Kaushik Mukherjee | Indian Institute of Technology Delhi (original) (raw)

Papers by Kaushik Mukherjee

The importance of clinical studies notwithstanding, the failure assessment of implant–bone struct... more The importance of clinical studies notwithstanding, the failure assessment of implant–bone structure has alternatively been carried out using finite element analysis. However, the accuracy of the finite element predicted results is dependent on the applied loading and boundary conditions. Nevertheless, most finite element–based evaluations on acetabular component used a few selective load cases instead of the eight load cases representing the entire gait cycle. These in silico evaluations often suffer from limitations regarding the use of simplified musculoskeletal loading regimes. This study attempts to analyse the influence of three different loading regimes representing a gait cycle, on numerical evaluations of acetabular component. Patient-specific computer tomography scan-based models of intact and resurfaced pelvises were used. One such loading regime consisted of the second load case that corresponded to peak hip joint reaction force. Whereas the other loading regime consisted of the second and fifth load cases, which corresponded to peak hip joint reaction force and peak muscle forces, respectively. The third loading regime included all the eight load cases. Considerable deviations in peri-acetabular strains, standard error ranging between 115 and 400 µε, were observed for different loading regimes. The predicted bone strains were lower when selective loading regimes were used. Despite minor quantitative variations in bone density changes (less than 0.15 g cm−3), the final bone density pattern after bone remodelling was found to be similar for all the loading regimes. Underestimations in implant–bone micromotions (40–50 µm) were observed for selective loading regimes after bone remodelling. However, at immediate post-operative condition, such underestimations were found to be less (less than 5 µm). The predicted results highlight the importance of inclusion of eight load cases representing the gait cycle for in silico evaluations of resurfaced pelvis.

The 3D microscale implant-bone interface model, comprising of Porocast Bead of BHR implant, granulation tissue and bone, was developed and meshed in ANSYS (Fig. 1b). Frictional contact (µ=0.5) was simulated at all interfaces. The displacement fields were transferred and prescribed at the top and bottom boundaries of the microscale model from a previously investigated macroscale implanted pelvis model (Fig. 1a) [4]. Periodic boundary conditions were imposed on the lateral surfaces. Linear elastic, isotropic material properties were assumed for all materials. Young's modulus and Poisson's ratios of bone and implant were mapped from the macroscale implanted pelvis [4]. A cell-phenotype specific mechanoregulatory algorithm was developed where various cellular activities and tissue formation were modeled with seven coupled differential equations [1, 2]. In order to evaluate the influence of various cellular activities, a Plackett-Burman DOE scheme was adopted. In the present study each of the cellular activity was assumed to be an independent factor. A total of 20 independent two-level factors were considered in this study which resulted in altogether 24 different combinations to be investigated. All these cellular activities were in turn assumed to be regulated by local mechanical stimulus [3]. The mechano-biological simulation was run until a convergence in tissue formation was attained.

The cell-phenotype specific algorithm predicted a progressive transformation of granulation tissue into bone, cartilage and fibrous tissue (Fig. 1c). Various cellular activities were found to influence the time to reach equilibrium in tissue differentiation and, thereby, attainment of sufficient implant fixation (Fig. 2, Table 1). Negative regression coefficients were predicted for the significant factors, differentiation rate of MSCs and bone matrix formation rate, indicating that these cellular activities favor peri-prosthetic bone ingrowth by facilitating rapid peri-prosthetic bone ingrowth. Osteoblast differentiation rate, on the contrary, was found to have the highest positive regression coefficient among the other cellular activities, indicating that an increase in this cellular activity delays the attainment of equilibrium in bone ingrowth prohibiting rapid implant fixation.

Implant-induced bone remodeling has been identified as a potential reason behind aseptic loosenin... more Implant-induced bone remodeling has been identified as a potential reason behind aseptic loosening of uncemented acetabular cups. Using three-dimensional Finite Element models of intact and implanted pelvis, in combination with bone remodeling algorithm, the present study aims at gaining an insight into the evolutionary bone adaptation around a press-fit uncemented acetabular component. Eight static load
cases of normal walking cycle, modeled by 21 muscle forces and hip joint reaction force, were considered in the present study in order to investigate deviation in load transfer due to implantation and peri-acetabular bone adaptation. Based on the results of the present study, a press-fit acetabular component was found to increase load transfer through acetabular cortex. Consequently, predominant bone apposition was observed within the acetabular peripheral cancellous bone. However, a reduction in the density of cancellous bone near the acetabular pole was also observed.

Several mechanobiology algorithms have been employed to simulate bone ingrowth around porous coat... more Several mechanobiology algorithms have been employed to simulate bone ingrowth around porous coated implants. However, there is a scarcity of quantitative comparison between the efficacies of commonly used mechanoregulatory algorithms. The objectives of this study are: (1) to predict peri-acetabular bone ingrowth using cell-phenotype specific algorithm and to compare these predictions with those obtained using phenomenological algorithm and (2) to investigate the influences of cellular parameters on bone ingrowth. The variation in host bone material property and interfacial micromotion of the implanted pelvis were mapped onto the microscale model of implant–bone interface. An overall variation of 17–88 % in peri-acetabular bone ingrowth was observed. Despite differences in predicted tissue differentiation patterns during the initial period, both the algorithms predicted similar spatial distribution of neo-tissue layer, after attainment of equilibrium. Results indicated that phenomenological algorithm, being computationally faster than the cell-phenotype specific algorithm, might be used to predict peri-prosthetic bone ingrowth. The cell-phenotype specific algorithm, however, was found to be useful in numerically investigating the influence of alterations in cellular activities on bone ingrowth, owing to biologically related factors. Amongst the host of cellular activities, matrix production rate of bone tissue was found to have predominant influence on peri-acetabular bone ingrowth.

Fixation of uncemented implant is influenced by peri-prosthetic bone ingrowth, which is dependent... more Fixation of uncemented implant is influenced by peri-prosthetic bone ingrowth, which is dependent on the mechanical environment in the implant-bone structure. The objective of the study is to gain an insight into the tissue differentiation around an acetabular component. A mapping framework has been developed to simulate appropriate mechanical environment in the three-dimensional microscale model, implement the mechanoregulatory tissue differentiation algorithm and subsequently assess spatial distribution of bone ingrowth around an acetabular component, quantitatively. The FE model of implanted pelvis subjected to eight static load cases during a normal walking cycle was first solved. Thereafter, a mapping algorithm has been employed to include the variations in implant-bone relative displacement and host bone material properties from the macroscale FE model of implanted pelvis to the microscale FE model of the beaded implant-bone interface. The evolutionary tissue differentiation was observed in each of the 13 microscale models corresponding to 13 acetabular regions. The total implant-bone relative displacements, averaged over each region of the acetabulum, were found to vary between 10 and 60μm. Both the linear elastic and biphasic poroelastic models predicted similar mechanoregulatory peri-prosthetic tissue differentiation. Considerable variations in bone ingrowth (13 – 88%), interdigitation depth (0.2 – 0.82mm) and average tissue Young’s modulus (970 – 3430MPa) were predicted around the acetabular cup. A gradual increase in the average Young’s modulus, interdigitation depth and decrease in average radial strains of newly formed tissue layer were also observed. This scheme can be extended to investigate tissue differentiation for different surface texture designs on the implants.

Peri-acetabular bone ingrowth plays a crucial role in long-term stability of press-fit acetabular... more Peri-acetabular bone ingrowth plays a crucial role in long-term stability of press-fit acetabular
cups. A poor bone ingrowth often results in increased cup migration, leading to aseptic loosening of the
implant. The rate of peri-prosthetic bone formation is also affected by the polar gap that may be introduced
during implantation. Applying a mechano-regulatory tissue differentiation algorithm on a two-dimensional
plane strain microscale model, representing implant-bone interface, the objectives of the study are to gain an
insight into the process of peri-prosthetic tissue differentiation and to investigate its relationship with
implant-bone relative displacement and size of the polar gap. Implant-bone relative displacement was found
to have a considerable influence on bone healing and peri-acetabular bone ingrowth. An increase in implantbone
relative displacement from 20 µm to 100 µm resulted in an increase in fibrous tissue formation from
22% to 60% and reduction in bone formation from 70% to 38% within the polar gap. The increase in fibrous
tissue formation and subsequent decrease in bone formation leads to weakening of the implant-bone
interface strength. In comparison, the effect of polar gap on bone healing and peri-acetabular bone ingrowth
was less pronounced. Polar gap up to 5 mm was found to be progressively filled with bone under favourable
implant-bone relative displacements of 20 µm along tangential and 20 µm along normal directions.
However, the average Young’s modulus of the newly formed tissue layer reduced from 2200 MPa to 1200
MPa with an increase in polar gap from 0.5 mm to 5 mm, suggesting the formation of a low strength tissue
for increased polar gap. Based on this study, it may be concluded that a polar gap less than 0.5 mm seems
favourable for an increase in strength of the implant-bone interface.

7th World Congress of Biomechanics

Peri-prosthetic bone ingrowth influences the long-term fixation and stability of uncemented aceta... more Peri-prosthetic bone ingrowth influences the long-term fixation and stability of uncemented acetabular implant. The objective of the study is to develop a three-dimensional (3-D) microscale FE model representing an implant-bone interface and to investigate the effects of implant-bone relative displacements and interface conditions on peri-prosthetic bone ingrowth using a mechano-regulatory algorithm. A 3-D microscale model of implant-bone interface, representing Porocast Bead of BHR implant, granulation tissue and bone, was developed and meshed in ANSYS (Fig. 1a). Both debonded (with friction coefficient μ=0.5) and bonded interfaces were taken into consideration. Three different levels of displacement fields at the top and bottom boundary of the microscale model were transferred and prescribed from a previously investigated macroscale implanted pelvis model [1]. Periodic boundary conditions were imposed on the lateral surfaces. Linear elastic, homogeneous isotropic material properties were assumed for all materials. Young’s modulus and Poisson’s ratios of bone and implant were mapped from the macroscale implanted pelvis. Tissue differentiation within the granulation tissue was modeled using a sequential, mechano-regulatory algorithm. Depending upon the local mechanical stimulus, comprising of hydrostatic pressure and deviatoric strain, the migrated and proliferated mesenchymal stem cells differentiate into different connective tissue phenotypes. The mechano-biological simulation was run for a post-operative period of two years. Results predicted progressive transformation of granulation tissue into bone, cartilage and fibrous tissue (Fig. 1b). The debonded interface model with higher implant-bone relative displacement predicted ~40% bone formation in inter-bead spacing, which is similar to earlier clinical investigations. An increase in the overall bone ingrowth for all interface conditions was also observed with a reduction in implant-bone relative displacement, which was similar to earlier 2-D FE predictions with debonded interface. However, bonded interface condition was found to predict quantitatively lower bone formation as compared to the debonded interface. The progressive increase in stiffness of the newly formed peri-prosthetic tissue layer was found to follow the characteristic S-shape. The 3-D FE microscale model of implant-bone interface is useful to gain an insight in the peri-prosthetic bone formation. Both debonded and bonded interface conditions predicted reduction in bone formation with an increase in implant-bone relative displacement.

12th International Symposium on Computer Methods in Biomechanics and Biomedical Engineering

Long-term biological fixation and stability of uncemented acetabular implant are influenced by pe... more Long-term biological fixation and stability of uncemented acetabular implant are influenced by peri-prosthetic
bone ingrowth which is known to follow the principle of mechanoregulatory fracture healing. Over the last two
decades, several algorithms, broadly classified as cell-phenotype specific [1,2] and phenomenological [3], have
been developed to quantitatively assess the tissue formation in the fracture callus. However, the efficacy of these
algorithms to predict bone ingrowth, with regard to evolutionary mechanical properties of the implant-bone
interfacial layer, is yet to be investigated. Using a three-dimensional (3D) microscale FE model representing an
implant-bone interface, the objective of the study is to quantitatively compare the cell-phenotype specific and
phenomenological mechanoregulatory algorithms for different implant-bone relative displacements.
The 3D microscale implant-bone interface model, comprising of Porocast Bead of BHR implant, granulation
tissue and bone, was developed and meshed in ANSYS (Fig. 1b). Frictional contact (μ=0.5) was simulated at all
interfaces. Three different levels of displacement fields, at the top and bottom boundaries of the microscale
model, were transferred and prescribed from a previously investigated macroscale implanted pelvis model (Fig.
1a) [4]. Periodic boundary conditions were imposed on the lateral surfaces. Linear elastic, isotropic material
properties were assumed for all materials. Young’s modulus and Poisson’s ratios of bone and implant were
mapped from the macroscale implanted pelvis [4]. Two sequential mechanoregulatory tissue differentiation
algorithms, cell-phenotype specific ([1, 2] and phenomenological [3], were developed in order to model the
tissue formation within the interbead spaces. In cell-phenotype specific algorithm (, various cellular activities
and tissue formation were modeled with seven coupled differential equations [1, 2]. However, in
phenomenological algorithm [3], all the cellular activities and tissue formation were indirectly combined and
modeled using a single diffusion equation. Both the algorithms assumed various cellular activities to be
regulated by local mechanical stimulus. The mechano-biological simulation was run for a post-operative period
of two years.
Both the algorithms predicted progressive transformation of granulation tissue into bone, cartilage and fibrous
tissue (Fig. 1c). However, bone formation and average tissue stiffness predicted by cell-phenotype specific
algorithm were found to be 2 – 5% lower than those predicted by phenomenological algorithm. The
phenomenological algorithm with higher implant-bone relative displacement predicted ~40% bone formation in
inter-bead spacing, which is similar to earlier clinical investigations. Both the algorithms predicted an increase in
the overall bone ingrowth with a reduction in implant-bone relative displacement. The progressive increase in
stiffness of the newly formed peri-prosthetic tissue layer was found to follow the characteristic S-shape.
The phenomenological algorithm, being less computationally expensive, was found to be an effective predictor
to quantitatively assess peri-prosthetic tissue formation and evolutionary tissue stiffness as compared to cellphenotype
specific algorithm.
[1] Andreykiv et al., Biomech Model Mechanobiol,7,443–461.
[2] Isaksson et al., JTheor Biol,252,230–246.
[3] Claes and Heigele, JBiomech,32,255–266.
[4] Ghosh et al.,Proc Inst MechEng H,227, 490–502.

Stress shielding–induced bone resorption around cementless acetabular components has been indicat... more Stress shielding–induced bone resorption around cementless acetabular components has been indicated as a potential failure mechanism that may threaten long-term fixation. Using a bone remodelling algorithm in combination with three-dimensional finite element models of intact and implanted pelvises and musculoskeletal loading during normal walking, the objectives of the study were to investigate the deviations in load transfer due to implantation and bone adaptation around cementless metallic and ceramic acetabular components. Variations in implant–bone interfacial condition affected strain shielding and bone remodelling; strain shielding was higher for the bonded condition as compared to the debonded condition. For bonded interfacial condition, severe bone resorption, 20%–50% bone density reduction, was observed within the acetabulum. Considering debonded implant–bone interface, bone density increase of 50%–60% was observed around the supero-posterior part of acetabulum, whereas bone density reductions were low (2%–15%) in other locations. The implant–bone interface appeared less likely to fail, post-operatively and after bone remodelling. Moreover, the implant–bone micromotion was found to be low, less than 100 µm. Strain shielding and bone remodelling were almost similar for the metallic and ceramic components. Based on the results of this study, the ceramic acetabular component appeared to be a viable alternative to metal.

Short-stem resurfaced femoral implant has been found to be a promising alternative to the long-st... more Short-stem resurfaced femoral implant has been found to be a promising alternative to the long-stem design,
due to reduced risk of initial femoral neck fracture and more physiological load transfer. The clinical effect
of metal ion release and continued concerns regarding the use of Metal-on-Metal bearing warrants an
investigation of an alternative material, like ceramics, as a low-wear bearing couple. The objective of this
study was to investigate the effect of a short-stem ceramic resurfacing implant, in comparison with the
metallic design, with regard to stress-strain related failure mechanisms and bone adaptation. The maximum
principal (tensile) stress in the ceramic implant, occurring at the stem-cup junction, was found to increase
from 73 MPa at the post-operative condition to 86 MPa after bone remodelling. However, the tensile
stresses generated in the cement mantle were low, around 3 MPa. The elevated bone strains occurring at
the proximal femoral neck-cup junction region were progressively reduced with bone remodelling. Bone
density distribution inside the femoral head was found to be similar to those for the metallic short-stem
design. Although bone resorption, 50 − 90% reduction in bone density was predominantly observed at the
supero-proximal femoral head, bone apposition, 10 – 30% increase in bone density occurred in the other
regions of the femoral head. Apart from better wear resistivity and chemically inert nature of ceramics, it
appears from this study that alumina ceramic is a viable alternative to the metallic design.

Despite the generally inferior clinical performance of acetabular prostheses as compared to the ... more Despite the generally inferior clinical performance of acetabular prostheses as compared
to the femoral implants, the causes of acetabular component loosening and the extent to
which mechanical factors play a role in the failure mechanism are not clearly understood
yet. The study was aimed at investigating the load transfer and bone remodelling around
the uncemented acetabular prosthesis.
The 3-D FE model of a natural right hemi-pelvis was developed using CT-scan data. The
same bone was implanted with two uncemented hemispherical acetabular components,
one metallic (CoCrMo alloy) and the other ceramic (Biolox delta), with 54 mm outer
diameter and 48 mm bearing diameter. The FE models of the implanted pelvis
(containing ~116000 quadratic tetrahedrals) were generated using a submodelling
approach, which were based on an overall full model of implanted pelvis (containing
~217600 quadratic tetrahedrals) acted upon by hip joint force and twenty one muscle
forces. The apparent density (ρ in g cm-3) of each cancellous bone element was calculated
using linear calibration of CT numbers of bone, from which the Young’s modulus (E in
MPa) was determined using the relationship, E = 2017.3 ρ2.46 [1].
Implant-bone interface
conditions, fully bonded and debonded with friction coefficient μ = 0.5, were simulated
using contact elements. Applied loading conditions consist of two load cases during a gait
cycle, corresponding to 13% and 52% of the walking cycle. Fixed constraints were
prescribed at the pubis and at the sacroiliac joint. The bone remodelling algorithm was
based on strain energy based site-specific formulation [2]. The FE analysis, in
combination with the bone remodelling simulation, was performed using ANSYS FE
software.
The predicted changes in peri-prosthetic bone density were similar for the metallic and
the ceramic implant. For debonded implant-bone interface, stress shielding led to ~20%
reductions in bone density at supero-anterior, infero-anterior and posterior part of the
acetabulum (Fig. 1). However, bone apposition was observed at the supero-posterior part
of the acetabulum, where implantation led to ~60% increase in bone density (Fig. 1). The
effect of bone resorption was higher for the fully bonded implant-bone interface, wherein
bone density reductions of 20 – 50% were observed in the cancellous bone underlying the
implant (Fig. 1), which is indicative of implant loosening over time. However,
implantation led to an increase in bone density around the acetabular rim for both the
interface conditions (Fig. 1). These results are well corroborated by the earlier studies
[3,4]. Implantation with a ceramic component resulted in 2 – 7% increase in bone density
at supero-posterior part of the acetabulum as compared to the metallic component, for the
debonded interface condition. Considering better wear resistant properties and absence of
metal ion release, results of this study suggest that the ceramic component might be a
viable alternative to the metallic prosthesis.

"The effects of metal ion release and wear particle debris in metal-on-metal articulation warran... more "The effects of metal ion release and wear particle debris in metal-on-metal articulation
warrants an investigation of alternative material, like ceramics, as a low-wear bearing
couple [1]. Short-stem resurfacing femoral implant, with a stem-tip located at the centre
of the femoral head, appears to provide a better physiological load transfer within the
femoral head and therefore seems to be a promising alternative to the long-stem design
[2]. The objective of this study was to investigate the effect of evolutionary bone
adaptation on load transfer and interfacial failure in cemented metallic and ceramic
resurfacing implant.
Bone geometry and material properties of 3D finite element (FE) models (intact, shortstem
metallic and ceramic resurfaced femurs of 44 mm head diameter) were derived from
the CT scan data. The FE models consisted of 170352 quadratic tetrahedral elements and
238111 nodes with frictional contact at the implant-cement (μ = 0.3) and stem-bone
interfaces (μ = 0.4) and fully bonded cement-bone interface. Normal walking and stair
climbing were considered as two different loading conditions. A time-dependant “site
specific” bone remodelling simulation was based on the strain energy density and internal
free surface area of bone [3]. The variable time-step was determined after each
remodelling iteration. The Hoffman failure criterion was used to assess cement-bone
interfacial failure.
Predicted change in bone density due to bone remodelling was very much similar in both
the metallic and ceramic resurfaced femurs (Fig. 1). Both the metallic and ceramic
implant resulted in strain reduction in the proximal regions (Region of interest, ROI 2 and
4) and subsequent bone resorption, average bone density reduction by 72% (Fig. 1).
Higher strains were generated in ROI 5 and 7, which caused bone apposition, an average
increase in bone density of 145% (Fig. 1). The tensile stresses in the resurfacing implants
increased with change in bone density; a maximum stress of 83 MPa and 63 MPa were
observed in the ceramic and the metallic implants, respectively. The tensile stress in the
cement mantle also increased with bone remodelling. Although the cement-bone interface
was secure against interface debonding in the post-operative situation, calculations of
Hoffman number indicated that risk of cement-bone interfacial failure was increased with
peri-prosthetic bone adaptation.
During the remodelling simulation, maximum tensile stress in the implant and the cement
was far below its strength. However, with bone adaptation greater volume of cement
mantle was exposed to higher stresses which, in-turn, resulted in greater risk of interfacial
failure around the periphery of the cement mantle. Both the short-stem ceramic and
metallic resurfacing component, under debonded stem-bone interface, resulted in more
physiological stress distribution across the femoral head. Based on these results, shortstem
ceramic resurfacing component appears to be a viable alternative to the metallic
design."

7th World Congress of Biomechanics

12th International Symposium on Computer Methods in Biomechanics and Biomedical Engineering