The role of obesity, biomechanical constitution of the pelvis and contact joint stress in progression of hip osteoarthritis

OBJECTIVE

The aim of our study was to explore whether earlier hip arthroplasty for idiopathic osteoarthritis (OA) might be explained by enlarged contact stress in the hip joint, and to what amount can that be attributed to obesity and biomechanical constitution of the pelvis.

METHOD

Fifty subjects were selected from a list of consecutive recipients of hip endoprosthesis due to idiopathic OA; standard pelvic radiographs made years prior to surgery were the main selection criteria. For 65 hips resultant hip force and peak contact hip stress normalized to the body weight (R/Wb and p(max)/Wb) were determined from the radiographs with the HIPSTRESS method. Body weight and body mass index (BMI) were obtained with an interview. Regression analysis was used to correlate parameters of obesity (body weight, BMI), biomechanical constitution of the pelvis (R/Wb, p(max)/Wb) and mechanical loading within the hip joint (R, p(max)) with age at hip arthroplasty.

RESULTS

Younger age at hip arthroplasty was associated with higher body weight (P=0.009), higher peak contact hip stress normalized to the body weight - p(max)/Wb (P=0.019), higher resultant hip force -R (P=0.027) and larger peak contact hip stress - p(max) (P<0.001), but not with BMI (P=0.121) or R/Wb (P=0.614).

CONCLUSION

Our results suggest that enlarged contact stress (p(max)) plays an important role in rapid progression of hip OA with both obesity (increased body weight) and unfavorable biomechanical constitution of the pelvis (greater p(max)/Wb) contributing.

Encapsulation of small spherical liposome into larger flaccid liposome induced by human plasma proteins

We show that human plasma can induce the encapsulation of small spherical liposomes into larger flaccid liposomes. To explain the observed phenomena, it is proposed that the orientational ordering of charged plasma proteins induces attractive interaction between two like-charged liposome surfaces in close contact. It is observed that the encapsulation of the spherical liposome is possible only if the membrane of the target liposome is flexible enough to adapt its shape to the shape of the spherical liposome. In the theoretical model, the shapes of the two agglutinated liposomes are determined by minimisation of the sum of the adhesion energy and the membrane elastic energy. In the simulations, the membrane of liposomes is considered as an elastic structure and discretised via the finite element method using spring elements. It is shown that the observed agglutination of liposomes and encapsulation of smaller spherical liposomes into larger flaccid liposomes may be explained as a competition between the membrane deformation energy and the membrane adhesion energy.

Higher peak contact hip stress predetermines the side of hip involved in idiopathic osteoarthritis

BACKGROUND

Biomechanical parameters of the hip have been suggested to have an important influence on the development of osteoarthritis. We aimed to find out whether higher stress is generated in a hip that subsequently results in earlier hip arthroplasty compared to the contralateral hip in the same subject.

METHODS

Standard anterior-posterior pelvic radiographs with no or subtle radiological signs of hip osteoarthritis, of 59 female patients, who underwent hip arthroplasty for primary osteoarthritis years later, were selected from the archives. For each subject peak contact hip stress of the hip with earlier arthroplasty and of the contralateral hip (pair of hips), was calculated from the radiographically obtained geometrical parameters with the HIPSTRESS program, which is based on a three-dimensional biomechanical model of the resultant hip force in the one-legged stance and a three-dimensional mathematical model of the contact hip stress distribution. Differences in peak contact hip stress within pairs of hips were determined for subjects with unilateral (22 pairs of hips) and bilateral disease (37 pairs of hips) by using paired-samples T-test.

FINDINGS

In the population of subjects with unilateral osteoarthritis, average peak contact hip stress was significantly higher (P = 0.007) in hips with arthroplasty (2.44 kPa/N) than in contralateral hips (2.32 kPa/N). In the population of subjects with bilateral osteoarthritis, average peak contact hip stress was significantly higher (P<0.001) in hips with earlier arthroplasty (2.54 kPa/N) than in contralateral hips (2.35 kPa/N).

INTERPRETATION

Results are consistent with the hypothesis that higher peak contact hip stress results in earlier hip arthroplasty due to faster development of idiopathic osteoarthritis.

Membrane skeleton detachment in spherical and cylindrical microexovesicles

We observed that amphiphile-induced microexovesicles may be spherical or cylindrical, depending on the species of the added amphiphile. The spherical microexovesicle corresponds to an extreme local difference between the two monolayer areas of the membrane segment with a fixed area, while the cylindrical microexovesicle corresponds to an extreme local area difference if the area of the budding segment is increased due to lateral influx of anisotropic membrane constituents. Protein analysis showed that both types of vesicles are highly depleted in the membrane skeleton. It is suggested that a partial detachment of the skeleton in the budding region is favoured due to accumulated skeleton shear deformations in this region.

Shape transformation of giant phospholipid vesicles at high concentrations of C12E8

Giant unilamellar phospholipid vesicles were prepared by the method of electroformation from 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine (POPC). We studied the influence of different concentrations of the surfactant octaethyleneglycol dodecylether (C(12)E(8)) on the spontaneous shape transformations of POPC vesicles at room temperature. In accordance with previous results, we observed that low concentration of C(12)E(8) increased the speed of the characteristic vesicle shape transformation, starting from the initial shape with thin tubular protrusion, through beaded protrusion where the number of beads gradually decreased, to final spherical shapes with invagination, whereby the average mean curvature of the vesicle membrane monotonously decreased. In contrast, higher concentration of C(12)E(8) initially induced the shape transformation in the "opposite direction": in the protrusion, the number of beads gradually increased and eventually a tube was formed whereby the average mean curvature of the vesicle membrane gradually increased. However, at a certain point, an abrupt shape change took place to yield the vesicle with invagination. In this transition, the average mean curvature of the vesicle membrane discontinuously decreased. After this transition, the vesicle began to shrink and finally disappeared. We discuss possible mechanisms involved in the observed transformations.

High contact hip stress is related to the development of hip pathology with increasing age

BACKGROUND

High contact hip stress is believed to be one of the key biomechanical factors involved in the hip cartilage degeneration and osteoarthritis. Accordingly, with increasing age high contact hip stress is expected to cause elimination of subjects from the population of healthy hips, but its predictive value has not been evaluated so far. The objective of the paper is to investigate whether the exposure of healthy hips to estimated high contact hip stress is related to the development of hip pathology with increasing age.

METHODS

A cross-sectional age- and gender-matched analysis of the peak contact hip stress calculated from pelvic geometry was made in 103 adult subjects with healthy hips. The peak contact hip stress was calculated from anterior-posterior pelvic radiographs of healthy hips by using a mathematical model of the human hip in the static one-legged stance.

FINDINGS

In both female and male population, the average values of the peak contact hip stress normalized to the body weight are significantly higher and the values are also more dispersed in younger subjects when compared to older subjects.

INTERPRETATION

The hip joints which remain healthy in the old age have lower average estimated peak contact hip stress. These results are consistent with the explanation that subjects with high estimated peak contact hip stress are more likely to develop hip disease in the course of life.

Influence of contact hip stress on the outcome of surgical treatment of hips affected by avascular necrosis

INTRODUCTION

Biomechanical analysis is an important tool that could improve the treatment of a diseased hip. However, it is still unclear how the biomechanical status affects the clinical outcome of a certain disease. In this work we studied the long-term effect of contact hip stress on the clinical outcome of hips that were operated on by various intertrochanteric osteotomies due to avascular necrosis of the femoral head. The hypothesis being tested is that the hips with a more favourable postoperative distribution of contact hip stress have a better clinical outcome.

MATERIALS AND METHODS

The study was performed on a population of 30 hips. For each hip, we determined the peak contact hip stress before the operation and immediately after the operation by using a recently developed method based on a three-dimensional mathematical model and the data from standard anteroposterior roentgenographs of both hips and pelvis. The hips were evaluated clinically 9-26 years after the operation and divided into a successful and an unsuccessful group. The average change of the peak stress due to the operation was calculated for each group, and the values were compared by t-test.

RESULTS

In the successful group the operation caused an average decrease of the peak hip stress of about 10%, while in the unsuccessful group the operation caused an average increase of the peak hip stress of about 4%, the difference between the respective changes of the peak stress due to the operation being statistically significant ( p=0.001).

CONCLUSION

Our results support the hypothesis that the hips with a more favourable postoperative distribution of contact hip stress have a better clinical outcome.

Polyethylene wear in total hip prostheses: the influence of direction of linear wear on volumetric wear determined from radiographic data

PURPOSE

To develop a new mathematical model for calculating the volumetric wear of polyethylene cups from known values of the radius of the prosthesis head, the extent of linear wear and the direction of linear wear determined from standard antero-posterior radiographs.

METHOD

A new mathematical model was developed. The results of this new mathematical model were compared with the results obtained using the standard, frequently used mathematical model, which takes into consideration only the radius of the prosthesis head and the extent of linear wear of the polyethylene cups. The results of both mathematical models were further compared with the results obtained by direct measurement of volumetric wear using the fluid displacement method.

RESULTS

Comparison of the mathematical models shows that the average volumetric wear calculated using the new mathematical model is 8.5% smaller than the average volumetric wear determined by the fluid displacement method, while the average volumetric wear calculated by standard mathematical model is 17.5% higher. The results of the new mathematical model are, thus, notably less biased than those of the standard one.

CONCLUSION

In calculating the volumetric wear from antero-posterior radiographs, not only the radius of the prosthesis head and the extent of the linear wear but also the direction of the latter has to be considered.

Mathematical estimation of stress distribution in normal and dysplastic human hips

By using a mathematical model of the adult human hip in the static one-legged stance position of the body, the forces acting on the hip, peak stress in the hip joint and other relevant radiographic and biomechanical parameters were assessed. The aims were to examine if the peak stress in dysplastic hips is higher than in normal hips and to find out which biomechanical parameters contribute significantly to higher peak stress. The average normalized peak stress in dysplastic hips (7.1 kPa/N) was markedly higher (to approximately 100%) than the average normalized peak stress in normal hips (3.5 kPa/N). The characteristic parameters that contributed to higher peak stress in dysplastic hips included the smaller lateral coverage of the femoral head, the larger interhip distance, the wider pelvis, and the medial position of the greater trochanter. These results are consistent with the hypothesis that stress distribution over weight-bearing surface of the hip joint is the relevant parameter for assessment of the risk for developing coxarthrosis.

Hip stress reduction after Chiari osteotomy

A mathematical model was developed to study the effect of the Chiari osteotomy on the distribution of contact hip stress over the weight-bearing area. It was shown that Chiari osteotomy can increase the weight-bearing area directly (on the lateral side), owing to the additional area formed by the ala ossis ilii segment, and indirectly (on the medial side), owing to the shift of the stress pole in the medial direction. As a consequence, the contact hip stress is reduced after Chiari osteotomy. The indirect effect is important and often larger than the direct one. Using the proposed mathematical model and standard anteroposterior roentgenographs from archives, the average peak stress on the weight-bearing area, normalised with respect to the body weight (pmax/ W(B)), was determined before and after Chiari osteotomy (8,310m(-2) and 4,480 m(-2), respectively) on a population of 29 dysplastic hips. The difference was statistically significant (p < 0.005). Based on the results presented, it can be concluded that the hip joint contact stress in dysplastic hips considerably decreases after Chiari osteotomy, indicating a favourable biomechanical effect of this operation.

Oxyethylene chain-cation complexation: nonionic polyoxyethylene detergents attain a positive charge and demonstrate electrostatic head group interactions

We report literature data indicating that the polyoxyethylene chain of polyoxyethylene detergents attracts cations via dipole-ion interactions thereby attaining a positive charge character. This implies that nonionic polyoxyethylene detergents like Triton X-100 and C12E8 may interact electrostatically with phospholipid head groups. We describe how a positive charge character of Triton X-100 and C12E8 can explain their hitherto mysterious stomatocytogenic shape altering effect in human erythrocytes.

On stability of circular hole in membrane bilayer

It was observed recently that nonionic surfactant octaethyleneglycol dodecylether (Cl2E8) decreases threshold for irreversible electroporation in membrane bilayers. In accordance, it is shown theoretically in this work that anisotropic C12E8 membrane inclusions may stabilize circular hole in a flat membrane segment.

Biomechanical evaluation of hip joint after Salter innominate osteotomy: a long-term follow-up study

The biomechanical state of the hip after a Salter innominate osteotomy was investigated by using the radiographic data of 38 operated and 21 contralateral nonoperated hips from our archives. The centre-edge angle of Wiberg was determined from the radiographs taken shortly after the operation. From the radiographs of the latest follow-up (7-13 years after the operation), we also determined the peak value of contact hip joint stress normalized by the body weight, and the functional angle of the weight-bearing area. A mathematical model was used. We show that the geometrical parameters aside from the centre-edge angle may considerably influence the contact hip stress distribution. We also show that the functional angle of the weight-bearing area is a more relevant parameter than the normalized peak stress if the exact magnification of the images is not known and if there is considerable variation of the image size within the sample. The development of the centre-edge angle of the operated hips and of the contralateral hips was also studied. We found that the centre-edge angle increases on average during the follow-up time in the operated hips as well as in the contralateral nonoperated hips, but the average increase is smaller in the former. It is shown that an unfavorable stress distribution is connected to the decrease of the centre-edge angle over time. Finally, we found a weak positive correlation between the centre-edge angle shortly after the operation and the functional angle of the weight-bearing area at the of the latest follow-up.

Gemini (dimeric) surfactant perturbation of the human erythrocyte

We studied the ability of di-cationic gemini surfactantsdi (amphiphiles), i.e. 1,4-butanediammonium-N,N-dialkyl-N,N,N',N'-tetramethyl bromides (Di-Cm-di-QAS (s = 4), where m = 8, 11, 13, 16 and s = the number of alkyl groups in the spacer) to induce shape alteration, vesiculation, haemolysis and phosphatidylserine exposure in human erythrocytes, and to protect erythrocytes against hypotonic haemolysis. At high sublytic concentrations the Di-Cm-di-QAS (s = 4) amphiphiles rapidly induced echinocytic (spiculated) shapes and a release of exovesicles, mainly in the form of tubes, from the cell surface. Following 60 min incubation erythrocytes were sphero-echinocytic and a few cells with invaginations/endovesicles were observed. No phosphatidylserine exposure was detected. The haemolytic potency increased with an increase of the alkyl chain length. At sublytic concentrations the Di-Cm-di-QAS (s = 4) amphiphiles protected erythrocytes against hypotonic haemolysis. It is suggested that the Di-Cm-di-QAS (s = 4) amphiphiles perturb the membrane in a similar way as single-chain cationic amphiphiles, but that they do not easily translocate to the inner membrane leaflet.

Amphiphile-induced vesiculation in aged hereditary spherocytosis erythrocytes indicates normal membrane stability properties under non-starving conditions

Aged HS erythrocytes with a defined primary defect in band 3 protein or ankyrin were incubated with amphiphiles (detergents) at sublytic concentrations (37 C, 60 min) or glucose-starved (37 C, 24 h). In line with previous studies, the release of AChE (exovesicles) from HS erythrocytes during glucose-starvation was significantly higher (11%) compared to that from control erythrocytes (1%). Control and HS cells responded, however, similarly to amphiphile-treatment (non-starving conditions). Amphiphiles induced similar types of shape alterations and a similar amount of AChE release (14-15%). Furthermore, the size and shape of amphiphile-induced exo- and endovesicles released from control and HS erythrocytes were similar. The results suggest that the stability properties of the membrane are not seriously disturbed in aged HS erythrocytes under non-starving conditions.

Theoretical analysis of shape transformation of V-79 cells after treatment with cytochalasin B

We observed that after treatment of V-79 fibroblasts with cytochalasin B the area of cell contact with the substrate is essentially reduced, the microtubules are organized into rodlike structures and the actin filaments are disintegrated. Remnants of the actin cortex become concentrated in the form of discrete patches under the plasma membrane. The described changes in the organization of the cytoskeleton and of the cortical shell are accompanied by the formation of a cell shape resembling the Greek letter phi. We calculated that the phi shape corresponds to the minimum of the stretching energy of the cortical shell at relevant geometrical constraints. In line with this result, if cytochalasin B treatment was followed by colchicine application which disrupted the microtubular rod, the characteristic phi shape completely disappeared. This study suggests that the effect of the microtubular rod on the cell shape can be theoretically well described by taking into account some basic conditions for the mechanical equilibrium of the cell cortical shell and the appropriate geometrical constraints.

Determination of contact hip stress from nomograms based on mathematical model

Nomograms are presented that enable determination of maximal stress on the hip joint weight bearing area if certain geometrical parameters of the hip and pelvis and the body weight are known. The nomograms are calculated by using previously developed mathematical models. It is demonstrated how the maximal stress on the hip joint weight bearing area is determined from the presented nomograms for a hip for which the geometrical parameters were obtained from a standard anteroposterior rentgenograph. This simple and noninvasive method may give insight into the biomechanical status of the hip which should be considered in routine surgical planning and as a part of the routine examination of the patient without the use of any additional tools.

Biochemical aspects of Salter's osteotomy for treatment of acetabular dysplasia

The center-edge (CE) angle was measured on serial antero-posterior radiographs of 44 hips treated by Salter's innominate osteotomy for developmental dysplasia of the hip. Radiographic examination according to Severin was performed and the peak hip joint pressure was calculated using geometrical parameters determined from radiographs at the most recent follow-up examination, 7 to 13 years postoperatively. At the latest follow-up assessment, there was a positive correlation between the postoperative CE angle and radiographic results. Negative correlation was found between the postoperative CE angle and peak hip joint pressure at the latest follow up. In conclusion, Salter's osteotomy performed to treat developmental dysplasia of the hip should involve radical acetabular correction resulting in maximum increase of the CE angle.

Evaluation of biomechanical status of dysplastic human hips

The evaluation of the biomechanical status of human hip joint was performed. Required parameters were assessed from standard antero-posterior rentgenographs and the value of contact stress on the weight bearing area is calculated. We analysed 45 dysplastic human hips and compared measured values to 81 healthy hips. The peak contact stress on the weight bearing area is considerably and statistically significantly higher in dysplastic hips compared to healthy hips. The Wiberg centre-edge angle is statistically significantly smaller in group of dysplastic hips compared to healthy hips.

Different operative treatment of slipped capital femoral epiphysis: a comparative study of biomechanical status of the hip

The biomechanical status of the hips subject to two different operative treatments was studied. The biomechanical status was determined by the peak stress on the weight bearing area using the 3-d mathematical model. It was found that the procedure according to Imhäuser yields considerably and statistically significantly higher peak stress than the procedure according to Dunn-Fish.

Peak contact stress in human hip during gait

The contact stress in a human hip is not uniform and it changes with different body positions. The changing location of the peak contact stress during gait may indicate the predilection sites for further development of osteoarthritis in the hip. On the basis of laboratory measurements and by using mathematical models of forces and stresses in human hip we determined the points of the peak contact stress in successive phases of gait. Results show that the peak stress points are mostly located in the posterior-medial portion of the weight bearing area, which corresponds well to the clinical observations. It is also shown that in the pathological conditions of hip dysplasia the peak contact stress trajectory is located more laterally and anteriorly.

Torocyte shapes of red blood cell daughter vesicles

The shape of the newly described torocyte red blood cell endovesicles induced by octaethyleneglycol dodecylether (C12E8) is characterized. A possible explanation for the origin and stability of the observed torocyte endovesicles is suggested. Three partly complementary mechanisms are outlined, all originating from the interaction of C12E8 molecules with the membrane. The first is a preferential intercalation of the C12E8 molecule into the inner membrane layer, resulting in a membrane invagination which may finally close, forming an inside-out endovesicle. The second is a preference of the C12E8-induced membrane inclusions (clusters) for small local curvature which would favour torocyte endovesicle shape with large regions of small or even negative membrane mean curvatures, the C12E8 membrane inclusion being defined as a complex composed of the embedded C12E8 molecule and some adjacent phospholipid molecules which are significantly distorted due to the presence of the embedded C12E8 molecule. The preference of the C12E8 inclusions for zero or negative local curvature may also lead to the nonhomogeneous lateral distribution of the C12E8 inclusions resulting in their accumulation in the membrane of torocyte endovesicles. The third possible mechanism is orientational ordering of the C12E8-induced inclusions in the regions of torocyte endovesicles with high local membrane curvature deviator.

Gemini (dimeric) surfactant perturbation of the human erythrocyte

We studied the ability of di-cationic gemini surfactantsdi (amphiphiles), i.e. 1,4-butanediammonium-N,N-dialkyl-N,N,N',N'-tetramethyl bromides (Di-Cm-di-QAS (s = 4), where m = 8, 11, 13, 16 and s = the number of alkyl groups in the spacer) to induce shape alteration, vesiculation, haemolysis and phosphatidylserine exposure in human erythrocytes, and to protect erythrocytes against hypotonic haemolysis. At high sublytic concentrations the Di-Cm-di-QAS (s = 4) amphiphiles rapidly induced echinocytic (spiculated) shapes and a release of exovesicles, mainly in the form of tubes, from the cell surface. Following 60 min incubation erythrocytes were sphero-echinocytic and a few cells with invaginations/endovesicles were observed. No phosphatidylserine exposure was detected. The haemolytic potency increased with an increase of the alkyl chain length. At sublytic concentrations the Di-Cm-di-QAS (s = 4) amphiphiles protected erythrocytes against hypotonic haemolysis. It is suggested that the Di-Cm-di-QAS (s = 4) amphiphiles perturb the membrane in a similar way as single-chain cationic amphiphiles, but that they do not easily translocate to the inner membrane leaflet.

Influence of band 3 protein absence and skeletal structures on amphiphile- and Ca(2+)-induced shape alterations in erythrocytes: a study with lamprey (Lampetra fluviatilis), trout (Onchorhynchus mykiss) and human erythrocytes

Amphiphiles which induce either spiculated (echinocytic) or invaginated (stomatocytic) shapes in human erythrocytes, and ionophore A23187 plus Ca(2+), were studied for their capacity to induce shape alterations, vesiculation and hemolysis in the morphologically and structurally different lamprey and trout erythrocytes. Both qualitative and quantitative differences were found. Amphiphiles induced no gross morphological changes in the non-axisymmetric stomatocyte-like lamprey erythrocyte or in the flat ellipsoidal trout erythrocyte, besides a rounding up at higher amphiphile concentrations. No shapes with large broad spicula were seen. Nevertheless, some of the 'echinocytogenic' amphiphiles induced plasma membrane protrusions in lamprey and trout erythrocytes, from where exovesicles were shed. In trout erythrocytes, occurrence of corrugations at the cell rim preceded protrusion formation. Other 'echinocytogenic' amphiphiles induced invaginations in lamprey erythrocytes. The 'stomatocytogenic' amphiphiles induced invaginations in both lamprey and trout erythrocytes. Surprisingly, in trout erythrocytes, some protrusions also occurred. Some of the amphiphiles hemolyzed lamprey, trout and human erythrocytes at a significantly different concentration/membrane area. Ionophore A23187 plus Ca(2+) induced membrane protrusions and sphering in human and trout erythrocytes; however, the lamprey erythrocyte remained unperturbed. The shape alterations in lamprey erythrocytes, we suggest, are characterized by weak membrane skeleton-lipid bilayer interactions, due to band 3 protein and ankyrin deficiency. In trout erythrocyte, the marginal band of microtubules appears to strongly influence cell shape. Furthermore, the presence of intermediate filaments and nuclei, additionally affecting the cell membrane shear elasticity, apparently influences cell shape changes in lamprey and trout erythrocytes. The different types of shape alterations induced by certain amphiphiles in the cell types indicates that their plasma membrane phospholipid composition differs.

Stable tubular microexovesicles of the erythrocyte membrane induced by dimeric amphiphiles

It is experimentally observed that adding a dimeric cationic amphiphile to the erythrocyte suspension results in a release of stable tubular microexovesicles from the erythrocyte membrane. Theoretical description starts from the single-inclusion energy, which takes into account anisotropic shape of the dimeric amphiphile. It is shown explicitly that the tubular shape of the microexovesicle is the extremal to the functional yielding the maximum of the average curvature deviator. It is derived for which intrinsic shapes of the membrane inclusions created by the intercalated amphiphiles the maximum of the average curvature deviator coincides with the minimum of the membrane free energy-thereby determining the stable tubular shape.

Weight bearing area during gait in normal and dysplastic hips

The size and the shape of the weight bearing area in adult human hips depend on the forces acting in the hip and therefore change during the body motion. In this work the size and the shape of the weight bearing area in several phases of gait are estimated. The forces acting in the hip were determined through laboratory measurements and analyzed by mathematical models. The dysplastic hips are distinguished from the normal ones by a smaller center-edge angle of Wiberg while the time course of the forces acting in the hip is assumed to be the same in both cases. It is shown how radial articular stress is distributed over the weight bearing area in both cases. In normal human hips the weight bearing area occupies a rather large portion of the acetabulum-femoral head contact area while in dysplastic hips stress distribution is unfavourably concentrated in a smaller weight bearing area.

Cylindrical shapes of closed lipid bilayer structures correspond to an extreme area difference between the two monolayers of the bilayer

The shapes of extreme area difference between the outer and the inner layer (deltaA) of the closed lipid bilayer structures at fixed membrane area (A) and fixed volume (V) are determined by stating and analytically solving a variational problem for axisymmetric shapes. It is shown that the spheres with at most two different radii and the cylinder are the solutions of this variational problem. The cylinder ended by a hemisphere on each end is the shape combined from these solutions and is therefore, itself the shape of the extreme deltaA at fixed V and A. The related cylindrical shapes of stearoyl-oleoyl-phosphocholine vesicles are shown.

Torocyte membrane endovesicles induced by octaethyleneglycol dodecylether in human erythrocytes

Endovesicles induced in human erythrocytes by octaethyleneglycol dodecylether (C12E8) were studied by confocal laser scanning microscopy, using fluorescein isothiocyanate dextran as a nonspecific fluid marker. The endovesicles appeared to consist mainly of a ring-formed toroidal part joined with a central flat membrane segment. The torocyte contour length was several microm. There was usually one torocyte endovesicle per cell. The endovesicles seemed to be located near the cell surface. In sections of C12E8-treated erythrocytes transmission electron microscopy revealed the frequent occurrence of flat membrane structures with a bulby periphery, which apparently are cross sections of torocyte endovesicles. The possible physical mechanisms leading to the observed torocyte endovesicle shape are discussed. The torocyte endovesicles seem to be formed in a process in which an initially stomatocytic invagination loses volume while maintaining a large surface area. Because intercalation of C12E8 in the erythrocyte membrane induces inward membrane bending (stomatocytosis) we assume that C12E8 is preferentially located in the inner lipid layer of the erythrocyte membrane, i.e., in the outer lipid layer of the endovesicle membrane. It is suggested that local disturbances of the lipid molecules in the vicinity of the C12E8 molecules in the outer lipid layer of the endovesicle membrane form membrane inclusions with the effective shape of an inverted truncated cone. If the interaction between the inclusion and the membrane is weak, the membrane of such an endovesicle can be characterized by its negative spontaneous curvature, which may lead to a torocyte endovesicle shape with a small relative volume. Effects of a possible strong interaction between the C12E8-induced membrane inclusions and the membrane on the stability of the torocyte endovesicles are also indicated.

Mathematical modelling of stress in the hip during gait

A mathematical model is developed for calculating the contact stress distribution in the hip for a known resultant hip force and characteristic geometrical parameters. Using a relatively simple single nonlinear algebraic equation, the model can be readily applied in clinical practice to estimate the stress distribution in the most frequent body positions of everyday activities. This is demonstrated by analyzing the data on the resultant hip force obtained from laboratory observations where a stance period of gait is considered.

Liposomes composed of a double-chain cationic amphiphile (vectamidine) induce their own encapsulation into human erythrocytes

Vectamidine is a liposome-forming double-chain cationic amphiphile. The present work was aimed to microscopically study the interactions of Vectamidine liposomes with the human erythrocyte plasma membrane. Vectamidine rapidly induced stomatocytic shapes. Attachment of Vectamidine liposomes to the erythrocyte induced a strong local invagination of the membrane. This frequently resulted in a complete encapsulation of the liposome. Liposomes composed of phosphatidylcholine (neutral) or phosphatidylserine/phosphatidylcholine (anionic) did not perturb the erythrocyte shape. Our results indicate that besides an attraction of Vectamidine liposomes to the plasma membrane, there is a preference of Vectamidine for the inner bilayer leaflet. We suggest that cationic amphiphiles may transfer from membrane-attached liposomes to the plasma membrane and then translocate to the inner bilayer leaflet where they induce a strong local inward bending of the plasma membrane resulting in an encapsulation of the liposome.

Amphiphile-induced spherical microexovesicle corresponds to an extreme local area difference between two monolayers of the membrane bilayer

It is shown that an increase of the area difference between the outer and the inner membrane lipid layers of the skeleton-free membrane segment as a result of exogenously added amphiphilic molecules results in budding of the segment. The process reaches its final point when the segment attains the shape of the local maximal area difference, corresponding to formation of a spherical microexovesicle.

Amphiphile induced echinocyte-spheroechinocyte transformation of red blood cell shape

A possible physical explanation of the echinocyte -spheroechinocyte red blood cell (RBC) shape transformation induced by the intercalation of amphiphilic molecules into the outer layer of the RBC plasma membrane bilayer is given. The stable RBC shape is determined by the minimization of the membrane elastic energy, consisting of the bilayer bending energy, the bilayer relative stretching energy and the skeleton shear elastic energy. It is shown that for a given relative cell volume the calculated number of echinocyte spicula increases while their size decreases as the number of the intercalated amphiphilic molecules in the outer layer of the cell membrane bilayer is increased, which is in agreement with experimental observations. Further, it is show that the equilibrium difference between the outer and the inner membrane leaflet areas of the stable RBC shapes increases if the amount of the intercalated amphiphiles is increased, thereby verifying theoretically the original bilayer couple hypothesis of Sheetz and Singer (1974) and Evans (1974).

Membrane skeleton and red blood cell vesiculation at low pH

Shapes of red blood cells at low pH were studied theoretically. It is assumed that the equilibrium shape of the red blood cell corresponds to the minimum of its membrane elastic energy which consists of the bending energy and relative stretching energy of the bilayer, the stretching energy of the skeleton and the interaction energy between the skeleton and the bilayer. It is shown that the aggregation of the skeleton at low pH can cause the red blood cell shape transformation from the stomatocytic shape to the cell shape composed of a spherical parent cell having the bilayer completely underlaid with the skeleton and spherical daughter vesicles without the skeleton.

Stability of spiculated red blood cells induced by intercalation of amphiphiles in cell membrane

The stability of spiculated red blood cells, induced by intercalation of amphiphilic molecules into the cell membrane, is studied. It is assumed that the stable red blood cell shape corresponds to the minimum of its membrane elastic energy, which consists of the local and non-local bilayer bending energies and of the skeleton shear elastic energy. The cell, volume and the membrane area are kept constant. It is calculated that the number of spicules of the stable echinocytic shape is larger when the amphiphile concentration is higher, which is in agreement with experimental observations. Also, it is established that, in explaining the stability of the echinocytic shape of the red blood cell, it is necessary to include the membrane skeleton shear elasticity.

A possible physical mechanism of red blood cell vesiculation obtained by incubation at high pH

The membrane of human red blood cells is essentially composed of two parts, the lipid bilayer and the membrane skeleton that interacts with the lipid bilayer. The normal resting shape of the red blood cells at physiological pH 7.4 is the discocyte. However, at alkaline pH approximately equal to 11 the shape of red blood cells is composed of a spherical parent cell and large spherical daughter vesicles. The daughter vesicles may be free or connected to the parent cell by a narrow neck. In this paper we show that the shapes of red blood cells at pH approximately equal to 11 correspond to some of the calculated shapes of a closed lipid bilayer having an extreme area difference between the outer and the inner monolayer. Therefore, it is suggested that the observed shapes of the red blood cells at pH approximately equal to 11 are a consequence of the abolishment of the skeleton bilayer interactions at this pH.

A possible mechanism determining the stability of spiculated red blood cells

In this work the stability of spiculated red blood cells, called echinocytes, is studied. It is assumed that the stable echinocyte shape corresponds to the minimum of its membrane elastic energy. It is shown that if the membrane skeleton shear elasticity is not taken into account the calculated stable echinocyte shapes always have only one spicule. However, by considering the skeleton shear elastic energy also, the calculated stable echinocyte shapes have many spicula in agreement with experimental observations.

Increased incidence of arthrosis in women could be related to femoral and pelvic shape

In this study various femoral and pelvic geometrical parameters important for hip joint contact stress were determined. The parameters were measured from standard anteroposterior radiographs of healthy adult subjects and analysed by using descriptive statistical procedures. Women proved to have a significantly smaller femoral head radius and larger distance between the inner acetabular rims than men, both features which lead to an increase of contact stress in the hip joint articular surface. Since too high, long-lasting contact stress is unfavourable regarding the development of arthrosis, we propose that these differences in the femoral and pelvic geometry could be one of the reasons for the increased incidence of arthrosis in women.

Stress distribution on the hip joint articular surface during gait

The magnitude and the direction of the resultant hip joint force are different in different body positions during gait. Therefore the stress distribution in the hip joint articular surface also changes. The aim of this work is to study how the stress distribution changes if the magnitude and the direction of the hip joint force is changed during gait. For this purpose a three-dimensional mathematical model is developed. We calculated the values of the peak stress and the location of the pole on the articular surface (where the stress is maximal) in the successive phases of the walking cycle. The values of the peak stress range from 0.8 MPa in the one limb stance phase to 2.6 MPa in the heel strike phase.

Determination of the femoral and pelvic geometrical parameters that are important for the hip joint contact stress: differences between female and male

The difference between male and female femoral and pelvic geometry was studied by considering some geometrical parameters such as interhip distance, inclination of the crista iliaca, diameter of the femoral head and centre-edge angle of Wiberg. The values of these parameters were determined for 79 healthy female and 21 healthy male subjects. Standard anterior-posterior radiographs were used and processed by the computer-aided system. The results show some important sex differences in femoral and pelvic geometrical parameters which determine the hip joint contact stress.

The hip-joint resultant force in healthy male and female population: a comparative study

The geometrical parameters of the pelvis and the femur which influence the hip-joint reaction force were obtained automatically for 21 male and 79 female healthy human subjects from standard AP radiographs, by using a computeraided system. To calculate the hip-joint reaction force a three-dimensional mathematical model of the hip in one-legged stance was used. In order to prepare the data as input to the mathematical model of the hip a nonhomogeneous scaling method based on a reference model of the hip musculature by Dostal and Andrews was applied. Our results show that the magnitude of the hip-joint reaction force and its inclination angle are significantly greater for females than for males. Since females have in addition significantly smaller femoral head radius than males, it may be concluded that the stress in the hip-joint articular surface is higher in the female population relative to the male population. Because the increased stress in the hip-joint articular surface is unfavourable regarding the arthrosis development, the presented results could partially explain the fact that females have greater incidence of arthrosis in the hip-joint than males.This is related not only to femoral, but also to pelvic geometry.

Depletion of membrane skeleton in red blood cell vesicles

A possible physical interpretation of the partial detachment of the membrane skeleton in the budding region of the cell membrane and consequent depletion of the membrane skeleton in red blood cell vesicles is given. The red blood cell membrane is considered to consist of the bilayer part and the membrane skeleton. The skeleton is, under normal conditions, bound to the bilayer over its whole area. It is shown that, when in such conditions it is in the expanded state, some cell shape changes can induce its partial detachment. The partial detachment of the skeleton from the bilayer is energetically favorable if the consequent decrease of the skeleton expansion energy is larger than the corresponding increase of the bilayer-skeleton binding energy. The effect of shape on the skeleton detachment is analyzed theoretically for a series of the pear class shapes, having decreasing neck diameter and ending with a parent-daughter pair of spheres. The partial detachment of the skeleton is promoted by narrowing of the cell neck, by increasing the lateral tension in the skeleton and its area expansivity modulus, and by diminishing the attraction forces between the skeleton and the bilayer. If the radius of the daughter vesicle is sufficiently small relative to the radius of the parent cell, the daughter vesicle can exist either completely underlaid with the skeleton or completely depleted of the skeleton.

Relative abductor strength after varus and valgus osteotomy of the proximal femur

Relative abductor strength (RAS) is defined as the difference between the available (maximum) abductor force and the required abductor force i.e. the force needed to maintain the mechanical equilibrium of the pelvis. In this work the dependence of RAS on the centrum-collum-diaphyseal angle and on the position of the greater trochanter was studied using a 3-D mathematical model of the human hip in the monopodal stance. Simulation of the varus and valgus osteotomy was done for the normal, 3 cm distal and 5 cm proximal position of the greater trochanter before the operation. It was shown that after valgi-sation a significant reduction in RAS is to be expected. On the other hand, varisation osteotomy is not associated with a significant change in RAS. The changes in RAS after valgisation for normal and distal position of the greater trochanter occur within the scope of the negative Trendelenburg sign. A negative RAS and, consequently, a positive Trendelenburg's sign occur only in extreme valgisation with a proximally situated greater trochanter. Reduction in RAS may reduce the capability of the hip muscles during strenuous physical activity and may thus participate to earlier muscle fatigue. The importance of special rehabilitation programme after valgisation osteotomy is stressed. Key words: hip biomechanics, abductor muscles, varus and valgus osteotomies, proximal femur.

Biomechanical study of various greater trochanter positions

A mathematical model was used in order to evaluate the mechanical situation after lateral, medial, distal and proximal displacements of the greater trochanter. It was calculated that lateral displacement may considerably reduce the hip joint contact force, while medial displacement greatly increases it. The influence of proximalization and distalization is much less pronounced. It was further shown that, regarding the postoperative relative hip abductor muscle strength, lateral and distal displacements of the greater trochanter are favourable, while proximal and medial displacements are not.

Reducing the Stress in the Articular Surface of the Hip Joint after Shifting the Upper Part of the Body towards the Painful Hip

In this work the change of stress distribution in the hip joint articular surface after shifting of the upper part of the body towards the painful hip due to pain reflex is estimated theoretically by using a three dimensional mathematical model. It is shown that after displacement of the upper part of the body towards the painful hip the stress in the hip joint can be in case of poor femoral head coverage and small inclination of the pelvis very little decreased in spite of the fact that the resultant hip joint force is reduced considerably. Key words: stress in the hip joint, body shitting.

Biomechanical analysis of various operative hip joint rotation center shifts

A mathematical model was used to evaluate the mechanical situation after various operative shifts of the hip joint rotation center. It was concluded that while performing different pelvic osteotomies and the total hip replacement the hip joint rotation center should be shifted as far medially as is technically possible to reduce the magnitude of the hip joint contact force. By contrast, lateralization of the hip joint rotation center strongly increases the magnitude of the hip joint contact force; therefore this should be avoided whenever possible. The superior shift of the hip joint rotation center decreases the strength of the patient's hip abductor muscles and must therefore also be avoided. The inferior shift of the hip joint rotation center is favorable because it increases the strength of the patient's hip abductor muscles.

Computer simulation of periacetabular osteotomy

A simple static three-dimensional mathematical model of an adult hip in one-legged stance was used to evaluate the mechanical situation after periacetabular osteotomy. We found that the hip joint rotation center shifted as a consequence of the osteotomy. This may have considerable effects on the hip joint resultant force and therefore also on the pressure on the femoral head, which could cause the development of arthrosis.