Stefan Zachow

Validation of linear elastic model for soft tissue simulation in craniofacial surgery

Physically based soft tissue modeling is a state of the art in computer assisted surgery (CAS). But even such a sophisticated approach has its limits. The biomechanic behavior of soft tissue is highly complex, so that simplified models have to be applied. Under assumption of small deformations, usually applied in soft tissue modeling, soft tissue can be approximately described as a linear elastic continuum. Since there exist efficient techniques for solving linear partial differential equations, the linear elastic model allows comparatively fast calculation of soft tissue deformation and consequently the prediction of a patients postoperative appearance. However, for the calculation of large deformations, which are not unusual in craniofacial surgery, this approach can implicate substantial error depending on the intensity of the deformation. The monitoring of the linearization error could help to estimate the scope of validity of calculations upon user defined precision. In order to quantify this error one even do not need to know the correct solution, since the linear theory implies the appropriate instruments for error detection in itself.

Mehr Mathematik wagen in der Medizin

In diesem Artikel wird an drei Erfolgsmodellen dargestellt, wie das Zusammenwirken von Mathematik und Medizin eine Entwicklung hin zu patientenspezifischen Modellen auf Basis moderner medizinischer Bildgebung angestosen hat, die in naher Zukunft dynamisch weiter Raum greifen wird. Dabei existiert ein Gleichklang der Interessen von Medizin und Mathematik: Beide Disziplinen wollen die Resultate schnell und zuverlassig. Fur die Klinik heist dies, dass notwendige Rechnungen in moglichst kurzer Zeit, und zwar auf dem PC, ablaufen mussen und dass die Resultate so genau und belastbar sein mussen, dass medizinische Entscheidungen darauf aufbauen konnen. Fur die Mathematik folgt daraus, dass hochste Anforderungen an die Effizienz der verwendeten Algorithmen und die darauf aufbauende Software in Numerik und Visualisierung zu stellen sind. Allerdings ist es noch ein weiter Weg, bis anatomische und medizinisch brauchbare funktionelle Modelle auch nur fur die wichtigsten Korperteile und die haufigsten Krankheitsfalle verfugbar sein werden. Fuhrende Universitatskliniken konnten, als Zentren einer interdisziplinaren Kooperation von Medizinern, Ingenieuren und Mathematikern, eine Vorreiterrolle dabei ubernehmen, mehr Mathematik in der Medizin zu wagen. Dies ware zweifellos ein wichtiger Schritt in Richtung auf eine individuelle quantitative Medizin, bei dem Deutschland die besten Voraussetzungen hatte, die Rolle des „Schrittmachers“ zu ubernehmen.

More Mathematics into Medicine

This article presents three success stories that show how the coaction of mathematics and medicine has pushed a development towards patient specific models on the basis of modern medical imaging and “virtual labs”, which, in the near future, will play an increasingly important role. Thereby the interests of medicine and mathematics seem to be consonant: either discipline wants the results fast and reliably. As for the medical side, this means that the necessary computations must run in shortest possible times on a local PC in the clinics and that their results must be accurate and resilient enough so that they can serve as a basis for medical decisions. As for the mathematical side, this means that highest level requirements for the efficiency of the applied algorithms and the numerical and visualization software have to be met. Yet there is still a long way to go, until anatomically correct and medically useful individual functional models for the essential body parts and for the most frequent diseases will be at hand. This will only be possible, if more mathematics enters into medicine.

Über die Qualität einer 3D Weichgewebeprädiktion in der Gesichtschirurgie Ein quantitativer Vergleich mit postoperativen CT-Daten

Am Beispiel eines 18 jahrigen Patienten mit ausgepragter Mittelgesichtshypoplasie wird die 3D Planung einer Knochen verlagernden Korrekturoperation unter Berucksichtigung der funktioneilen und asthetischen Rehabilitation demonstriert. Unterschiedliche Varianten einer Le Fort-I Osteotomie zur Oberkiefermobilisierung wurden am 3D Modell geplant und die Verlagerung hinsichtlich der dentalen Okklusion und der resultierenden Gesichtsform bewertet. Zur raumlichen Weichgewebepradiktion wird sowohl ein homogenens als auch ein inhomogenenes, volumetrisches Gewebemodell betrachtet und die jeweilige Simulationsgute anhand postoperativer CT-Daten quantitativ uberpruft.

Shape-based approach for the estimation of individual facial mimics in craniofacial surgery planning

Besides the static soft tissue prediction, the estimation of basic facial emotion expressions is another important criterion for the evaluation of craniofacial surgery planning. For a realistic simulation of facial mimics, an adequate biomechanical model of soft tissue including the mimic musculature is needed. In this work, we present an approach for the modeling of arbitrarily shaped muscles and the estimation of basic individual facial mimics, which is based on the geometrical model derived from the individual tomographic data and the general finite element modeling of soft tissue biomechanics.

Changes in Knee Shape and Geometry Resulting from Total Knee Arthroplasty

Changes in knee shape and geometry resulting from total knee arthroplasty can affect patients in numerous important ways: pain, function, stability, range of motion, and kinematics. Quantitative data concerning these changes have not been previously available, to our knowledge, yet are essential to understand individual experiences of total knee arthroplasty and thereby improve outcomes for all patients. The limiting factor has been the challenge of accurately measuring these changes. Our study objective was to develop a conceptual framework and analysis method to investigate changes in knee shape and geometry, and prospectively apply it to a sample total knee arthroplasty population. Using clinically available computed tomography and radiography imaging systems, the three-dimensional knee shape and geometry of nine patients (eight varus and one valgus) were compared before and after total knee arthroplasty. All patients had largely good outcomes after their total knee arthroplasty. Knee shape changed both visually and numerically. On average, the distal condyles were slightly higher medially and lower laterally (range: +4.5 mm to −4.4 mm), the posterior condyles extended farther out medially but not laterally (range: +1.8 to −6.4 mm), patellofemoral distance increased throughout flexion by 1.8–3.5 mm, and patellar thickness alone increased by 2.9 mm (range: 0.7–5.2 mm). External femoral rotation differed preop and postop. Joint line distance, taking cartilage into account, changed by +0.7 to −1.5 mm on average throughout flexion. Important differences in shape and geometry were seen between pre-total knee arthroplasty and post-total knee arthroplasty knees. While this is qualitatively known, this is the first study to report it quantitatively, an important precursor to identifying the reasons for the poor outcome of some patients. Using the developed protocol and visualization techniques to compare patients with good versus poor clinical outcomes could lead to changes in implant design, implant selection, component positioning, and surgical technique. Recommendations based on this sample population are provided. Intraoperative and postoperative feedback could ultimately improve patient satisfaction.

Biomechanisches Modell zur Abschätzung der individuellen Gesichtsmimik

In dieser Arbeit prasentieren wir ein biomechanisches Modell des Weichgewebes inklusive der Gesichtsmuskulatur zur Abschatzung der individuellen Gesichtsmimik in der Gesichtschirurgie.

Validierung eines linear elastischen Modells für die Weichgewebesimulation in der Mund-Kiefer-Gesichtschirurgie

In dieser Arbeit untersuchen wir den Gultigkeitsrahmen eines linear elastischen Modells fur die Weichgewebesimulation in der Mund-Kiefer-Gesichtschirurgie. Insbesondere die Quantifizierung und die Uberwachung des auf die geometrische Nichtlinearitat zuruckzufuhrenden Linearisierungsfehlers bei groβen Deformationen werden diskutiert.