CC BY
27
Review
UDC 617.3:57.089.67:539.3:539.4
LONG TERM EVOLUTION OF BONE RECONSTRUCTION WITH
BONE GRAFT SUBSTITUTES
Martynenko O. V.1, Zolochevsky O. O.2, Allena R.3
1 V. N. Karazin Kharkiv National University, Kharkiv, Ukraine
2 National Technical University «Kharkiv Polytechnic Institute», Kharkiv, Ukraine
3 Arts et Métiers ParisTech, Paris, France
The review involves clinical and experimental data, constitutive modeling, and computational investigations towards an understanding on how mechanical cyclic loads for long periods of time affect damage evolution in a reconstructed bone, as well as, lifetime reduction of bone graft substitutes after advanced core decompression. The outcome of the integrated model discussed in this paper will be how damage growth in femur after advanced core decompression subjected to mechanical cyclic loading under creep and fatigue conditions may be controlled in order to optimize design and processing of bone graft substitutes, and extend lifetime of bone substitutes.
KEY WORDS: advanced core decompression, bone graft substitute, damage, stress, creep, fatigue
ДОВГОСТРОКОВА ЕВОЛЮЦ1Я РЕКОНСТРУКЦП К1СТОК ЗА ДОПОМОГОЮ К1СТКОВИХ
ЗАМ1ННИК1В - МПЛАНТАНТ1В
Мартиненко О. В.1, Золочевський О. О.2, Аллена Р.3
1 Харювський нацюнальний ушверситет iMeHi В. Н. Каразша, м. Харюв, Украша
2 Нацюнальний техшчний ушверситет «Харювський полггехшчний шститут», м. Харюв, Украша
3 Паризький шститут наук та технологш, м. Париж, Франщя
Даний огляд включае клшчш та експериментальш дат, визначальнi сшввщношення, та обчислювальш дослщження, спрямованi на розумшня того як механiчнi циклiчнi навантаження протягом тривалих перiодiв часу впливають на зростання пошкоджуваностi i скорочення довговiчностi iмплантатiв, що використовуються для компресшного замiщення дефекту кiстки. У результат моделювання, розглянутого в цш статп, буде встановлено як зростання пошкоджуваносп протягом механiчних циклiчних навантажень в умовах повзучост та втоми iмплантатiв пiсля компресiйного замiщення дефекту стегново! кiстки можна контролювати з метою оптимiзацil проектування та виготовлення юсткових замiнникiв- iмплантатiв i збшьшення термiну служби кiсткових замiнникiв.
КЛЮЧОВ1 СЛОВА: компресшне замiщення дефекту юстки, кiстковий замiнник- iмплантат, пошкоджувашсть, напруга, повзучють, втома
ДОЛГОСРОЧНАЯ ЭВОЛЮЦИЯ РЕКОНСТРУКЦИИ КОСТЕЙ С ПОМОЩЬЮ КОСТНЫХ
ЗАМЕНИТЕЛЕЙ - ИМПЛАНТАНТОВ
Мартыненко А. В.1, Золочевский А. А.2, Аллена Р.3
1 Харьковский национальный университет имени В. Н. Каразина, г. Харьков, Украина
2 Национальный технический университет «Харьковский политехнический институт», г. Харьков,
Украина
3 Парижский институт наук и технологий, г. Париж, Франция
Данный обзор включает клинические и экспериментальные данные, определяющие соотношения, и вычислительные исследования, направленные на понимание того как механические циклические нагрузки в течение длительных периодов времени влияют на рост повреждаемости и сокращение
© Martynenko O. V., Zolochevsky O. O., Allena R., 2Ü17
долговечности имплантатов, используемых для компрессионного замещения дефекта кости. В результате моделирования, рассматриваемого в этой статье, будет установлено как рост повреждаемости вследствие механических циклических нагрузок в условиях ползучести и усталости имплантатов после компрессионного замещения дефекта бедренной кости можно контролировать с целью оптимизации проектирования и изготовления костных заменителей - имплантатов и увеличения срока службы костных заменителей.
КЛЮЧЕВЫЕ СЛОВА: компрессионное замещение дефекта кости, костный заменитель-имплантат, повреждаемость, напряжение, ползучесть, усталость
INTRODUCTION
Every year, over two million people worldwide sustain a bone grafting procedure to repair bone defects stemming from a disease or a traumatic event [1].
Core decompression represents an established technique for treatment of early stage osteonecrosis and most commonly used for disease that affects the hip joint. The procedure is designed to decrease pressure within the bone by restoring blood flow to the bone. For the first time, this procedure was popularized by Ficat and Arlet [2] in France in 1980. At present, this technique is one of the most commonly used surgical treatment options.
Core decompression consists of drilling one or more small channels with an 8-10 mm diameter into the necrotic lesion (dead bone) from the lateral subtrochanteric region of femur
to remove an 8-10 mm core from the femoral head [3]. This is associated with a lack of structural support of the bone. Subtrochanteric stress fractures at the surgical entrance point of the core track were regularly described as a complication of conventional core decompression with a rate of about 1 -2 % or even higher fracture rate [4]. That is why patients normally are requested to be partial weight bearing for several, normally six weeks due to the risk of fracture.
The so-called advanced core decompression is a modified technique of core decompression that may allow better removal of the necrotic tissue by using a new percutaneous expandable reamer, and refilling of the drill hole and the defect with the implantation of a bone graft substitute (Fig. 1) [3-4]. Such technique gives the possibility to reduce the risk of fracture after surgery.
Fig. 1. A proximal femur with the drilling canal and the bone defect filled by a bone graft substitute [4]
Practical recommendations related to the advanced core decompression are mainly based on clinical experience. So there is a need for rigorous studies to determine specific indications for this kind of treatment.
The finite element method has recently become a powerful technique for numerical simulation in the mechanics of femur. A three-dimensional finite element model derived from the reconstruction of core decompression or magnetic resonance (tomographic) images may help to effectively simulate the influences of core decompression on the mechanical behavior of femur.
The finite element studies concerning the advanced core decompression are given in [4]. The impact of the core decompression procedure and the surgical entrance point position on the stress distribution as well as on the fracture risk of the femur has been investigated. The effect of bone substitute stiffness on the biomechanical behavior of femoral bone after core decompression has been studied. Numerical results led to the conclusion that the success of advanced core decompression depends on the amount of necrotic tissue remaining in the femoral head after the procedure. Thus, modifications to the instrument are necessary to increase the amount of necrotic tissue that can be removed. Note also that all these studies are based on the linear elastic behavior of the femur and bone graft substitutes.
Different bone graft substitutes concerning the advanced core decompression have been used, such as a composite calcium sulphate (Ca S O4) - calcium phosphate (Ca P O4), tantalum or low-stiffness implants. The efficiency of these materials is still debated. One of alternative treatments is to use bioresorbable bone graft substitutes [1]. In this regard, the gradient elasticity theory was applied to study the effect of microstructure on remodeling of bones reconstructed with
have been considered.
Although the short term performance of femur after advanced core decompression is impressive, the long term performance is still unknown. Systematical studies related to the analyze the long term success and the long term risk of failure of bone graft substitute inside a
femoral head after advanced core decompression have not been published so far.
The understanding of bone behaviors and functioning is a key in the ability to predict their evolutions and be able to make adequate diagnostics, surgeries and planning, and predict postoperation states [6].
Biomechanical degradation of femur after advanced core decompression can be related to the load and time dependent phenomena, such as damage, creep and fatigue. These phenomena in bone can be investigated experimentally.
OBJECTIVE
The specific objectives are: to specify the mechanisms of biomechanical degradation of femur after advanced core decompression subjected to mechanical cyclic loading; to develop the constitutive laws of biomechanical behavior and kinetic equations of damage (stiffness reduction, creep, fatigue) in femur after advanced core decompression considering the interaction between osteoblasts and osteoclasts combined with the mechanical response of bone, and taking into account nonlinear elastic deformation and creep under mechanical cyclic loading conditions, fatigue and ratcheting, receiving and healing damage, damage interactions between tension and compression; to identify biomechanical parameters in the proposed bone remodeling model using different experimental data for bone, bone graft substitutes and femur after advanced core decompression; to incorporate an integrated biomechanical constitutive model developed in this research into the ANSYS codes in a form of the computer-based structural modeling tool for analyzing bone density distributions over time, as well as, stress distributions over time in femur after advanced core decompression, for damage analysis and for lifetime predictions of bone graft substitutes; to calculate the time-dependent bone density distribution and time-dependent multiaxial stress distribution (finite element modeling, cell population dynamics, structural mechanics), and changes in damage at a discrete site of bone remodeling (continuum damage mechanics) in femur after advanced core decompression subjected to mechanical cyclic loading as a function of femur parameters, bone graft parameters, as well as, loading conditions, and additionally to predict the lifetime of bone graft substitutes; to find the relationship between bone cell architecture,
bone graft substitute, biological environment, loading conditions and degradation of femur over time after advanced core decompression (combination of 2, 3, 4 and 5); to compare the lifetime predictions obtained in this research against clinical and experimental data available for femur after core decompression in combination with bone substitutes.
MATERIALS AND METHODS
Bone damage. Mechanically, bone behaves identically to any other material in that it undergoes deformation and damage when subject to an external load. Bone sustains millions of loading cycles over the course of a
lifetime and rarely breaks without a major traumatic event, and, thus, damage in bone is a naturally occurring event [7]. Damage is not detectable using clinical imaging modalities, but decreases bone's stiffness, strength, and toughness and eventually leads to collapse of whole bones [8].
There are three distinct varieties of damage in bone (Table 1), which can be identified as linear microcracks, diffuse microdamage, and microfractures. These types are distinguished by the way they form and their morphology; the nature of the stimuli that cause them to form, as well as, their location; and the manner in which they are repaired [7].
Table 1
Types of damage and their characteristics [7]
Shuptf Slifit TJviw hAnhat Ap; Hi-pviir
I}Jmtn.vl<№ mode pnipurlii^ lirt-jlioti
l.]iii:3r milnicrjk:l..> hhijhicid t 'nmpri^myi; m<xr-t: hrrfllk itiIlvxliIijI okiçr kl'iikkil'i inf
_-BO n I KJOft|xm_
Diffuse Mknxiamiigf X]№|knWidl Tensile Mure ductile Willi in initxvMLar Younfer Remodeling1
_Urttn-OETI kH.Ultl_piukfth JIKl ratLPUri_
MicroTnwturei Complete frutlure Bcndinj^blieiir Off-usit Trabecuîar Oklcr Endochondral
rriLllE^I II in uul HL'J[|I in
Obviously that diffuse microdamage means microcracks on a lower length scale. Microcracks appear linear and spatially organized in 2D histological sections with a pertinent length of 10-70 ^m [8]. In 3D, microcracks appear in approximately elliptical shape with an aspect ratio of 4:1 to 5:1. In histology studies, tensile microdamage appears to be more diffuse while compressive damage is rather expressed as linear microcrack. Thus, different damage development in tension and compression is a characteristic feature of bone.
Microfractures, on the other hand, are entirely different than the other forms of damage. Microfractures occur within cancellous bone and represent complete fractures of one or more trabeculae [7].
Also, damage interactions between tension and compression in bone have been considered [8-11].The mechanisms how bone damage is accumulated under different loading modes and coupled into another loading mode have been discussed. Impact of damage interactions on bone strength has been analyzed.
Damage reduces the bone's future capacity to absorb energy prior to fracture, and in this sense deteriorates the mechanical properties of
bone. However, the paradox of this is that the initiation and growth of microcracks in itself dissipates energy and delays a catastrophic complete fracture from occurring [7]. This presumes that the damage will be repaired in an efficient manner, before significantly more damage can be created [12]. This requires a signaling mechanism, and suggests a physiological role, not just a mechanical one, for bone damage [7, 13].
Creep. The consideration of the linear elastic deformation of femur after advanced core decompression is quite important in the structural analysis. However, this is not enough in order to understand the mechanisms of degradation of femur over time that affect essentially the lifetime reduction of bone graft substitute inside a femoral head.
It is known [14] that bones exhibit creep deformation considered as a time dependent irreversible deformation process. Both the tensile and compressive creep behaviors of cortical bone and trabecular bone are well documented [15-19]. They are characterized by creep strain versus time curves that have three distinct regimes (Fig. 2) (primary, secondary and tertiary) by analogy with the engineering
materials (steels, cast irons, light alloys) at high temperatures.
Fig. 2. Typical creep curve for trabecular bone with a time to failure of 25.5 h and a failure strain of 2.5 % [15]
Creep deformation changes the microstructure of bone by introducing microcracks (creep damage) in the final stage of the creep process. Furthermore, the velocity of the growth of already existing microcracks and of the nucleation of new ones essentially depends on the intensity of creep deformation. On the other hand, creep deformation of bone is influenced by the growth of microcracks. This influence begins at the primary and secondary stages of the creep process, and can be visible in the tertiary stage due to increase of the creep strain rate, preceding the creep rupture. The
creep rupture case without increase in the creep strain rate can also be observed in bone. Thus, creep deformation and growth of creep damage in bone occur parallel to each other, and they have a reciprocal effect.
Figure 3 shows stress versus time to failure data in bone for tensile and compressive loading types under creep conditions. All specimens are normalized with Young's modulus. The experimental data are linear on a log-log plot which is similar to power law known for other materials.
FAILURE tseecnds) Fig. 3. Experimental creep ruptures data on human femoral cortical bone [20]
Now, a number of comments need to be made. First, creep curves obtained in bone from uniaxial tests under tensile and compressive loading types for one and the same absolute value of constant stress are essentially different and depend on the sign of the stress. This difference can be very large in the tertiary creep state due to the different creep damage growth in tension and compression. Thus, it is necessary to take into account the tension/ compression creep asymmetry of femur after advanced core decompression subjected to mechanical cyclic loading. Second, the creep and creep damage parameters of femur in the constitutive model should be a function of the bone density. Third, creep of composite calcium
sulphate (Ca S O4) - calcium phosphate (Ca P O4) has been studied in [21].
Fatigue and ratcheting. Among various loading, cyclic loading (including axial, torsional and multiaxial load) plays an important role to damage bone [22]. Damage accumulation under cyclic loading is a major factor of failure in implants.
Fatigue data are extensively reported [2225] for trabecular part and cortical part of bone. Also, it is found [26] the stiffness loss related to the damage growth in bone (Fig. 4) under cyclic loading. It is seen that stiffness loss under fatigue conditions is dependent on the type of loading.
Fig. 4. Average stiffness loss profiles for specimens subjected to Zero-Tension (0T), Zero-Compression (0C) and zero-Torsion (0T) loading [26]
Fatigue damage in bone was identified as diffuse damage and linear microcracks using histological analysis [26]. Mode I fracture creates and propagates microcracks in the transverse direction for specimens subjected to Zero-Tension loading (Fig. 5). In contrast, the compressive group displayed Mode II cracking when crack surfaces slide over one another; damage is on a single plane (Fig. 5). Thus, there are differences in the kind of damage associated with fatigue in tension and compression.
Mode III fracture (Fig. 5) for specimens subjected to Zero-Torsion loading is similar to a tearing motion where the crack surfaces move relative to each other on multiple planes .
The fatigue life data for human femoral cortical bone [20] are presented in Fig. 6.
Fatigue tests in specimens subjected to Zero-Tension and Zero-Compression loading were conducted at the two load frequencies (2 and 0.02 Hz). It is seen (Fig. 6) that fatigue lives of bone are longer in compression than in tension.
A comparison of the fatigue behavior of human trabecular and cortical bone tissue [24] was conducted under cyclic four-point bending (Fig. 7). The results show that trabecular specimens have significantly lower fatigue strength than cortical specimens, despite their higher mineral density values. Thus, the parameters of femur in the kinetic equation of fatigue damage should be a function of the bone density.
__-J
Fig. 5. Schematic representation of microcrack development in specimens subjected to Zero-Tension (Mode I) (a), Zero-Compression (Mode II) (b) and Zero-Torsion (Modes II and III) (c) loading [26]
Fig. 6. Tensile (O-T) and compressive (O-C) cyclic loading data plotted as normalized stress versus cycles to failure [20]
Fig. 7. Median S-N curves for each specimen group. The numbers on arrows indicate the number of run-out specimens for given stress levels [24]
Analysis of permanent strain during tensile fatigue of cortical bone (Fig. 8) shows that ratcheting occurs in cortical bone due to the
cyclic softening of bone. Hence, ratcheting is considered as an irreversible deformation process dependent on the number of cycles.
Fig. 8. Ratcheting strain in cortical bone as a function of the number of cycles for different levels of maximum stress [27]
Also, ratcheting was observed experimentally in trabecular bone for specimens subjected to Zero-Compression loading [28-30] and for samples subjected to a combination of
torsion and compression fatigue [31].
Systematic studies of ratcheting during tensile,
compressive, and shear fatigue of human
cortical bone were conducted in [32].
Cell population dynamics model. Long
term biomechanical adaptation is particularly significant to implant integration and stability in the postoperative state [33]. Wolff s law postulates [14] that bone can be remodeled based on the forces applied during its normal function, modifying its internal and external architecture and changing its shape and density. The remodeling phase of healing can continue for months or even years [34]. Biological cells continuously interact with and remodel the tissue in their immediate environment to establish a well-defined microstructural arrangement in healthy tissue. Local remodeling by cells becomes the crucial connecting point between the biological and mechanical fields [6, 34].
Various mathematical models of bone remodeling have been proposed in the literature [35]. In the present paper, the cell population dynamics model has been considered.
At the cellular scale, bone is composed of (i) bone matrix, infiltrated with minerals and with the osteocyte network; and (ii) vascular pores, containing soft tissues and cells [36]. Changes
in bone microstructure occur by dissolution of old bone matrix by bone-resorbing cells (osteoclasts) and deposition of new bone matrix by bone-forming cells (osteoblasts). The bone remodeling process is governed by the interactions between osteoblasts and osteoclasts through the expression of several autocrine and paracrine factors that control bone cell populations and their relative rate of differentiation and proliferation [37].
The variation in bone density p at the remodeling site is expressed in terms of percentage of the initial mass depending on the number of osteoclasts and osteoblasts [37]:
Here k1 and k2 are the normalized activities, XC and XB are, respectively, the numbers of actively resorbing osteoclasts and forming osteoblasts at a remodeling site defined by Komarova et al. [38]:
Xc-xc- Xc if xc > Xc
Xc = 0 if xc < xc
and
X& = Xp - XB if Xp > X[f
XR = 0 if xw 5 h
where xC and xB are, respectively, the number of osteoclasts and osteoblasts at steady state. The system of differential equations describing the osteoclast and osteoblast rates and interactions using parameters, which characterize the autocrine and paracrine factors, can be expressed by [37]:
where ai is the osteoclast production rate, Pi is osteoclast removal rate, a2 is the osteoblast production rate, p2 is the osteoclast removal rate. Parameter gii describes the combined effects of all the factors produced by osteoclasts that regulate osteoclast formation (osteoclast autocrine regulation). Parameter g22 describes the combined effects of all the factors produced by osteoblasts to regulate osteoblast formation (osteoblast autocrine regulation). Parameter gi2 describes the combined effects of all the factors produced by osteoclasts that regulate osteoblast formation, such as TGFp (osteoclast-derived paracrine regulation). Parameter g21 describes the combined effects of all the factors produced by osteoblasts that regulate osteoclast formation, such as OPG and RANKL (osteoblast-derived paracrine regulation). In this proposal, special attention is paid to the particular case, where a bone cell grows normally and only influences its neighbor's activity, but does not produce autocrine factors. Therefore, we can write [37].
SU =S22 =0
gU = Ai + Zi,f-ViS<*.'>
where A1, B1, A2, B2, y1, and y2 are model parameters that regulate the production of paracrine factors, S(x, t) denotes the mechanical stimulus function. The mechanical stimulus used here is expressed in terms of strain energy density.
The bone adaptation approach given above allows for the computation of changes in density of femur after advanced core decompression at a discrete site of bone remodeling at a macroscopic scale. In order to simulate the remodeling process from a mechanobiological point of view, this approach needs to be implemented, for example, into an
ANSYS code (considering bone density instead of temperature in the finite element model in Fig. 9).
Fig. 9. Finite element model of femur generated by ANSYS [4]
Structural mechanics model. The cell population dynamics model needs to be coupled to the structural mechanics model. Total strains in femur are assumed to be composed of nonlinear elastic part, part due to creep and ratcheting part accumulated during cycling loading.
The creep strain rates are related to the stresses under multiaxial loading as follows [39]:
de
kl
dt
(1 -í
3 As,
kl
v2 S
+ Cd
kl
(1),
where se = Asi + Cskdk
3
kPkl, s 2 sklskl , sklis
the stress deviator, skl is the stress tensor, t is time and A, C, n, m are material parameters. A continuum damage parameter by Kachanov-Rabotnov f has been introduced into the creep law given by Eq. (1) with the formulation of the following creep damage growth equation
df dt
Sk
(1 -f
(2),
where Se = A0ai + C0sklSkl, Aq, C0, k and l are material parameters. Equations (1) and (2) reflect the tension/compression asymmetry of creep and creep damage in femur.
c
n
a
e
m
Also, description of ratcheting and fatigue damage in femur is considered. The components of the ratcheting strain tensor can be defined as follows [39]:
ski --
(1 -j) f
3 OkkL 2 ti
+ cd
ki
(3),
where N is a number of
Te - ati + ctklÔkl,
"2 KklKkl
kis
cycles, the
stress amplitude deviator during cycling , rki is the tensor of the mean stresses during cycling, dot above the symbol denotes the derivative with respect to the number of cycles, and a, c, p, q and f are material parameters. Also, description of ratcheting and fatigue damage in femur is considered. The components of the ratcheting strain tensor can be defined as follows [39]:
ekl --
(1 -j)
f
3 akkl 2 ti
+ cd
kl
(3)
where pe = dtt + ezklSkl, d, e, x, b and v are material parameters. Equations (3) and (4) reflect the tension/compression asymmetry of ratcheting and fatigue damage in femur.
Note that material parameters in Eqs. (1)-(4) are functions of bone density and bone mineralization, and can be identified from the basic experiments under tension and compression [40].
Diffusion model to describe osteogenesis within a porous Ca P O4 scaffold needs to be considered. In this regard, the concentration of mesenchymal stem cells can be found using diffusion model developed in [41].
CONCLUSION
Analysis of bone density, stress and damage distributions over time in femur after advanced core decompression as well as lifetime prediction studies in this review are related to the consideration of the physically nonlinear initial/three-dimensional boundary value multiphysics problem. Therefore, commercial software package ANSYS needs to be used for structural analysis, computational modeling and simulation, when the integrated constitutive framework discussed in this paper will be implemented into its codes.
The lifetime predictions obtained in this research need to be compared against clinical and experimental data available for femur after core decompression in combination with bone substitutes.
The outcome will be how damage growth in femur after advanced core decompression subjected to mechanical cyclic loading under creep and fatigue conditions may be controlled in order to optimize design and processing of bone graft substitutes, and extend lifetime of bone substitutes.
PROSPECTS FOR FUTURE STUDIES
The new knowledge obtained in this research needs to be transferred to research communities related to advanced core decompression. Also, the young professionals training needs to be provided at the Arts et Métiers ParisTech, France, and at the V. N. Karazin Kharkiv National University, Ukraine, on how to use the computer-based structural modeling tool developed in this research.
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