The analysis of human femurs and prostheses

electr6nic speckle pattern interferometry by J. NI. Petzing, C. Heras-Palou, J. Kinq J and J. RI Tyrer

The potential lijtime o f h@ replacements is reduced by aseptic loosening-an inadequatejxation o f the implant. Increasing the l$ o f the surgical procedure requires knowledge o f the interaction between prosthesis andfemur. The authors have used electronic speckle pattern inte@rometry (ESPI), a laser-based metrology technique developedfor the analysis of d'isplacements and strains, to develop an understanding o j the biomechanics o f the proximalfemur whilst mounted in a compression test yig which also simulates muscle and tendon behaviour. Cadaveticfemora were studied under physiological loads, before and dJer the implantation o f thefemoral component o f a total h@ replacement.

Introduction

ip replacements have become a very common and successful operation in orthopaedic surgery world-wide. However, complications H can occur with t h s procedure, the main one

being aseptic loosening, defined as inadequate fixation of the implant, whch reduces the potential life-time of the surgical procedure. Increasing thu life-time would greatly benefit patient health and would reduce the total number of hip replacements required per year. Ths requires knowledge of the change of strain and stress dstributicln whch occurs when a prosthesis is implanted into a femur, compared to a complete healthy femur during typical load cycles (i.e. wallung).

It is recognised that in-service assessment of strain dstribution profile and history of implants is at best very difficult, if not unobtainable. A more practical approach is to measure femur performance in the laboratory under suitably modelled condtions, examining the femurs before and after prosthesis implantation. Measurement of strain within an

engineering environment is traditionally catered for by the use of surface contact resistance strain gauges, whch provide excellent point source strain readmgs.

There are, however, two problems with this approach for the measurement of strain in femurs. Firstly, the devices are effectively point source and a large mesh of gauges would be needed to provide wholefield information. Secondly, the strain readmgs are heady influenced by the quahty and consistency of strain gauge bonding to the object. The femur surfaces provide poor bondmg characteristics for the gauges and can lead to erroneous data.

The approach taken in this work has been to consider the use of non-contact optical techniques to provide the data required. Specifically, wholefield measurement methods such as photoelasticity and SPATE' have been considered whch wd provide a large grid of continuous data. In this context, holo- graphc interferometry has previously been reviewed and applied as a general tool for biomedical experi- mentation in orthopaed~cs~~~ and specifically applied to the study of femurs and prostheses4a5. This application

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was successful, but was limited in its versathty and data generation. The major problem was found to be the successll extraction of in-plane displacement compo-

A related, but alternative, approach used for the analysis of the femurs and prostheses has been electronic speckle pattern interferometry (ESPI) . This technique has previously been developed for the analysis of displacements in complex engineering components and structures but has received little attention in the fields of biomedicine and bio- mechanics. The predominant reasons for applying ESPI to t h s study have been its abhty to measure independently in-plane and out-of-plane dsplacement components, and to achieve this in ‘real-time’ (25 Hz camera frame rate). To date work has been completed using ESPI whereby fringe counting has been used to

, nents required for the determination of strain data.

greater trochanter \ fovea capitis

-- proximal end neck - lesser trochanter

anterior side

.. lateral side

medial epicondyle ’ 1) 6 1( lateral condyle i

medial condyle --c!&sJ + distal end

Fig. 1

generate numerical d a d 7 . It is the intention of ths work to demonstrate the abdlty to produce wholefield calibrated dqlacement data from human cadaveric femora.

Medical names for parts of the femur

Structure of the femur

The femur is the longest, strongest and heaviest bone in the body (Fig. 1) and provides the ‘ball’ of the pelvic ball and joint socket. The neck structure improves the articulation at the b p joint, but is also the weak link in the bone structure, with most Gactures occurring in this area. The proximal end of the femur consists of the femoral head, neck, greater and lesser trochanters. The head is slightly more than half a sphere and articulates in the socket of the pelvis.

The trochanter positions are the normal attachment sites for the buttock muscles (gluteus medus and gluteus minimus) whdst the thigh muscles (dlotibial band) connect between the knee and pelvis. The shaft of the femur is slightly bowed anteriorly and is quite smooth except for a longitudnal posterior ridge (linea

aspera), whch provides attachment sites for further muscle groupings.

The procedure for implanting the prosthesis is to remove the femoral head to a prescribed depth with respect to the prosthesis being used. The prosthesis is effectively a stainless steel or titanium ball joint mounted on a spike whch is fitted into the femur via the neck. Again depending upon the type of femur being used, surgical bone cement (a mechanical interlock fixation) may be employed to ensure the lochng of the prosthesis into the femur, using a variety of application methods.

The reaction of the body to the introduction of a hgh-density met&c component is complex, but causes bone to gradually erode away from the surgical site, as the body attempts to restore a strain and stress equhbrium in the bone and muscle groupings. If the strain dstribution of the bone/cement/metal matrix can be assessed and understood, then potentially a prosthesis could be designed whch would not grossly alter the bone/muscle strain/stress equhbrium, there- fore prolonging the operational life of the prosthesis.

Electronic speckle pattern interferometry

Electronic speckle pattern interferometry (ESPI), or less commonly TV-holography is the name given to several laser speckle based techniques whch are used for measuring discrete displacement components. Two drfferent optical designs are avadable, one to produce out-of-plane (OOP) displacement data, and the other to produce horizontal and vertical in-plane d s - placement data (HIP and VIP), all of whch rely on CCD-TV cameras at the image plane for the recording of

A schematic dragram of the in-plane ESPI system used for the bone analysis is shown in Fig. 2, whch shows two dluminating wavefronts at equal but opposite angles to the surface normal and camera axis. The speckle pattern observed on the bone is recorded at the image plane of the CCD-TV camera, and is then post-processed in order to generate the correlation h.inges describing in-plane displacement.

The total light received at the image plane from the two dluminating wavefronts is U1 + U2 = UT. More importantly the intensity of the light for any point at the image plane is proportional to the square of the total light field, i.e. I cc UTUT*, which, via mathematical manipulation, can be reduced to a term synonymous with speckle metrology:

IA = I1 + I2 + 24a COSY (1)

In this instance, the descriptor I A is used as a means of identdjnng the intensity distribution of the object in its initial state, 11 and I2 are the two dumination wave- front intensity contributions, and Y is a generahsed phase angle term.

If the object receives a static displacement, a phase change A(x,y) is introduced into the object wavefront.

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Using the same arguments as for the initial object state, the new intensity hstribution at any given point can be described as:

The interferometer data is displayed on a TV monitor as correlation fringes, whch may be formed via a subtraction process using software- or hardware-based frame stores, or via an addition process at the image plane. For subtraction fringes, the change of intensity between the initial object state and the displaced state (61 = IA - IB:I is produced by storing the initial undsplaced phase ‘map’ as a reference image, and subtracting all subsequent, displaced phase maps from t h s reference. Tlis process is described mathematically as:

(3)

Ths brief summary of the laser speckle physics describes the formation of the correlation fringe data, but an interpretation of the fringes is required in order to be able to understand what the data represents. Fig. 3 represents the laser wavefront llluminating the object surface art some angle 8, with the reflected component travdhng to the interferometer optics and image plane. ABC is the static object path length, whilst DEF is the dsplaced path length. The change of optical path length, S l , due to object displacement is:

A simdar result can be produced for the second object illumination beam of the in-plane interferometer:

612 = d,(l + cos02) + &sin82 (5)

If the two dunninating wavefionts are at equal but opposite angles i(01 = -02, Fig. 2) then eqn. 5 can be

camera axis

lens and I aperture unit ~ I laser \ / laser

wavefront 1 W T n t 2

el i e2

Fig. 2 Schematic of an in-plane ESP1 system

The brightness of the TV-monitor d change as the object surface moves in the x direction dong the x-axis. The image wdl show dark subtraction correlation fringes wherever A = 2nn, where n is an integer fiinge number. Hence eqn. 6 can be simplified and drectly related to the direct measurement of in-plane dis- placement:

nh 2 sin0

=-- (7)

where U is the horizontal in-plane displacement com- ponent along the x-axis.

Experimental procedure

A hydrauhc mechanical testing rig was designed to hold the femur in a correct attitude with respect to the load- ing ram and a simulated pelvic joint mounting (Fig. 4). For the one :leg stance phase of gait, the most important components in action are the abductors of the hip and

rewritten in term of 01: The optical phase change, A,

associated with this alteration of optical path length is geometrically defined as A = k r d , , where k = 2 n / A is the wavenumber and defines the optical phase change per unit displacement, 1’ is the fringe sensitivity factor (no - n3), and d, is the geom.etry sensitivity vector function. Via substitution of the path length description equations 4 and 5 , the optical phase change can now be redefined:

A

F

C

I I I

I I

I 4n A A = - U sin611 (6) big. 3 Change of laser illumination path length

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the hotibial band. Con- sideration was therefore given to simulating the tensions applied along the lateral side of the femur by these groupings. Ths was completed in order to attempt to hold the femur in a state of strain/stress equhbrium, as in the body. The abductor simulator was acheved by the attachment of existing tendon groups (sited at the greater trochanter) to the simulated pelvis mounting. The iliotibial band was introduced using a strain-gauged tensioning mechanism between the two ends of the femur.

Cadaveric bones were

outer casing \

knee simulator

iliotibial band

abductor simulator

Fig. 4 The femur loading test-rig

collected and cleaned of soft tissues whilst preserving the tendons of the gluteus medius and minimus, to whlch a ring was surgically attached to allow Gxation to the pelvic unit. The specimens were kept kozen at -20°C in a bone freezer, and then defrosted overnight before each test session. During experimentation, the femur was wiped with formalin to reduce biological risk and to prevent the onset of dehydration, whch could alter the mechanical behaviour of the bone. The hydradc ram was used to apply the loadngs to the

femur. The test-rig had previously been assessed for structural integrity up to a pressure loadmg of 6894 k N m-2 (1000 psi) with the bone system replaced by a rigid steel strut to apply the ram force to the outer casing. Throughout these prov- ing tests, the in-plane ESPI interferometer demonstrated that the steel strut behaved in pure compression.

The ESPI interferom- eter used an inka-red &ode laser at 860 nm, coupled into a pair of optical fibres to provide the two arms of the interferometer with the angle of illumCnation of

each arm set at 0 = 9". These settings defined the sensitivity of the in-plane interferometer, with each subtraction correlation fringe representing 5.5 pm of in-plane displacement, with the dumination vector set to measure dsplacement in the y axis (vertical in-plane displacement). A P u h ~ TM500 CCD-TV camera was used to record the speckle patterns on the bone surface, the video signal being passed into a hardware- based Game store where the subtraction process was completed. Results were &splayed in 'real-time'

-.-

Fig. 5 In-plane ESP1 fringes on a section of a femur Fig. 6 Unwrapped optical phase map

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I 0 -

10

20 E E If

.- 2 30 U)

Q

40

50

-

-

-

-

-

L I 1 I I

0 10 20 30 40 50 position, mm

Fig. 7 Contour and vector plot of in-plane displacement (microns)

(25 Hz camera frame rate) on a TV-monitor, with data being stored in an image processor for post-processing.

The fibre interferometer included phase-stepping fachties whch were used and controlled via the image processor. Three sets of images for each load case were grabbed with an input optical phase change of W 2 applied between each image. The three phase-stepped correlation interferograms were processed in the image processor to produce a wholefield map of wrapped optical phase, which was unwrapped using a cosine- transform-based phase unwrapping algorithm. Finally the data were calibrated with respect to the in-plane ESP1 interferometer to give wholefield in-plane &s- placement data, which could be used to calculate strain vectors.

Initial experimentation was performed on full-sized replica polymer-based femurs, which provided a more straightforward approach to test-rig and interferometer optimisation. Bone cement moulds were produced for each femur to be analysed, to support the femurs at the distal and proximal ends. Due to natural variation between the femurs, several sets of moulds were manufactured. These moulds improved the load transfer characteristics between the test-rig and the femurs and stopped any rotation of the femur in the rig during loachng cycles. It should be noted that the pelvic simulator was hinged in order to stop femur rotation.

In-plane ESP1 results

Due to the long, thin nature of the femur, examining the whole bone in one stage was not practical because the spatial information on the TV-monitor was a thin line of approximately 15% of the entire picture, causing poor resolution of the correlation hinges and making post-processing of-the data very difficult. The approach adopted was to concentrate on the femoral head and

neck, these being the critical areas with respect to the implantation of the prosthesis.

Analysis of the polymer-based bone proceeded without any difficulties, although it was found necessary to apply a removable coating of aerosol-based white powder to the bone surface to reduce specular reflection and to provide a uniform intensity speckle pattern. In-plane correlation figures were formed during load application and these were successfully phase stepped, leadmg to the calculation of wholefield in-plane chsplacement. It was noted that the plastic specimen produced consistent dsplacements (strains) for the respective loads, which were repeatable.

Analysis of the cadaveric femurs was much more problematic. The femur is a complex anisotropic heterogeneous material structure, made up of a calcium-based matrix supporting tissue and water- based fluids. The femurs were also left with an intact skin-like layer known as the periosteum. During the compression cycles, the bone exlbited compression, but fluid was forced out of the structure and accumulated on the external surfaces. This caused varying amounts of specular reflection and, because the fluid was moving, speckle decorrelation, whch disrupted the quallty of the subtraction correlation fringes. The enforced addition of formahn to the bone increased surface moisture and exacerbated the situation. Specular reflection could initially be catered for by the application of a layer of white aerosol spray, but continuous seepage of fluid tended to remove this temporary layer.

After much optimisation, subtraction-based correla- tion fringes were produced and an example of one is shown in Fig. 5. This set of data was produced when a load of 200 kN m-’ was applied to the system, on top of a preload of 25 kN m-z. In t h s particular example, the fiinges contain some &agonal orientation which is

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attributable to slight rotation of the femur in the test- rig during the compression cycle.

Application of the phase-stepping software enabled the image processor to capture three phase-stepped images, from whch a map of wrapped optical phase was produced. The data was then phase unwrapped to generate a continuous grey scale image of optical phase (0-255 grey scales), whch is shown in Fig. 6. Ths work has been fortunate in having access to phase- unwrapping software whch is very robust in nature, and can cope with the inherent speckle and optical noise associated with fiinges obtained from such a difficult subject matter. The optical phase data has been cahbrated with respect to the in-plane ESPI inter- ferometer and is shown in Fig. 7. The maximum dsplacement over thus region of interest (50 mm) amounted to 6.3 pm, leadmg to a first approximation of 126 y-strain.

Generation and capture of the correlation kinges highhghted another problem associated with the material characteristics of the femur. The bone material structure is highly complex, composed of a calcium base matrix of varylng density, containing water-based fluids and soft cellular structures. The consequence of applying a load across the bone was that the system tended to relax after the load was applied, which caused fringe drift. This behaviour had not been encountered previously when optimising the experimentation using the plastic bone. Clearly the presence of fi-inge drift can lead to issues and concerns about excessive experi- mental uncertainties, on top and beyond those whch would nornidy be associated with the wholefield speckle pattern interferoinetric techniques. To date the extent of tlvs fringe drift has not been quantified although qualitative evidence suggests that the drift can be influenced by the initial preload used to settle the test-rig before measurement compression loads are applied.

It should be noted that the bone is a complex three- dimensional structure, with extreme curvature over various portions of the surface. Ths means that the interferometer sensitivity and &hinge hnction d change with respect to the surface geometry. A further development to be implemented wdl be the intro- duction of surface-contouring instrumentation to produce a dgital map of the femur surface, which will allow the hsplacement data to be cahbrated with respect to the geometry.

Conclusions

The successful conclusion of this stage of the examma- tion of the human cadaveric femurs has demonstrated that in-plane electromc speckle pattern mterferometry can be used to generate wholefield calibrated maps of in-plane dsplacement The imtlal data has allowed first order approxlmatlons of strain components in the bone. The use of ESPI does not require any modficaoon of the femur surface whch could potentidy dstort the object behamour. The rapid

acquisition rate (25 Hz) and the vector sensitlvity selectlon of the optm promde much greater versathty of experimentabon than holographc interferometry

In order to design a r e a h c loadmg system, an understandng of the basic biomechamcs has been acquired whch has emphasised the simulation of hotibial band and abductor muscles/tendons, whch provides a model of the musculoskeletal system, rather thanjust the skeletal system Ths has been identlfied as a prerequisite for successful completion of ths research, because it wdl allow the vlsuahsation of changes of stradstress w t h n the system in addbon to indvidual components This test-rig system also promdes the abhty to complete many tests in a short period oftime, augmenting the stabshcal sigrvficance and credbhty of the findmgs.

Acknowledgments

The authors would like to acknowledge the assistance of staff at Glenfield Hospital (Leicester) and Leicester General Hospital. Further thanks are extended to Mr. T. Slater and Mr. V. Scothern for their technical expertise.

References

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STOYLE, T. E , and GREGG, E! J.: ‘The use of electronic speckle pattern interferometry to study the biomechanics of human bone and prostheses’. Proceedings of Optical and Imaging Techniques in Biomedicine, SPIE, September

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0 IEE: 1998

Dr. J. N. Petzing, Mr. J. Kmg and Dr. J. R. Tyrer are with the Department of Mechanical Engineering, Loughborough University, Loughborough, Leicestershire LE1 1 3TU, UK.

Dr. C. Heras-Palou is with Glenfield General Hospital, Leicester, UK.

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