1 Introduction

• 1.1 A brief introduction to osteochondral healing

  • 1.1.1 The clinical problem

  • 1.1.2 Searching for a solution

• 1.2 Cartilage analysis and function

  • 1.2.1 Joint diseases and treatments

    • 1.2.1.1 Techniques to stimulate repair

      • 1.2.1.1.1 Debridement and lavage

      • 1.2.1.1.2 Blot clot techniques

      • 1.2.1.1.3 Osteotomy

      • 1.2.1.1.4 Soft tissue transplantation

      • 1.2.1.1.5 Autologous chondrocyte implantation

    • 1.2.1.2 Transplantation techniques

      • 1.2.1.2.1  Autologous graft transplantation

      • 1.2.1.2.2 Allografts

      • 1.2.1.2.3 Xenografts

  • 1.2.2 Cartilage characterization

    • 1.2.2.1 Mechanical parameters of cartilage and bone

      • 1.2.2.1.1 Young’s module (E)

      • 1.2.2.1.2 Poisson’s ratio (ν)

      • 1.2.2.1.3 Permeability (k)

      • 1.2.2.1.4 Material orientation

    • 1.2.2.2 Test description

      • 1.2.2.2.1 Indentation

      • 1.2.2.2.2 Unconfined compression (E, ν)

      • 1.2.2.2.3 Confined compression (H_A, k)

      • 1.2.2.2.4 Porosity (φ)

    • 1.2.2.3 Recently developed devices and techniques for measuring mechanical cartilage properties in vivo and in vitro.

    • 1.2.2.4 Determination of the magnitudes of the mechanical parameters

  • 1.2.3 Osteochondral repair

  • 1.2.4 Current models used to simulate bone remodeling and tissue differentiation

    • 1.2.4.1 Bone remodeling model based on a mechanical stimulus to stimulate bone adaptation (Huiskes’s model).

    • 1.2.4.2 Strain fields of each tissue type regulating the fracture healing process (Claes’s model).

    • 1.2.4.3 Mechanoregulation of differentiated tissues during fracture repair (Prendergast’s model).

    • 1.2.4.4 Influence of growth factors and mechanical stimulus during fracture repair (Bailon-Plaza’s model)

• 1.3 Preliminary work

  • 1.3.1 Bone joint mechanics: biomechanical analysis of proximal humerus

    • 1.3.1.1 Previous work realized by Lill and his group

  • 1.3.2  In vivo analysis of an osteochondral defect

    • 1.3.2.1 Description of an animal model of osteochondral defect healing

    • 1.3.2.2 Surgical Procedures

    • 1.3.2.3 Boundary conditions

    • 1.3.2.4 Gait analysis

    • 1.3.2.5 Histological analysis

    • 1.3.2.6 Histomorphometrical analysis

  • 1.3.3 Results used from the preliminary work

    • 1.3.3.1 Results used from the humerus analysis (Lill et al.)

    • 1.3.3.2 Results used from the animal model (Bail et al.)

• 1.4 Hypotheses and aims

  • 1.4.1 Hypotheses

  • 1.4.2 Aims

2 Materials and methods

• 2.1 Bone-joint mechanics (humerus project)

  • 2.1.1 Mechanical in vitro testing of proximal humerus defects

  • 2.1.2 Straining of intact and fractured proximal humerus under physiological loads

    • 2.1.2.1 Simulation of the used human specimens and FEM validation

    • 2.1.2.2 Simulation of physiological loads

• 2.2 Osteochondral healing (Galileo project)

  • 2.2.1 The tissue differentiation model

    • 2.2.1.1 The concept

    • 2.2.1.2 Numerical analysis of the histological sections

    • 2.2.1.3 Implementation of the tissue differentiation model

  • 2.2.2 Boundary conditions

  • 2.2.3 Parameter study

    • 2.2.3.1 Analysis of the defect size

    • 2.2.3.2 Influence of the local joint curvature

    • 2.2.3.3 Analysis of the stiffness of defect fillings

  • 2.2.4 The developed algorithm

    • 2.2.4.1 Additional tools developed for analysis of the data

3 Results

• 3.1 Bone-joint mechanics (humerus project)

  • 3.1.1 Fixation stiffness in vitro and in the simulation

  • 3.1.2 Straining of intact and fractured proximal humerus under physiological loads

• 3.2 Osteochondral healing (Galileo project)

  • 3.2.1 Strain Analysis

    • 3.2.1.1 Histological sections

    • 3.2.1.2 Defect model

  • 3.2.2 Comparison of the simulated healing to spontaneous repair in vivo

• 3.3 Influence of mechanical conditions on osteochondral healing

  • 3.3.1 Influence of the defect size

  • 3.3.2 Influence of the local joint curvature

  • 3.3.3 Influence of the defect fillings stiffness

4 Discussion

• 4.1 Discussion of the method

  • 4.1.1 Bone-joint mechanics (humerus project)

  • 4.1.2 Osteochondral healing (Galileo project)

    • 4.1.2.1 On the selection of Young’s elastic modulus to simulate differentiation

    • 4.1.2.2 On the selection of biphasic soil behavior to represent cartilage mechanics.

    • 4.1.2.3 Convergence during healing simulation

    • 4.1.2.4 On the selection of mechanical conditions to evaluate repair

    • 4.1.2.5 On the selected cases to be analyzed

    • 4.1.2.6 On the quantification of the differentiated tissues during healing

    • 4.1.2.7 On the algorithm

• 4.2 Discussion of the results

  • 4.2.1 Bone-joint mechanics (humerus project)

  • 4.2.2 Osteochondral healing (Galileo project)

    • 4.2.2.1 Theory supporting the tissue differentiation model

    • 4.2.2.2 Straining of histological sections

    • 4.2.2.3 Influence of mechanical conditions on osteochondral healing

      • 4.2.2.3.1 On the influence of the defect size on osteochondral healing

      • 4.2.2.3.2 Influence of the local joint curvature and usage of defect fillings on healing

• 4.3 Comparison with other studies

• 4.4 Clinical relevance

5 Conclusion

6 Future works

• 6.1 Future works related to the usage of the tissue differentiation model

• 6.2 Future works related to the algorithm

• 6.3 Future works related with the finite element model

7. References

Annex 1

Annex 2

Acknowledgements

Publications

Curriculum vitae

EIDESSTATTLICHE ERKLÄRUNG

Table 2.1: Weight, muscles and joint contact forces in Newton in 90° abduction

Table 2.2: Limits used in the tri-linear curves defining the differentiation process for each tissue type where E_min ^tissue < E _elem≤ E_max ^tissue.

Table 2.3: Initial material properties used in the finite element analysis (Guo, 2001;Lacroix and Prendergast, 2002;Smith and Mansour, 2000).

Table 4.1: Tensile properties of the human femoral condyle cartilage. The elastic modulus of Young is affected due to pathological conditions of the cartilage (Mow and Ratcliffe, 1997).

Fig. 1.1: Schematic representation of the relationship between age and types of chondral defects. Osteochondral defects included osteochondritis dissecans and low energy osteochondral fractures occur most frequently in skeletally immature individuals and individuals who recently have completed skeletal growth. Chondral defects, localized tears or disruptions of articular cartilage that do not extend into subchondral bone occur most frequently in young adults. With increasing age the frequency of degenerative lesions of the articular surface increases (Buckwalter, 1999) (figure with corresponding text).

Fig. 1.2: Schematic representation of the cartilage zones. The mechanical properties of cartilage are changing in a functional – structure relation. The elastic modulus of Young is reduced from the upper zone (tangential) to the deeper regions (Mow and Ratcliffe, 1997).

Fig. 1.3: ICRS classification of osteochondral defects. In this project osteochondral defects grade 4B (severely abnormal) were modeled.

Fig. 1.4: Schematic illustration of unconfined (a) and confined (b) compression test for cartilage samples (Boschetti, et al., 2004).

Fig. 1.5: Huiskes’s model. Cell activity is represented by a tri-linear curve. High values of strain energy density conduce to growth activity, low values of strain energy density conduce to resorption activity. The dead zone represents cellular inactivity (Huiskes, et al., 1987).

Fig. 1.6a:Claes’s model. Characteristic limit values of strain and stresses are defined for each tissue type to simulate diaphyseal fracture healing (cortical remodeling through enchondral ossification) (Claes and Heigele, 1999).

Fig. 1.6b: Fuzzy logic in combination with mechanical stimulus applied to simulate healing of trabecular fractures (intramembranous ossification). Fixed rules including biological factors regulate building or resorption of different tissue types (Shefelbine, et al., ).

Fig. 1.7:Prendergast’s model. Prendergast developed a mechanoregulation schema regulated by shear strains and fluid velocities defined for each tissue type (Lacroix and Prendergast, 2002).

Fig. 2.1: Proximal humerus with defect localization and a LCP-PH implant under compressive loads. Left: Finite element model of the proximal humerus with implant, analyzed in this project. Middle: X-ray of a specimen with implant but prior to the osteotomy. Right: Specimen in material testing machine under pure compression. Reflective markers (distance between marker trees = 60 mm) are attached to each segment to allow determination of the interfragmentary movements. From these movements and loads, the stiffness of the bone implant construct was computed (Maldonado, et al., 2003).

Fig. 2.2: Initial osteochondral defect created at the femoral condyle in Yucatan minipigs (Ø = 6mm, depth = 2mm). Left: from: (Bail, et al., 2003), right: from: (Duda, et al., 2005).

Fig. 2.4: Tri-linear curve used to simulate tissue differentiation. The center point corresponds to the strain value of an intact situation.

Fig. 2.5: Schematic representation of the tissue differentiation model. Differentiation was simulated by incremental changes in the elastic modulus of Young. Minimum principal strains were used as mechanical stimulus.

Fig. 2.6: Loads and boundary conditions used during healing simulation. TA represents the “total area” in which the percentages (number of elements) of the newly formed tissues were quantified during repair.

Fig. 3.1: Finite element model of the proximal humerus under physiological-like loading conditions. Minimum principal strains of the bone surface are given for the neutral position (left), 90° forward flexion (center) and for 90° abduction (right).

Fig. 3.2: Minimum principle strains at the anterior bone surface. Osteoporotic, poor quality bone with a bone defect stabilized by an angle stable osteosynthetic device is shown for three different arm positions: 0°, 90° forward flexion (F) and 90° abduction (A).

Fig. 3.3: Distribution of cortical bone elements for different strain ranges. Strains are given as minimum principal strain values for different arm positions under physiological-like loading conditions for the specimen with poor bone quality and a 5 mm osteotomy at the level of the surgical neck of the humerus.

Fig. 3.4: Distribution of cancellous bone elements for different strain ranges. Strains are given as minimum principal strain values during 90° abduction for a specimen with reference bone quality and defect, and a specimen of poor bone quality, both with and without defect. Defects were stabilized using an angle-stable osteosynthetic device.

Fig. 3.5: Histological sections of osteochondral defect healing at 4, 6 and 12 weeks stained with Safranin-Orange von Kossa (top) and Safranin-light green (bottom). 4^th week: First cartilage cells at the defect wall as well as a resorption region at the basis are visible. 6^th week: the cartilage growths from the lateral borders of the defect. It is calcified forming cancellous bone as far as the subchondral plate. Fibrous tissue fills the defect with low formation of hyaline cartilage. At the center a defect region can be seen. 12^th week: the cancellous bone has completely regrown; the fibrous tissue is differentiated to hyaline cartilage (Bail, et al., 2003;Duda, et al., 2005).

Fig. 3.6: Left: histology at the 4^th week, stained with Safranin-Orange von Kossa. Right: Straining of the formed tissues during healing in a selected histological section at the 4^th week.

Fig. 3.7: Left: histology at the 6^th week, stained with Safranin-O vK. Right: Straining of the formed tissues during healing in a selected histological section at the 6^th week.

Fig. 3.8: Left: histology at the 12^th week, stained with Safranin-O vK. Right: Straining of the formed tissues during healing in a selected histological section at the 12^th week.

Fig. 3.9: Straining of the newly differentiated soft tissues at the defect region during healing after numerical analysis of histological sections at 4 (left), 6 (center), and 12 weeks (right). The quadrilateral represents the initial defect (Ø = 6mm, depth = 2mm).

Fig. 3.10:Straining of the initial defect situation.

Fig. 3.11: Simulation of osteochondral defect healing. The selected iterations correspond to the histological staining after 4 (top), 6 (center) and 12 weeks (bottom).

Fig. 3.12: Simulated osteochondral defect healing: With an increased cartilage thickness only fibrous tissue was generated (A). When the defect width was increased, only slight variations compared to the initial healing prediction were found (B). When the depth was increased only fibrous tissue formation was predicted (C).

Fig. 3.13: Simulated healing process. Left: Healing process in a flat interface. Right: Healing process in a concave interface. The healing pattern appears to be independent of the local geometry. Time points compared approximately from top to bottom: 4, 6 and 12 weeks in the animal experiment.

Fig. 3.14: Tissue quantification during healing. Top: flat interface. Center: convex interface. Bottom: concave interface. The mechanical conditions in a concave interface (bottom) appear to be more favorable for healing based on the larger quantity of differentiated hyaline cartilage.

Fig. 3.15: Simulated healing for a convex interface. For each tissue type, the range of the maximal and minimal values of the stiffness was subdivided. The slope for tissue differentiation and the quantity of reached stiffnesses during healing are illustrated.

Fig. 3.16: Quantification of stiffnesses reached (tissue types) and slope of differentiation during simulated healing for a concave interface.

Fig. 3.17: Quantification of stiffnesses reached (tissue types) and slope of differentiation during simulated healing for a flat interface.

Fig. 3.18: Resorption regions observed in the cancellous bone (Z1, Z2, Z3) during simulated osteochondral healing. Specific elements at the same regions, remarked in red, were select to compare its differentiation pattern.

Fig. 3.19: Pore pressure (top) and fluid flow (bottom) as mechanical stimuli to simulate differentiation. Fluid flow was unable to reproduce the characteristic resorption region at the defect basis.

Fig. 3.20: Tissue quantification during healing using defect fillings. Top: Graft with the same stiffness as the cancellous bone (P1). Bottom: Graft with a stiffness of 50% of the cancellous bone (P2). Although a higher percentage of resorption is observed in P1, it shows a higher percentage of hyaline cartilage compared with P2. Additionally it shows calcified cartilage formation.

Fig. 3.21: Differentiated tissues after healing (equilibrium) using a cylindrical graft with two different stiffnesses: 100% and 50% of the cancellous bone stiffness are compared. The usage of defect fillings with the same stiffness than the cancellous bone forms tissues with a better mechanical quality during healing. However, a slight resorption at the cancellous bone is observed, as well as calcified cartilage differentiation.