University of Ljubljana

Faculty of Mathematics and Physics

Department of Physics

Ivo List

seminar

Biomechanics of the Hip Joint

Mentor: prof. dr. Vera Kralj Igli£

Biomechanics includes research and analysis of the mechanics of living or-ganisms and the application of engineering principles. In this seminar, adetermination of the contact stress in the human hip joint is presented. Twodi�erent methods are outlined. The �rst method involves in vivo measure-ments by a specially designed hip endoprosthesis. While the second method isbased on a simple mathematical model, which uses as input data, a standardanteroposterior radiograph of both hips and pelvis. Conclusions obtained byusing both methods indicate, that hip biomechanics is useful in designing theoptimal treatment of the diseased hip as well as the rehabilitation process.

Ljubljana, February 2008

Contents

1 Introduction 3

2 Human hip joint 4

3 Hip stress measurement 4

3.1 The instrumented prosthesis . . . . . . . . . . . . . . . . . . . 53.2 Contact pressures in the hip joint measured in vivo . . . . . . 6

4 Model of hip forces and stress distribution 9

4.1 Resultant hip force . . . . . . . . . . . . . . . . . . . . . . . . 94.2 Stress distribution . . . . . . . . . . . . . . . . . . . . . . . . . 11

5 Conclusion 13

References 14

2

1 Introduction

Degenerative processes in the hip leading to coxarthrosis (a degradation of thehip cartilage) a�ect a population of elderly in the developed world. This pop-ulation is increasing in number since its life expectation increases. Coxarthro-sis can occur secondary to hip disorders such as necrosis of the femoral heador dysplasia of the hip. In hips with necrosis of the femoral head, a part ofthe head decays and in an advanced stage of the disease cannot bear weight.In hip dysplasia, malformations of the femur and the acetabulum (such asnot having enough lateral coverage of the femoral head by the acetabulum)are present. In both cases, the weight bearing area is decreased leading toan increase of the contact hip stress and early coxarthrosis. Such conditionsare treated by osteotomies intended to redistribute and diminish weight andalso by implantation of the hip endoprosthesis.

Measurements of the hip stress are important to optimize the treatementand recovery of patients. Here we present two methods for determination ofthe contact hip stress. The direct measurement with a specially designed en-doprosthesis yielded information on the general e�ect of particular activitieson hip stress [1, 2, 3, 4]. This method can not be used in clinical practicewhere the method should be noninvasive, simple, and not too expensive.Therefore, simple methods based on mathematical models are more appro-priate. We brie�y present the method Hipstress for determination of thecontact hip stress distribution [5, 6, 7].

3

2 Human hip joint

Figure 1: Structure of the hip joint. From [4].

The hip joint is a synovial joint formed by the articulation of the roundedhead of the femur and a cup-like acetabulum of the pelvis. It is classi�edas a ball and socket joint. It forms the primary connection between thebones of the lower limb and the axial skeleton of the trunk and pelvis. Bothjoint surfaces are covered with a strong, but lubricated layer, called articularhyaline cartilage. Figure 1.

3 Hip stress measurement

Forces and stress measurements in vivo were performed by a special prosthe-sis with implanted measuring devices[4, 1, 2, 3]. The devices were mountedinto the prosthesis stem and into the joint contact area of the prosthesis[6, 8].Such prosthesis gives us direct data, but such measurements can only be madeon patients which need a prosthesis and therefore the data is only partiallyequivalent to healthy hips.

A miniaturized radio telemetry device has been developed which can mon-itor the magnitude and distribution of stress generated between cartilage-covered surface of human hip socket and the surface of a hip prostheseswhich replaces the spherical head of the femur in the hip[4, 1, 2, 3]. Theprosthesis consists of several pressure transducers and the telemetry systemusing an external power source.

4

Figure 2: Cross section of the pressure transducer. From [4].

3.1 The instrumented prosthesis

The instrumented prosthesis contains two principal components � a networkof 14 identical pressure transducers and a miniaturized telemetry device.

Each pressure transducer consists of two main elements � a diaphragmwhich converts the applied pressure into a mechanical motion, and a displace-ment sensing device which measures the diaphragm motion and produces anelectrical signal proportional to the diaphragm motion. A cross section ofa complete transducer is shown in Figure 2. The diaphragm is circular andis machined directly into the wall of the prosthesis ball. In this manner thesphericity of the outer surface of the ball is preserved and there are no edgesor holes that might damage the cartilage surface in the acetabulum. A slidingpin held in plastic bushing couples the motion of the centre of the diaphragmto the free end of a cantilever beam. The cantilever beam is a silicon crystalwhich has four semiconductor strain gauges di�used into its surface, whichsense the bending of the beam and produce an electrical signal in responseto the pressure applied to the diaphragm.

The pressure transducer is designed to operate between 0 and 690 Ncm2

and has sensitivity of approximately 10 µV cm2

V N. The natural frequency of the

transducer is approximately 10 kHz, and the strain gage bridge is a linearfunction of pressure to within one percent of the full-seal output. Temper-ature stability of the transducers is not a problem, partly due to the in-herent temperature compensation of the four-active-arm strain gage bridge,but primarily because the transducers will operate in temperature controlledenvironment (the human body).

A full complement of 14 transducers mounted into prosthesis hemisphereis shown in Figure 3. The diameter of the hemisphere is 4.8 cm.

A radio telemetry device is incorporated into the instrumented prosthesisto eliminate the possibility of infection that would exist if wires were broughtout through the experimental subject's skin. With the exception of a smallcoil mounted on the end of the prosthesis stem, the implanted telemetry

5

Figure 3: Fourteen pressure transducers mounted in the hemisphere of a pros-thesis. From [4].

device is completely enclosed and hermetically sealed within the ball of theprosthesis.

The telemetry device contains no batteries � it is totally powered bya source external to the subject's body by means of a transformer power-induction link. This approach to powering the telemetry device helps solvetwo design problems � device size and operating lifetime. The availabilityof relatively large amounts of power at relatively high voltages (several tensof volts) allows considerable freedom in terms of component selection andcircuit design. In addition, the power induction system eliminates severalproblems associated with batteries, such as low energy storage density, ex-ternally operated switches, and the potential toxic hazards of batteries usedin long-term implantations.

3.2 Contact pressures in the hip joint measured in vivo

A pressure-measuring prosthesis was implanted in a 68-year-old patient whohad sustained a displaced fracture of the femoral neck [2]. The data revealvery high local (up to 18 MPa) and nonuniform pressures, with abrupt spatialand temporal gradients [2]. Figure 4 shows locations of transducers.

6

Figure 4: Drawing of the endoprosthesis with pressure-measuring instrumen-tation showing the locations of the transducers. From [2].

Activity Pressure

(MPa)

Transducer

number

Postoperative activitiesBalanced suspension 0.7 7Supine (bed rest) 1.4 5Buck traction (22 N) 1.5 5Riding stationarybicycle 1.6 5Use of continuouspassive motion 1.7 5Abductor splint 2.6 10Use of bedpan 3.2 5

Resisted isometriccontractionHip adductors 5.0 5Hip extensors 4.9 5Hip abductors 4.2 5Hip �exors 3.5 5

Activity Pressure

(MPa)

Transducer

number

MobilizationParallel bars 3.4 5Walker 3.8 5Partial weightbearing crutches

3.5 5

Cane � 65N 5.1 3Cane � 130N, 220N 4.8 3Unsupported 5.5 3

Everyday activitiesRising from a 38 cmhigh chair

15.0 1

Rising from a 56 cmhigh chair

9.2 1

Stair-climbing 10.2 1Jogging 7.7 2Jumping 7.3 5

Table 1: Peak stress in di�erent activities and transducers. From [2]

7

This table 1 shows the maximum pressure registered on the transducerthat had the highest reading during the activity at that particular testingsession. The largest maximum pressures occurred during isometric adductionand extension of the hip [2]. Isometric muscle contractions caused maximumpressures in the hip that were nearly equal to those generated during normalwalking.

To initiate walking postoperatively, the patient started by using parallelbars and progressed to using a walker, to non-weight-bearing with crutches,to partial weight-bearing with crutches, to using a cane, and �nally to unsup-ported gait. Progress through this process of rehabilitation did not alwaysresult in progressively increasing pressures. Rather, non-weight-bearing withcrutches produced the lowest maximum pressure � a reduction of 56 percent compared with the maximum pressure during normal walking. Partialweight-bearing on crutches reduced the pressure by only 35 per cent. A sin-gle cane in the opposite hand, when loaded at 130 N, produced a reductionin maximum pressure of only 11 per cent compared with unassisted walking.When an additional 90 N of force was applied to the cane, maximum pressurewas not further reduced. The use of ischial-bearing brace (a brace strappedonto upper part of the leg and knee, that bears the lower part of the pelvis)was as e�ective as partial weight-bearing with crutches in reducing maximumpressure.

During the gait cycle, the pressure was typically maximum at transducer3, which articulated with the superior acetabular dome. This shows that thepressure distribution has its pole in the superior region and its size corre-sponds with the weight applied to the leg.

As rehabilitation proceeded, measurements were recorded for the morestrenuous activities of rising from a chair, stair-climbing, jogging and jump-ing. Rising from a chair produced a maximum pressure that was approxi-mately three times that which occurred during walking and approximatelytwice that occurring during jogging or jumping. The maximum pressure de-creased as the height of the chair increased. The greatest maximum pressurewas 18 MPa on transducer 1, when the patient rose from a normal chair(45 cm high) twelve months postoperatively.

These measurements suggested that postoperatively, using crutches with-out bearing weight and using a stationary bike is bene�cial for the patientsince the motion at low hip stress is enabled. On the other hand, risingfrom a low position was not advised. The results of the direct measurementsindicated practical advice which helped improve the treatment.

8

4 Model of hip forces and stress distribution

The advantages of mathematical modelling over direct measurement is no-invasiveness and making it possible to study large groups of hips. Input datafor such models are, for example, geometrical parameters of the body, accel-erations of certain points of the body and external forces. The shortcomingsof the mathematical models are that simpli�cations are introduced, thereforetheir accuracy is limited.

The hip load can be described with a vector sum of all forces, that aretransferred from the acetabulum to the head of the femur (this sum de�nes

resultant hip force ~R) and with the distribution of this force over the load

bearing area � e.g. pressure that acts on the hip. ~R can be either measureddirectly or calculated via a mathematical model combined with external mea-surements.

4.1 Resultant hip force

In the biomechanical description, the body is divided into segments connectedwith joints. Each segment is described as a rigid body of a certain mass (m),center of gravity (G) and rotational momentum (J). The movement of the

segment is caused by forces which act on it: its weight ~W and forces of othersegments (inter-segment forces). The inter-segment force is a vector sumof all forces, which act on the joint surface and forces which are caused byanatomical structures (t.i. muscles, ligaments). The contact point of theinter-segment force is at the connection between two segments. Such forcesfor a any chosen segment are shown on Figure 5.

9

Figure 5: Forces that act upon a chosen segment. C is the rotational axis, Gis the centre of mass, ~W weight, ~FI1 and ~FI2 are the inter-segment forces of the�rst and the second segment acting upon the chosen segment. From [9].

The segment dynamics are described by equations of motion:

~W +∑

i~FIi = m~a, (1)

( ~rCG × ~W ) + ( ~rCG ×m~a) +∑

i( ~rCIi× ~FIi) +∑

i~MIi = J~α, (2)

where ~α is angular acceleration of the segment, ~rCG is a vector from therotational axis (C) to the centre of mass (G) and ~rCI is a vector from rota-tional axis (C) to the point where inter-segmental force of segment i acts on

the chosen segment, ~MIi is the inter-segmental torque, of the segment i onthe chosen segment. Index i runs over all segments which act on the chosensegment.

In particular, when describing forces acting on the hip, we mark one legas a �rst segment and the rest of the body as the second segment.

The inter-segment force which acts between two segments is equal to thesum of the joint force ~R and the force exerted by the muscles ~F [6]. Here,ligament forces are neglected.

~FI = ~R + ~F . (3)

To estimate the resultant hip force ~R, we have to know the inter-segmentaland muscle forces. If we were to include the forces which act upon the

10

segment into the model, the number of unknowns would exceed the numberof equations. Several methods for solving this problem were introduced, oneof them based on the reduction of the number of unknowns (e.g. neglectingthe forces of ligaments and tendons).

The resultant hip force ~R can be estimated by using weight and geom-etry data obtained from anteroposterior radiographs. By determining somecharacteristic points on the pelvis and the femur, the muscle insertion pointsare estimated by re-scaling the reference points determined on a cadaver [7].

4.2 Stress distribution

Since the resultant hip force acts over the load bearing area of the hip, wewould also like to describe its spatial distribution � i.e. the stress distributionover the load bearing area.

~R =∫

p d ~A, (4)

where p is stress and d ~A is the area element. Within a simple model Hip-stress it is assumed that p = p0 cos γ, where p0 is stress at the stress pole, γis the angle between the radius vector from the centre of the femoral head tothe chosen point on the femoral head and the radius vector from the centreof the femoral head and the stress pole. The cosine function implies perfectspherical shape of the femoral head and acetabulum and the validity of theHooke's law for the deformation of the soft cartilage between bony acetab-ulum and the femoral head upon the loading of the hip. The integration isperformed over the load bearing area, which is de�ned on the lateral side bythe coverage of the femoral head by the acetabulum and on the medial sideby the condition of vanishing stress.

The Hipstress model was used to analyze di�erent populations of hips.When estimating a resultant hip force, a representative position (the onelegged stance) was used.

The results showed that an elevated hip stress represents a risk factor fordevelopment of coxarthrosis: in patients with higher peak stress the implan-tation of the endoprothesis occured at a younger age (Figure 6). Elevated hipstress produces a less favorable enivronment, which speed up degradation ofthe cartilage.

The model was also applied to the partial and total hip endoprosthesis.In total hip endoprosthesis, the friction between the ball and the socket ofthe prosthesis produces debris which causes microinfection at the prothesis-tissue interface leading to the deterioration of the bone and eventually thewear of the prothesis. By using the Hipstressmethod, a positive correlation

11

between the maximal contact hip stress and a linear wear of the polyethylenecup, was found ten years postoperatively (Figure 7).

Figure 6: Dependence between age at implantation of hip endoprosthesis and hip stress(B.Pompe, I.Rigler, I.Rato²a, R. Vengust, V. Antoli£, A. Igli£, V. Kralj-Igli£, not pub-lished)

Figure 7: Correlation between maximal stress and linear wearing downof polyetyl cup used in prosthesis(R. Ko²ak, M. Daniel, V. Antoli£, A. Igli£, V. Kralj-Igli£, not published)

The Hipstress method proved to be useful in clinical practice for de-termination of the risk factors for coxarthrosis, for determination of the hipdysplasia and for determining the optimal position of the endoprothesis asto minimize the production of wear debris.

12

5 Conclusion

Hip biomechanics is useful in planning the treatment and rehabilitation ofdiseased hips. Using instrumented prosthesis hip stress was measured invivo during rehabilitation and later on during everyday activities. Experi-mental data showed the need to change the rehabilitation routine for patientswith such prosthesis. Unfortunately, due to ethical standards, such measure-ments can rarely be done in vivo, and therefore statistical representation isextremely small. On the other hand simple methods based on mathemati-cal models are non-invasive and can help analyze larger populations. Suchanalysis veri�es their correctness and enables those methods to be used todetermine risk factors for diseased hips and to plan the treatment.

13

References

[1] Hodge W, Fijan R, Carlson K, Burgess R, Harris W, Mann R. Contactpressures in the human hip joint measured in vivo. Proc Natl Acad SciUS A. 1986; 83 (9): 2879�83.

[2] Hodge W, Carlson K, Fijan R, Burgess R, Riley P, Harris W, et al.Contact pressures from an instrumented hip endoprosthesis. The Journalof Bone and Joint Surgery. 1989; 71 (9): 1378�1386.

[3] Krebs DE, Elbaum L, Riley P, Hodge W, Mann R. Exercise and gaite�ects on in vivo hip contact pressures. Phys Ther. 1991; 71 (4): 301�9.

[4] Carlson CE, Mann RW, Harris WH. A Radio Telemetry Device for Mon-itoring Cartilage Surface Pressures in the Human Hip. Biomedical Engi-neering, IEEE Transactions on. 1974; p. 257�264.

[5] Igli£ A, Kralj-Igli£ V. Computer system for determination of hip jointcontact stress distribution from standard AP pelvic radiographs. RadiolOncol. 1999; 33: 263�266.

[6] Brand RA, Pedersen DR. Computer modelling of surgery and a consid-eration of the mechanical e�ects of proximal femur osteotomies. The hipsociety award papers (USA). 1984; p. 193�210.

[7] Dostal WF, Andrews JG. A three-dimensional biomechanical model ofhip musculature. J Biomech. 1981; 14 (11): 803�12.

[8] Hodge WA, Carlson KL, Fijan RS, Burgess RG, Riley PO, Harris WH,et al. Contact pressures from an instrumented hip endoprosthesis. J BoneJoint Surg Am. 1989; 71 (9): 1378�86.

[9] Ivanovski M, List I. Pomen kol£nega sklepnega tlaka pri nastanku nekrozekol£ne glavice (Pre²ernova naloga). Medicinska Fakulteta Univerze vLjubljani; 2006.

14