Individual vertebral bodies for Thoracic spine

Hi Gregor,

These angles (L3L4Jnt.Pos[0], L4L5Jnt.Pos[0]) are relative to the original configuration (defined by the kinematic rhythm). They are exactly what needed - “rotation for a motion segment”, e.g. segment L3L4 or L4L5. The individual joints are not experiencing moments at 0 thoracopelvic angle.

Regards,
Pavel

Hello Pavel

Thank you for your answer, now I understand how the relative angles are defined. The angles are based on the spine rhythm (SR Matrix). My question is regarding this spine rhythm:

  1. There are already several discussions in the forum about. But there is no clear answer how exactly the SRMatrix was build. Because when I apply the beam theory on the lumbar spine, I don’t get the same values (see below). At the moment the spine rhythm of the thoracic spine in my model is based on the beam theory. So it would be great if you could tell me if this is OK, or how I have to define the spine rhythm for the thoracic spine (SRMatrix).

Factor for the angle relative to T12L1 Joint (Flexion/Extension and lateral bend):

In AnyBody
SacrumPelvis: 0.0711
L5Sacrum: 0.2277
L4L5: 0.4021
L3L4: 0.5785
L2L3: 0.7462
L1L2: 0.9132

Beam Theory (one fixed and one free end): flexion=F/(EI)(Lx^2/2-x^3/6)
SacrumPelvis: 0.0292
L5Sacrum: 0.1108
L4L5: 0.2362
L3L4: 0.3965
L2L3: 0.5831
L1L2: 0.7872

Thank you for your answer

Additional information:
I implemented in my model 24 Multifidus and 27 Semispinalis muscles on each side. The model with these additional muscles is able to control the rotational degrees of freedom of the thoracic vertebral bodies. Thus the Joints between the thoracic vertebras are real spherical joints (no AnyReacForce).

Regards,
Gregor

Hello Gregor,

These are great news - I would be very interested at looking at the model. Have you got any experimental measurements to verify against?

It’s very hard to say what is different between our attempts to compute the spine rhythm - could you explain how you achieved your numbers. I suspect we may have some different input measurements.

Best regards,
Pavel

Hello Pavel

Can I send you the model by e-mail? Because my supervisor doesn’t want to put the model in the forum.

I was wrong with my last numbers; they were built as relative factors of the deformation.

The SRMatrix defines the relative factors of the angles, thus I computed these factors based on the angle in function of the path based on the elastic beam theory: angle= F/(EI)(Lx-x^2/2). With this fomula I computed the angles for each level. Then I computed the factor relative to the angle of T12L1Jnt. But the values are still not the same than in the model (lumbar spine).

Factors for the angle relative to T12L1 Joint (Flexion/Extension and lateral bend)

Beam Theory (one fixed and one free end): angle=F/(EI)(Lx-x^2/2)
SacrumPelvis: 0.265
L5Sacrum: 0.490
L4L5: 0.673
L3L4: 0.816
L2L3: 0.918
L1L2: 0.980

So it is still not clear for me how to get the values for the SRMatrix. What do you mean with “input measurements”? All the constants (E,I,F,L) drop out when we build the relative factors, or am I wrong?

Thank you for answer

Regards, Gregor

Hi Gregor,
I was about to suggest the same for the same reasons. Of course: peg@anybodytech.com

Best regards,
Pavel

Hello Pavel

Thank you for your answer. I included your file (DiscStiffnessNonLinear.any) in my model. Now I have a question regarding your definition of the nonlinear stiffness of the IVB’s;
Han K-S et al (2011) is defining the stiffness in function of the angle (based on the values from Heuer et al. 2007). In my opinion this stiffness should then multiplied by the angle to get the Moment. It seems to me that the moment is the stiffness in your file.

Best regards,
Gregor

Hi Gregor,

Yes, this is a good observation. Please add them in your version.

Regards,
Pavel

Hello Pavel

According to your suggestion, I defined the motion in the entire spine with FDK;

AnyKinEqSimpleDriver FDK_Measure = {


AnyKinLinear L4L5Trans = {
AnyRefNode &L5Node = …HumanModel.BodyModel.Trunk.SegmentsLumbar.L5Seg.L4L5JntNode;
AnyRefNode &L4Node = …HumanModel.BodyModel.Trunk.SegmentsLumbar.L4Seg.L4L5JntNode;
};
AnyKinRotational L4L5Rot = {
Type = RotAxesAngles;
Axis1 = x;
Axis2 = y;
Axis3 = z;
AnyRefNode &L5Node = …HumanModel.BodyModel.Trunk.SegmentsLumbar.L5Seg.L4L5JntNode;
AnyRefNode &L4Node = …HumanModel.BodyModel.Trunk.SegmentsLumbar.L4Seg.L4L5JntNode;


DriverPos = {0,…}
DriverVel = {0,…}
Reaction.Type ={ Off,Off,On,On,On,Off….}
CType = {ForceDep, ForceDep, Hard, Hard, Hard, ForceDep…}

Between all vertebral bodies is rotational and translational stiffness (Also between L5-Sacrum). Rotation in the lumbar spine is non-linear (according your file), all other stiffness is linear. FDK is considered in 2D; compression and shear (Posterior-Anterior) forces and extension/flexion moment.

In this model the deformation is still unrealistic (too few boundary conditions; only posture Driver T12-Pelvis for motion), thus spine rhythm for rotation in the lumbar and the thoracic spine was reinserted. For translation still FDK. The SacrumPelvis joint in the lumbar spine rhythm was taken out (these dof’s are driven by the SacrumPelvisDriver). In this model I use also the linear stiffness of the IVD’s for the lumbar spine, because the non-linear stiffness combined with the spine rhythm is resulting in too high muscle activity (Psoas, Rectus abdominus, Erector spinae). And this is leading to high compression and shear forces.

To summarize

  • The current model possess linear stiffness for rotation and translation between all VB’s (with the values form the literature; Markolf K.L. (1970), PANJAB M.M. (1976), Heuer et al. (2007), Bisschop A. (2011)). The rotational motion is defined with two spine rhythms for the lumbar and thoracic spine. The Translational motion is defined with FDK in the entire spine. I also inserted the lumbar ligaments to gain more stiffness.

  • The Buckle is attached on T12.

  • Rectus abdominus is attached on T12. When RA is attached on T11 or further above, then psoas major is very active because in this case this muscle has to create the bending of the lumbar section.

  • I use the polynomial (3) solver, because this solver has a lower muscle activity (envelope) as the AuxMinMax solver. The motion is a flexion of 30 degree between pelvis and T12 (posture Driver). The motion between T1 and T12 is zero (T12T1 Driver).

What do you think about this model, could anything cause problems in this condition?

I also implemented the thoracic ligaments, but they are not active at the moment, this is only for future proposes when information about the properties is available. Anyway, I saw that the reference (li) in the lumbar ligament definition is not correct for L3L4Ligaments.any und in L4L5Ligaments.any, what is the reason therefor?

I send you my current model and the first results in a separate e-mail.

Thank you for your answer
Regards, Gregor