; Tukey’s post hoc tests, p < 0.001)). The fixation of a standard Mason type-III fracture in a sawbone model using the FFS system provides a better quality of reduction than that when using conventional techniques. There was a significantly better stability using FFS implants, miniscrews and K-wires than when using miniplates


The Journal of Bone & Joint Surgery British Volume
Vol. 85-B, Issue 4 | Pages 594 - 599
1 May 2003
Reilly P Amis AA Wallace AL Emery RJH

Differential strain has been proposed to be a causative factor in failure of the supraspinatus tendon. We quantified the strains on the joint and bursal sides of the supraspinatus tendon with increasing load (20 to 200 N) and during 120° of glenohumeral abduction with a constant tensile load (20 to 100 N). We tested ten fresh frozen cadaver shoulders on a purpose-built rig. Differential variable reluctance extensometers allowed calculation of the strain. Static loading to 100 N or more increased strains on the joint side significantly more than on the bursal side. During glenohumeral abduction an increasing and significant difference in strain was measured between the joint and bursal sides of the supraspinatus tendon, which reached a maximum of 10.6% at abduction of 120°. The joint side strain of 7.5% reached values which were previously reported to cause failure. Differential strain causes shearing between the layers of the supraspinatus tendon, which may contribute to the propagation of intratendinous defects that are initiated by high joint side strains


The Journal of Bone & Joint Surgery British Volume
Vol. 92-B, Issue 2 | Pages 315 - 319
1 Feb 2010
Lalliss SJ Branstetter JG

Using an osteotomy of the olecranon as a model of a transverse fracture in 22 cadaver elbows we determined the ability of three different types of suture and stainless steel wire to maintain reduction when using a tension-band technique to stabilise the bone. Physiological cyclical loading simulating passive elbow movement (15 N) and using the arms to push up from a chair (450 N) were applied using an Instron materials testing machine whilst monitoring the osteotomy site with a video extensometer. Each osteotomy was repaired by one of four materials, namely, Stainless Steel Wire (7), No 2 Ethibond (3), No 5 Ethibond (5), or No 2 FiberWire (7). There were no failures (movement of > 2 mm) with stainless steel wire or FiberWire and no significant difference in the movements measured across the site of the osteotomy (p = 0.99). The No. 2 Ethibond failed at 450 N and two of the five of No. 5 Ethibond sutures had a separation of > 2 mm at 450 N. FiberWire as the tension band in this model held the reduction as effectively as stainless steel wire and may reduce the incidence of discomfort from the hardware. On the basis of our findings we suggest that a clinical trial should be undertaken


The Journal of Bone & Joint Surgery British Volume
Vol. 82-B, Issue 7 | Pages 1059 - 1064
1 Sep 2000
Rupp S Seil R Kohn D Müller B

Our aim was to analyse the effect of avascularity on the morphology and mechanical properties (tensile strength, viscoelasticity) of human bone-patellar-tendon-bone (BPTB) grafts in vitro. These were harvested at postmortem and stored submerged in denaturated human plasma at a constant pH, pO. 2. , pCO. 2. , temperature and humidity under sterile conditions. Mechanical testing was performed two and four weeks after removal of the graft. The mean ultimate strength was 1085.7 ± 255.8 N (control), 1009.0 ± 314.9 N (two weeks cultured) and 1076.8 ± 414.8 N (four weeks cultured). There was no significant difference in linear stiffness or deformation to failure between the groups. There was a difference in viscoelasticity between the control group and the avascular grafts and the latter had significant lower peak load-to-load ratios after 15 minutes compared with the control group. After two and four weeks the graft contained viable fibroblasts. There was regular cellularity in the superficial layers and decreased cellularity in the midportion. The structure of the collagen including the crimp pattern appeared to be normal in polarised light. We conclude that avascularity does not significantly affect ultimate failure loads or stiffness of BPTB grafts. Slight changes in viscoelasticity were induced, but the significance of the increased stress relaxation is not fully understood


The Journal of Bone & Joint Surgery British Volume
Vol. 78-B, Issue 3 | Pages 363 - 368
1 May 1996
Hamer AJ Strachan JR Black MM Ibbotson CJ Stockley I Elson RA

There have been conflicting reports on the effects of gamma irradiation on the material properties of cortical allograft bone. To investigate changes which result from the method of preparation, test samples must be produced with similar mechanical properties to minimise variations other than those resulting from treatment. We describe a new method for the comparative measurement of bone strength using standard bone samples. We used 233 samples from six cadavers to study the effects of irradiation at a standard dose (28 kGy) alone and combined with deep freezing. We also investigated the effects of varying the dose from 6.8 to 60 kGy (n = 132). None of the treatments had any effect on the elastic behaviour of the samples, but there was a reduction in strength to 64% of control values (p < 0.01) after irradiation with 28 kGy. There was also a dose-dependent reduction in strength and in the ability of the samples to absorb work before failure. We suggest that irradiation may cause an alteration in the bone matrix of allograft bone, but provided it is used in situations in which loading is within its elastic region, then failure should not occur


The Journal of Bone & Joint Surgery British Volume
Vol. 78-B, Issue 3 | Pages 349 - 356
1 May 1996
Bishop NE Ferguson S Tepic S

The fatigue failure of bone cement, leading to loosening of the stem, is likely to be one mode of failure of cemented total hip replacements. There is strong evidence that cracks in the cement are initiated at voids which act as stress risers, particularly at the cement-stem interface. The preferential formation of voids at this site results from shrinkage during polymerisation and the initiation of this process at the warmer cement-bone interface, which causes bone cement to shrink away from the stem. A reversal of the direction of polymerisation would shrink the cement on to the stem and reduce or eliminate the formation of voids at this interface. We have investigated this by implanting hip prostheses, at room temperature or preheated to 44°C, into human cadaver femora kept at 37°C. Two types of bone cement were either hand-mixed or vacuum-mixed before implantation. We found that the area of porosity at the cement-stem interface was dramatically reduced by preheating the stem and that the preheating temperature of 44°C determined by computer analysis of transient heat transfer was the minimum required to induce initial polymerisation at the cement-stem interface. Temperature measurements taken during these experiments in vitro showed that preheating of the stem caused a negligible increase in the temperature of the bone. Reduction of porosity at the cement-stem interface could significantly increase the life of hip arthroplasties


The Journal of Bone & Joint Surgery British Volume
Vol. 93-B, Issue 1 | Pages 120 - 125
1 Jan 2011
Lim H Bae J Song H Teoh SH Kim H Kum D

Medial open-wedge high tibial osteotomy has been gaining popularity in recent years, but adequate supporting material is required in the osteotomy gap for early weight-bearing and rapid union. The purpose of this study was to investigate whether the implantation of a polycaprolactone-tricalcium phosphate composite scaffold wedge would enhance healing of the osteotomy in a micro pig model. We carried out open-wedge high tibial osteotomies in 12 micro pigs aged from 12 to 16 months. A scaffold wedge was inserted into six of the osteotomies while the other six were left open. Bone healing was evaluated after three and six months using plain radiographs, CT scans, measurement of the bone mineral density and histological examination. Complete bone union was obtained at six months in both groups. There was no collapse at the osteotomy site, loss of correction or failure of fixation in either group. Staining with haematoxylin and eosin demonstrated that there was infiltration of new bone tissue into the macropores and along the periphery of the implanted scaffold in the scaffold group. The CT scans and measurement of the bone mineral density showed that at six months specimens in the scaffold group had a higher bone mineral density than in the control group, although the implantation of the polycaprolactone-tricalcium phosphate composite scaffold wedge did not enhance healing of the osteotomy


The Journal of Bone & Joint Surgery British Volume
Vol. 82-B, Issue 6 | Pages 910 - 920
1 Aug 2000
Nafei A Danielsen CC Linde F Hvid I

Our aim was to determine the relationship between age and the mechanical and physical properties of trabecular bone, to describe the patterns in which the variations in these properties take place, and to investigate the influence of the physical properties on the mechanical characteristics of trabecular bone during growth. We used 30 lambs in three age groups and 20 sheep in two age groups. Cubes of subchondral bone were cut from the proximal tibia according to a standardised protocol. We performed non-destructive compression tests of the specimens in three orthogonal directions and compression tests to failure in the axial direction. The physical properties of the specimens were also determined. The data were correlated with age and compared in skeletally immature and mature animals. Multiple regression analyses were performed between the mechanical and the physical properties. Age correlated positively with elastic modulus, bone strength, energy absorption to failure, elastic energy, mechanical anisotropy ratio, tissue density, apparent density, apparent ash density, and bone mineral content, and inversely with ultimate strain, viscoelastic energy absorption, relative energy loss, the collagen content of bone and the percentage porosity. The values of all variables were significantly different in the skeletally mature and immature groups. The apparent density of trabecular bone tissue was found to be the major predictor of its compressive mechanical properties. Together with the content of bone muscle and bone collagen, the apparent density could explain 84% of the variation in the elastic modulus, whereas only a small portion of the variation in ultimate strain could be explained by the variation in apparent density