Numerical design of hip stems with optimized shape and functionally graded material properties by means of additive manufactured porous materials

The biomechanics of the femur at the hip joint

Anatomy

The femur goes from the hip to the knee, and is the longest bone of the body. It has an almost-cylindrical shape in its central portion (diaphysis). Proximally, the almost-spherical head of the femur articulates with the congruent surface of the pelvic acetabulum, forming the hip joint. This joint can be seen as a ball-and-socket (or spheroidal) union that has good range of tridimensional motion and good stability to dislocation. Both articulating surfaces are covered with cartilage that reduces friction and helps to absorb the shocks. The whole joint is enclosed in the synovial capsule, which contains the synovial fluid that provides lubrication and nutrients to the cells of the cartilage as well as helps to absorb shocks. The joint is reinforced by ligaments and muscles that provide stability and generate the movements of the articulation (Tortora 2012).The reference system of the proximal femur is commonly centered in the femoral head (Bergmann, et al. 2001). Three planes are defined: the sagittal, coronal (or frontal) and transversal (or horizontal). Furthermore, three reference directions can be defined: medial-lateral, anterior-posterior and proximal-distal .

Forces

The load conditions at the proximal femur are dictated by the contact force of the hip joint and the muscular forces. The magnitude and direction of these loads depend on the activity(Bergmann, et al. 2001). The main attachment zones for the muscles at the proximal femur are the greater trochanter, situated laterally and the lesser trochanter, in medial orientation . An extensive description of the muscles attached to the femur is out of the scope of this work, and can be found, for instance in (Marieb 1999).
The values for the hip contact force have been measured by Bergmann et al. (2001) for different daily activities using instrumented implants. The authors found that this force can be up to 300% of the bodyweight. Heller et al. (2005) determined, using inverse dynamics, that in order to respect physiological-like loading conditions at the proximal femur, the muscle forces could be simplified to the action of the hip contact force and 5 muscular groups: abductor, ilio-tibial tract, tensor fascia latae, vastus lateralis and vastus medialis.

Total hip arthroplasty

Osteoarthritis (OA) or degenerative arthritis is the most common disease of the hip, and consists in the degeneration of the articular cartilage. In advanced stages, it is accompanied by severe pain and limitation in daily activities, and the solution is to perform a total hip arthroplasty (THA) (Siopack and Jergesen 1995, Pivec, et al. 2013). During the period 2013-2014 OA accounted for 74.7% of the hip arthroplasties in Canada while hip fracture was the second most common cause with 14.5% of the replacements (Canadian Institute for Health Information 2015). OA is also the main indication in other countries. For instance, it accounts for 85% of male and 79.8% of female arthroplasties in Sweden (Swedish Hip Arthroplasty Register 2013) and 93% of the replacements in the United Kingdom (UK National Joint Registry 2015).
In THA, both sides of the hip joint are replaced with the objective of reducing or eliminating pain and restoring the function of the hip (Pivec, et al. 2013).  Most modern prostheses allow some degree of modularity, with different choices for the stem neck and head in order to reproduce the adequate anatomy of a healthy hip. This thesis is focused in the femoral component, and in the following the terms (hip) implant or prosthesis will refer to this component.

Epidemiology and future perspectives

In Canada, 49,503 hospitalizations related to hip replacement were registered in the period 2013-2014, which represents an annual increase of 5% and a 5-year increase of 19.1% (Canadian Institute for Health Information 2015). Worldwide the same tendency has been observed, with more than a million THA performed every year and the prevision of doubling this number within the next two decades (Pivec, et al. 2013).
In addition, patients are younger: in Canada, 40.4% (males) and 26.8% (females) of all hip arthroplasties recipients in the period 2013-2014 were under 65 years old (Canadian Institute for Health Information 2015). In other countries, similar rates have been observed: in Sweden, the proportion of young patients increased from around 50% to almost 60% for men and from around 40% to almost 50% for women in the period 1992-2011 (Swedish Hip Arthroplasty Register 2013). Predictions are that up to 50% of all THA will be done in patients under 65 years old by 2030 (Kurtz, et al. 2009).

Main related problems

The commonly accepted lifespan of a hip stem is 15 years (Siopack and Jergesen 1995); however some studies have found up to 22.6 years implant survivorship (Khanuja, et al. 2011). Multiple factors affect this long-term survivorship of the arthroplasty, including a careful patient selection and surgical technique, the stem design and material resistance (Mai, et al. 2010, Pivec, et al. 2013). Younger patients are considered a risk population for hip arthroplasty, since they have higher activity levels and require implants with increased longevity (Kurtz, et al. 2009). This translates in higher failure rates for younger patients. For instance, in Canada the 5.44% revision rate for patients under 45 years old contrasts with the 1.72% for patients over 85 years old (Canadian Institute for Health Information 2015). In the United Kingdom, patients under 55 years old showed 7.26% 10-year revision rate whereas patients over 75 years old only showed 2.83% (UK National Joint Registry 2015). In Sweden patients under 50 years show up to 40% 20-year revision rate, compared to the 10% for patients over 75 years (Swedish Hip Arthroplasty Register 2013).

Mechanical causes of implant failure

It is believed that the bone loss caused by the stress shielding effect and the interfacial failure due to improper interfacial conditions may contribute to the aseptic loosening of the implant (Kuiper and Huiskes 1997, Arabnejad Khanoki and Pasini 2012).

Stress shielding

When the femoral bone is partially replaced by a stiffer metallic hip stem, a redistribution of the mechanical stimuli within the bone occurs in such a way that the stresses are decreased at the proximal femur. The bone is hence stress shielded, and being a living tissue that reacts to the mechanical stimuli (Huiskes, Weinans, et al. 1987), bone can be partially resorbed. The clinical impact of such bone resorption due to stress shielding may not be clear yet; however the diminution of the bone stock and quality that this phenomenon causes may compromise a future revision arthroplasty (Kuiper and Huiskes 1992, Mai, et al. 2010). Flexible and less invasive (i.e. smaller) implants have been shown to decrease the stress shielding (Huiskes and Boeklagen 1988, Weinans, et al. 1992, Kuiper and Huiskes 1992). In this way, Kuiper and Huiskes (1992) computed 70% decrease in the resorbed bone mass for a 70% reduction of the implant elastic modulus.

Interfacial failure

Large stresses at the bone-implant contact may result in the interfacial failure. In addition, it has been suggested that they can increase the level of pain and, in the immediate post-operative situation, result in larger interfacial micro-movements that would inhibit bone ingrowth (Kuiper and Huiskes 1997). Similarly to the stress shielding, the interfacial failure depends on the characteristics of the implant (mechanical properties and shape). Kuiper and Huiskes (1992, 1997) showed that the peaks of interfacial stresses are increased and shifted proximally with flexible stems, and Chanda et al. (2015) found that less invasive stems would result in more critical interfacial conditions.

Porous materials

Gibson and Ashby (1999) defined a porous material as “an interconnected network of solid struts or plates which form the edges and faces of cells”. Since such network has its own set of effective mechanical properties, it is a material itself and can be compared with common bulk materials (Ashby, 2006). The material can be found forming walls (or plates), resulting in “closed-cell” porosity; or struts, resulting in an interconnected network of “open-cell” pores (Gibson 2005). On the other hand, the porous material may have a random nature, in which case it is referred to as foam; or result from the 3D uniform repetition of a base unit cell (tessellation), in which case it is called lattice or well-ordered.
Three different size levels or scales can be identified in a porous material: macroscale, mesoscale and microscale . The macroscale defines the (external) dimensions of the part, and it can go from some millimeters to several centimeters. At the mesoscale, the details of the porous structure can be observed (e.g. unit cell shape and dimensions). This scale goes from hundreds to some thousands of microns, lying between the macroscale and the microscale. The microscale which cannot be seen to the naked eye, goes up to several micrometers and contains information at the strut level (e.g. crystallographic composition of the material).

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Table des matières

INTRODUCTION
CHAPTER 1 GENERAL CONCEPTS AND LITTERATURE REVIEW 
1.1 The biomechanics of the femur at the hip joint 
1.1.1 Anatomy
1.1.2 Forces
1.1.3 Mechanical properties
1.1.3.1 Elastic modulus
1.1.3.2 Strength
1.1.3.3 Interfacial strength
1.2 Total hip arthroplasty 
1.2.1 Epidemiology and future perspectives
1.2.2 Main related problems
1.3 Numerical analysis of hip implants
1.3.1 Mechanical causes of implant failure
1.3.1.1 Stress shielding
1.3.1.2 Interfacial failure
1.3.2 Improvement of stem performance
1.3.2.1 Optimization of implant shape
1.3.2.2 Functionally graded stems
1.4 Porous materials 
1.4.1 Well-ordered porous materials
1.4.2 Main geometrical parameters of porous materials
1.4.3 Additive manufacturing of porous materials
1.4.3.1 Irregularities of additively manufactured porous materials
1.4.3.1.1 Contribution related to this thesis
1.4.4 Mechanical properties of porous materials
1.4.4.1 Experimental testing of porous materials
1.4.4.2 Numerical modeling
1.4.4.2.1 Effect of manufacturing irregularities
1.5 Summary
CHAPTER 2 HYPOTHESIS, OBJECTIVES AND STRUCTURE OF THE THESIS 
2.1 Problem statement 
2.2 Hypothesis and objectives
CHAPTER 3 ARTICLE 1. FINITE ELEMENT MODELLING APPROACHES FOR WELL-ORDERED POROUS METALLIC MATERIALS FOR ORTHOPAEDIC APPLICATIONS: COST EFFECTIVENESS AND GEOMETRICAL CONSIDERATIONS 
3.1 Abstract 
3.2 Introduction 
3.3 Materials and Methods 
3.3.1 Geometrical parameters at mesoscale
3.3.2 Finite element (FE) modelling approaches
3.3.2.1 Finite size solid FE model
3.3.2.2 Finite size beam FE model
3.3.2.3 Infinite media model
3.3.3 Performed FE analyses
3.3.3.1 Determination of the cost-effective model approach
3.3.3.2 Unit cell geometry comparison: cubic and diamond
3.3.3.3 Criteria 1: similar bending and compressive behaviours
3.3.3.4 Criteria 2: mechanical properties close to bone
3.3.3.5 Criteria 3: Stress distribution uniformity within struts
3.4 Results
3.4.1 Determination of the cost-effective model approach
3.4.2 Unit cell geometry comparison: cubic and diamond
3.4.2.1 Criteria 1: similar bending and compressive behaviours
3.4.2.2 Criteria 2: mechanical properties close to bone
3.4.2.3 Criteria 3: stress distribution uniformity within struts
3.5 Discussion 
3.6 Conclusion 
3.7 Acknowledgements
CHAPTER 4 ARTICLE 2. FINITE ELEMENT MODELING OF MANUFACTURING IRREGULARITIES OF POROUS MATERIALS
4.1 Abstract
4.2 Introduction 
4.3 Materials and Methods 
4.3.1 Experimental data
4.3.2 FE modeling
4.3.3 Characterization and implementation of manufacturing irregularities in the FE model
4.3.3.1 Strut diameter variation
4.3.3.2 Strut inclination
4.3.3.3 Fractured struts
4.3.4 Finite Element Analyses
4.4 Results 
4.4.1 Characterization of manufacturing irregularities
4.4.2 Finite element analyses
4.4.3 Influence of the three geometrical irregularities for set S450P700
4.4.4 Simulation of the other sample sets
4.5 Discussion 
4.6 Conclusions
4.7 Acknowledgements 
CHAPTER 5 ARTICLE 3. NUMERICAL DESIGN OF HIP STEMS WITH OPTIMIZED SHAPE AND FUNCTIONALLY GRADED MATERIAL PROPERTIES BY MEANS OF ADDITIVE MANUFACTURED POROUS MATERIALS 
5.1 Abstract 
5.2 Introduction
5.3 Materials and Methods
5.3.1 Optimization strategy
5.3.1.1 Stem optimization at the macroscale
5.3.1.2 Porous material tailoring at the mesoscale
5.3.2 Finite element modeling
5.3.2.1 Stem and bone at the macroscale
5.3.2.2 Porous material at the mesoscale
5.4 Results
5.5 Discussion 
5.6 Conclusion 
5.7 Acknowledgements 
CHAPTER 6 GENERAL DISCUSSION
6.1 Synthesis of the articles
6.2 Limitations 
6.2.1 Limitations related to the porous material model
6.2.1.1 Unit cell geometry
6.2.1.2 Beam model
6.2.1.3 Manufacturing irregularities
6.2.2 Limitations related to the optimization of the hip stem
6.2.2.1 Dimensionality of the bone-implant model
6.2.2.2 Interfacial conditions
6.2.2.3 Evaluation of implant performance
6.2.2.4 Tailoring of the porous material
6.3 Future work
CONCLUSION

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