Mini-plate for the osteosynthesis of mandibular angle fractures | CDGudas
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Biomedical

Brief of scope and analysis

 

A mini-plate for the osteosynthesis of mandibular angle fractures was designed to improve the formation of new bone by reducing through its shape and configuration of the holes the maximum strains that occur in the cortical bone near the first attachment screw and propagate towards the edges of the fracture through the well known edge distance effect.

The plate was developed as part of a doctorand program at the University of Medicine and Pharmacy “ Carol Davila” – Bucharest, Romania with the analyses and FEA simulations preliminary to the development of the new design being done in large part in Australia. The physical prototypes were CNC machined, tested and inspected afterwards for major mechanical deterioration or any indications of metal fatigue damage. The new mini-plate has a brevet of invention.

For more information on this project visit this site  and this site

Mandible fragments after being reduced in healing position with the mini-plate installed and two screws each side of the fracture in optimal position for strain minimisation during biting

Entire  mandible with mini-plate and screws

Posterior fractured segment showing relative size of holes drilled at the surface of cortical bone

The posterior fragment

Mini-plate prototype during testing. On the right side the markings from previous tests are clearly visible

Mandible, mini-plate and screws in finite element discretization

(wireframe edges removed for clarity)

Physical prototype during testing

Loads and boundary conditions:   A biting force of 200 N was applied at the area of the lower incisive teeth and the mandible fragments were supported by fixing  all translations at the nodes on the outer surfaces of the condyles.

Bone properties:  For the cortical bone, properties like thickness, density, average elastic moduli etc. were represented for 31 regions of the vestibular and lingual sides of a semi-mandible.    An extract of the values used for these parameter is presented in the table below.

Extract of cortical bone orthotropic properties across the mandible

The cancellous bone was represented with isotropic properties defined by:

  • Modulus of elasticity:     0.50 GPa
  • Density:                            1.40 g/cm3
  • Poison ratio:                     0.38
Bio_5
Table of model statistics (as *.jpg)

Mini-plate and screw properties:  Medical grade titanium was considered for all hardware  with elasticity moduli of 113 and 140 GPa for the mini-plate and the screws respectively, and a Poison ratio of 0.32 .

Pre-processing

Coordinate systems for the definition of mandible bone properties shown on a semi mandible

A number of 64 cartezian coordinate systems were defined for each semi-mandible to represent the orthotropic bone properties of the cortical bone on the vestibular and lingual sides using MAT8 cards in MSC Nastran.

Six cylindrical coordinate systems were defined at the axes of the holes for quick generation of local meshing and for extraction of results around the holes in the cortical and in mini-plate.

All components were represented with 3D linear elements.

Over two hundred and eighty coordinate frames were required around the edge of the fracture surfaces for the definition of GAP elements used to represent the contact between the two fractured segments after the fracture was reduced and the mini-plate installed.
Additional gap elements were defined between the cortical and screws and  between the slots in the mini-plate and the screws.  The normal pressure fields generated by the torque used during the insertion of the screws was incorporated in the analysis.   The mini-plate and the screw meshed with six and eight nodes 3D elements.

Additional pre-processing was focused on establishing representative numbering systems for the nodes and the elements, especially around the holes and the surfaces of the fracture.

Numerical analysis

Non-linear analysis was carried out in 18 stages using the non-linear solution 106 in MSC Nastran.  The stages were at 2, 5, 10, 20, … , 120, 125, 130, 140 and 150% of the biting load.
In each stage there were 100 increments and the convergence criteria required tolerances no larger than 0.01 in displacements, residual forces and in energy (UPW)
The convergence factors obtained in most cases are smaller than 10-8.  For more details on the loading steps and final convergence factors select from the pictures on the right and click to enlarge.

Coordinate systems for the definition of the normal to the fracture edges shown on the posterior fragment
Combined table - extract of loading sub cases and iterations control

Loading Details

Convergence factors at 20% of load

Conv. Fact 20%

Convergence factors at 150% of the biting force

Conv. Fact 150%

Graphical post processing

Maximum principal strains 

    Range 0 to 3000 micro strains

200 N biting force

Maximum principal strains - 120% of load on a scale between 0 and 3000 microstrains

    Range 0 to 400 micro strains

Maximum principal strains - 120% of load on a scale between 0 and 400 microstrains

300 N biting force

Maximum principal strains - 120% of load on a scale between 0 and 3000 microstrains

   For a strain/stress evolution  to 150% of biting loads click here  

Maximum principal strains - 120% of load on a scale between 0 and 400 microstrains

Analytical post processing

Sample of loads extraction (global and at fastener locations)

Table with reactions at first screw for various fracture angles, distances to the fracture line and joint flexibility

Sample of cortical strains at the fracture line and around specified holes

Table with strains at first screw for various fracture angles, distances to the fracture line and circular layer around the hole edge

 

Graph with reactions at first screw for various fracture angles and distances to the fracture line

 

Graph with strains near the fracture edge for various distances to the first screw

If not noticed above and interested in the evolution of max. principal strains in the angle of the mandible near the fracture line or the overall stress distributions in the mini-plate for biting forces up to 300 N, the video clip to play is just below.

Testimonials:

We collaborated with Mr. Claudiu Gudas on a very important project. I can emphasize the indisputable qualities that impressed me: perseverance, seriousness and dedication to the subject under investigation.
In the future, I will certainly also investigate other medical issues alongside Mr. Gudas.

Dr. Teodora Pituru