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The impact of multi-objective numerical optimization in Biomedical Engineering: A gallery of industrial cases
L’innovazione nelle tecniche di simulazione numerica applicata a problemi biomedici è uno dei temi più attuali e complessi nel settore della sperimentazione virtuale. Le tematiche da affrontare sono molteplici e diverse, e gli obiettivi (e le sfide) particolarmente importanti ed ambiziosi.Un notevole contributo, sul piano metodologico, è dato dall’applicazione di tecniche di ottimizzazione, “design of experiments” e “robust design”. Se ne discute qui attraverso l’illustrazione di alcuni esempi tipici.
Una prima applicazione riguarda l’ottimizzazione di forma di un gruppo cuore-polmone artificiale, finalizzata ad incrementare le prestazioni del sistema in termini di scambi gassosi, migliorando, allo stesso tempo, la fluidodinamica interna, per prevenire la formazione di trombi. La sequenza di calcolo prevede il collegamento di un CAD parametrico con strumenti per la generazione automatica della griglia di calcolo, e, infine, con un solutore CFD. Questo processo è controllato e reso automatico da modeFRONTIER, utilizzando, per gli aspetti relativi all’ottimizzazione multi-obiettivo, un algoritmo genetico particolare, noto come MOGA-II. Il risultato è notevole, e dimostra la possibilità di seguire l’approccio multi-obiettivo anche in problemi che non possono essere semplificati a monte.
Il secondo caso presentato riguarda l’ottimizzazione di strumentazione medica: nello specifico di un dispositivo per la misurazione della pressione sanguigna. modeFRONTIER è stato utilizzato per gestire sequenze di calcoli fluidodinamici, con l’obiettivo, da un lato, di ridurre le perdite di carico introdotte nel flusso sanguigno dalla sonda del dispositivo e, dall’altro, di ottenere la massima uniformità del campo di pressione, per aumentare l’accuratezza. Il problema è stato impostato combinando calcoli su modelli CFD, con ricerche svolte, a vantaggio della celerità della soluzione, su opportune “superfici di risposta”. L’analisi di robustezza e sensibilità di alcuni parametri soggetti ad incertezza o variabilità operativa è, invece, l’argomento dell’ultima applicazione presentata. Un modello ad elementi finiti di un femore soggetto all’impianto di una protesi d’anca è stato integrato in un progetto modeFRONTIER. Lo scopo è quello di studiare l’influenza di parametri geometrici (dimensione della protesi e del paziente), fisici (proprietà dei materiali ossei, distribuzione del coefficiente d’attrito protesi/osso) e dinamici (carichi sulla protesi), sullo stato tensionale e sulle deformazioni di interesse biomeccanico. L’obiettivo finale, pienamente raggiunto, è stato quello di valutare l’influenza di tali parametri sulle “micro-motions” post-operatorie, che sono tra le principali cause asettiche del fallimento degli impianti in cui non si utilizzi cementazione. Il contributo di modeFRONTIER è stato nuovamente essenziale nel limitare il numero di simulazioni necessarie all’ottenimento di corrette informazioni statistiche, e nella loro gestione ed elaborazione numerica e grafica. |
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| Figure 1. Artificial Lung design |
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| Figure 2. Parametric geometry definition on the CAD, ready for the design optimization |
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| Figure 3. Scheme of the Process Integration realized by modeFRONTIER |
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| Figure 4. The set of optimal solutions in the space of the two objectives, as obtained by the MOGAII algorithm |
Nowadays, the demand for accurate and efficient design techniques is dramatically increasing in any engineering field. This motivates research institutions and universities to innovate and improve simulation methodologies and techniques faster than ever before. Numerical optimization, in combination with simulation, has a significant impact on this context: together, they allow, simultaneously, to improve the design, to shorten development times and to cut costs.
ESTECO’s modeFRONTIER optimization tool plays an important role in this technology: the software has the ability to couple and steer most of the commercial CAE tools and in-house codes, automating and allowing efficient optimization.
Here, in particular, some cases related to FEM and CFD in biomedical applications will be described. Emphasis will be put on the innovative approach and the application of optimization techniques. Hence, the aim of the work is to give an overview of the innovation chances that such procedures provide to researchers in this fast-developing engineering sector.
Introduction
The present work focuses mainly on the application of design of experiments, multi-objective optimization and robustness analysis technologies. Three examples are presented, the optimization of bone implants, blood pressure measurement devices and the design of an artificial lung.
Artificial lung design optimization
The first problem focuses on the application of multi-objective shape optimization techniques to improve the design of an artificial lung (Fig.1).
The objectives here are the simultaneous reduction of the thrombogenicity and the increment of the gas-exchange performances of the device.
The volume of the domain with flow rate less than 0.5 mm/s could be considered as an index of thrombogenicity: this threshold value has been fixed with regard to the flow rate of aggregation of red blood cells in a thrombus formation process. Therefore, the first objective of the optimization will be the minimization of such volume (“Min LV”).
The other objective is the minimization of the Standard Deviation of the flow rate in the fiber bundle (“Min SD”). This measure represents the gas exchange performances of the artificial lung, since blood should flow uniformly to the fiber bundle, avoiding stagnation and channeling.
Eight lengths were selected, to control the shape of the most important zones of the device geometry, accordingly to the freedom of the designer at the current stage of the product engineering phase (Fig.2).
The parametric CAD model of the lung was prepared, as well as automatic meshing routines and the CFD model. The code integration and the optimization were carried out with modeFRONTIER (Fig.3).
Here, an improved Multi-Objective Genetic Algorithm (MOGAII) is used to solve the optimization problem, and promising results are obtained: simultaneous reduction of stagnation zones (anti-thrombogenicity) in the range of 70%, and flow rate standard deviation (gas exchange performance) reduced by 30% (Fig.4).
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| Figure 5. The schematic representation of the optimization loop within modeFRONTIER (workflow) |
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| Figure 6. The Pareto Frontier with three different trade-off
solutions. |
Medical blood pressure measurement device design optimization
The second case is based on the preliminary design of a medical blood pressure measurement device.
A probe is designed with the aim to minimize the pressure loss introduced into the blood flow, keeping the pressure uniformity at the outlet as high as possible. The computational chain, made up by the meshing and the CFD tools, was integrated and driven by the optimizer (Fig.5).
The approach to this problem includes an exploration phase using Design of Experiments techniques, as well as a subsequent multi-objective optimization exploiting also response Surface Modeling techniques. This last feature has been used in order to accelerate the optimization process, replacing some CFD evaluations with such fast and accurate interpolations.
Once the set of optimal configurations (Pareto Frontier) was found, decision-making tools were used to find the best trade-off between the two different objectives (Fig.6).
Bone implant FEM model
stochastic validation
The last section is dedicated to the stochastic validation of an implant. The failure of cementless total hip replacements is mostly caused by aseptic loosening. Many authors consider the bone-implant relative micro-motion early after surgery (primary stability) as the main biomechanical cause of aseptic loosening in cementless implants. Animal and retrieval studies associate the failure of the osteo-integration process to primary micro-movements.
The present study is based on the FEM of a human femur implanted with a cementless anatomical stem (Fig.7), modeling frictional contact at the bone/implant interface. The aim is to evaluate the effect of some parameters on the predictions of the model (i.e. stress, strains).
The model was fully validated in a previous work against primary stability experimental measurements. Cancellous and cortical bone were both considered homogeneous materials. The first was assumed isotropic, while the second was assumed transversally isotropic. The cementless stem was modeled as made of titanium alloy, with a modulus of 105000 MPa.
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| Figure 7. The FEM model, with its three material parts: cortical bone, spongy bone, stem. |
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| Figure 8. Multi-variate distribution on two of the stochastic input variables: the friction coefficient for the stem/spongy bone interfaces, and the one for the spongy bone/cortical bone. |
Stochastic Input Variables
Bone mechanical proprieties are derived by cortical and cancellous tissue apparent density analyses. Ranges of 1.5 – 2.0 gr/cm3 for the cortical bone and of 0.1 – 0.7 gr/cm3 for the cancellous bone are investigated: Gaussian function has been set for both parameters.
In total hip arthroplasty, different stem sizes are required because of the anatomical difference of patients’ femurs. A scaling factor has been introduced to take into account nine different stem sizes (from 9 to 17), commonly used in surgery. The sizes were assigned with the same probability: this parameter allows to investigate whether the most critical condition shows up with small or large anatomic dimensions.
However, the most important aspect of the model is the bone/implant interface. Different interface conditions are taken into account, from the fully osseous-integrated condition to the presence of fibrous tissue at the bone implant interface. The contact condition was therefore assigned to the seventeen zones defined as contact surfaces, accordingly to a uniform probability distribution. The magnitude on the loading force is described applying an hip contact force in the range of 1200-2580 N with a Gaussian distribution.
Output Variables
Von Mises strain and stress are analyzed for the stem, cortical and cancellous bone (Fig.9). In addition, relative peak micro-motion and peak detachment were investigated at the bone implant interface, such as the “viable area” (defined as the fraction of the contact surface where micro-motions are under 40 microns). According to literature, this value can be considered as a threshold above which the osteo-integration process is strongly prevented. Peak contact pressures and peak frictional stresses are analyzed at the interface between the bone and the prosthesis.
Results
Stress and strain are strongly influenced by the femur-stem size, with an inverse relationship, as expected. Less effect is shown for the force magnitude, positively related. Spongy stresses are associated to the spongy apparent density with a positive relationship, while cortical strain and apparent density show an inverse relationship.
Interface conditions seem not to have a strong global effect on the stresses and strains. However, high relationship is detected between the stress and the contact status of some selected zones: the reason should be probably found in the way the stem geometry transfers the loads to the bone.
Micro-motion parameters are influenced by the interface conditions, as expected. The contact viable area is correlated to the overall contact condition with an inverse relationship, while little effect is associated to the loading force and to the apparent density of both bone tissues.
At constant loading condition, the model predicts widely higher micro-motions for larger anatomies respect to smaller ones. As far as greater patients have usually also higher body weights, it is reasonable to state that the probability of stem aseptic loosening is higher for them.
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| Figure 9. A FEM solution: femur displacements plot |
CONCLUSIONS
The DOE, optimization and robust design technologies proved to be effective in several biomedical applications.
Their implementation, based on to the modeFRONTIER environment, is straightforward, and can guarantee great improvements in design efficiency, time and cost savings, and productivity.
ACKNOWLEDGMENTS
Thanks to Mr. Ichiro Taga (Kawasumi Lab.s, Japan) who presented his work at the modeFRONTIER International Users’ Meeting, in 28th-29th September 2006 in Trieste, Italy.
For further information and to request the extended version of this article, please contact: Ing. Luca Fuligno
info@enginsoft.it
The present case study has been developed in cooperation with Laboratorio di Tecnologia Medica degli Istituti Ortopedici Rizzoli
Article published in the Magazine: EnginSoft Newsletter Year 4 n.3
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