Vertebral body replacement

Instrumented implant

Severe compression fractures of a vertebral body or a tumour in the region of the spine sometimes require the replacement of a vertebral body by an implant. The loads on such an implant are not well known. In order to measure these loads, the commercially available vertebral body replacement ‘SYNEX’ was modified. It allows the in vivo measurement of three force components and three moments acting on the implant. The 9-channel telemetry transmitter developed in our biomechanics laboratory was placed into the cylinder of the implant together with 6 load sensors and a coil for the inductive power supply. Usually, the spine is in addition stabilized dorsally by an internal spinal fixation device implanted from the back side.

 

Implant: vertebral body replacement

Coordinate system

The bone-based coordinate system was chosen according to ISO 2631. The x- axis in the median plane points anteriorly, the y-axis in the frontal plane to the left side, and the z-axis cranially.

The forces and moments are presented in the measuring units N and Nm.

This image has an empty alt attribute; its file name is CoorSysVerBodyRep_big.png
 
Coordinate system Vertebral body replacement
 

Patients

WP1WP2WP3WP4WP5

Table with basic information about those patients who had vertebral body replacements:

Patient Gender Weight [kg] Age at Implantation [years] Indication
WP1 m 66 62 Fracture L1
WP2 m 72 71 Fracture L1
WP3 f 64 69 Fracture L1
WP4 m 60 64 Fracture L1
WP5 m 63 67 Fracture L3

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Internal Spinal Fixator

Instrumented implant

Little was known about the loads acting on internal spinal fixators. In order to measure the loads, a commercially available implant was modified. A measuring cartridge was integrated into the longitudinal rod containing six load sensors, an 8-channel telemetry transmitter, and the secondary coil for the inductive power supply.

Both telemeterized fixators transmit their load values as a radio frequency pulse train outside the body. For the measurements, a flat power coil, fixed to the patient’s back, supplies the energy needed by both fixators. The power coil has an integrated antenna which delivers the signals to the external components of the telemetry system.

Implant: Internal spinal fixator

Coordinate system

The internal fixators were implanted pairwise. All reported data came from the left implant and are reported in a right-handed coordinate system.

The measured load components act at the centre of the cylindrical part of the implant. The z-axis is

the long axis of the fixator and points upwards. The y-axis is parallel to the axis of the Schanz screw and points ventrally. The x-axis is perpendicular to both others and is directed to the right side. All force components Fx, Fy, Fz act in axis directions while the moment components Mx, My, Mz turn clockwise around the axes.

Due to the anatomical conditions at the implantation site this coordinate system does not coincide exactly with the sagittal and frontal plane of the upper body. The forces and moments are presented in the measuring units N and Nm.

Patients

MSNFHSFJJT
BBJWHBLGAG

Table with basic information about those patients who had instrumented spinal fixators:

PatientGenderWeight [kg]Age at Implantation [years]Indication
MSf7559Degenerative instability L3
NFm9034Compression fracture (old)
HSf6654Compression frature L3
FJm8072Degenerative instability L4
JTm7536Compression fracture T11
BBm8142Degenerative instability L4
JWf5346Compression fracture (old) T12
HBf8562 Compression fracture (old) L1
LGf4847 Compression fracture L1
AGf6854 Compression fracture T12

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Knee joint

Instrumented implant

In order to obtain realistic loading data, a knee implant with a 9-channel telemetry transmitter was developed which enables six-component load measurements in a primary total knee replacement. Both forces in axial, medio-lateral and anterio- posterior direction and flexion-extension, varus-valgus and internal-external moments can be measured.The instrumented knee joint is a modification of the INNEXTM System, Type FIXUC (Zimmer GmbH, Winterthur, Switzerland). The standard femur component and tibial insert are used. Only the tibial component was modified to enable the integration of the electronic devices. During modification of the tibial component, the patients’ safety was deemed to be especially important.

Coordinate system

The coordinate system of the instrumented knee implant is a

a right- handed coordinate system fixed at the right tibial implant (not at the bone!). If forces and moments are measured in a left knee, they are transformed to the right side. The coordinate system is located at the height of the lowest part of the polyethylene insert. The z-axis is aligned with the stem axis of the implant.

The force components +Fx, +Fy and +Fz act in lateral, anterior and superior direction on the tibial tray. The moment Mx acts in the sagittal plane of the tibial component and turns clockwise around the +x-axis. The moment My acts in the frontal plane and turns clockwise around the +y-axis and the moment Mz turns clockwise

around +z-axis in the transverse plane. A positive moment Mz acts if the tibial implant component (or the femur) rotates inwards and/or if the tibia bone rotates outwards. The OrthoLoad videos show the load components relative to the tibial tray. The stem axis z of the tibial implant component is rotated backwards in the sagittal plane by about 7 degree relative to the long axis of the tibia bone. This slope of the implant varies inter-individually.

Coordinate system knee joint

Patients

K1LK2LK3RK4RK5R
K6LK7LK8LK9L

Table with basic information about the knee joint patients:

PatientSideGenderWeight [kg]Height [cm]Age at Implantation [years]Tibio-femoral anglePosterior slopeIndication
K1Lleftm100177633.0 – varus5Osteoarthritis
K2Lleftm93171715.0 – varus 11 Osteoarthritis
K3Rrightm95175703.5 – varus 10 Osteoarthritis
K4R right f92170634.5 – valgus3 Osteoarthritis
K5R right m94175601.0 – varus7 Osteoarthritis
K6Lleftf76174654.0 – valgus7 Osteoarthritis
K7L left f70166746.5 – varus7 Osteoarthritis
K8L left m77174704.0 – varus11 Osteoarthritis
K9L left m100166757.0 – varus6 Osteoarthritis

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Shoulder joint

Instrumented implant

The picture shows an instrumented shoulder implant capable of measuring forces, moments and, in addition, the temperature acting in the glenohumeral joint. It was developed in the Biomechanics Lab of the Charité and contains a measuring unit with 6 semiconductor strain gauges and a 9-channel telemetry transmitter. Each strain gauge requires one channel of the telemetry while the remaining three channels are used for transmitting the temperature, the current supply voltage and a synchronising signal. At the lower end, an inductive coil ensures the power supply. The measuring signals are led with a pacemaker feed-through to the antenna (protected by a cap of PEEK) which transmits the signals to the external measuring unit.

Implant: Shoulder joint

Coordinate system

Humerus system

All loads are displayed as acting at the humerus. They are based on the ISB- recommended coordinate system (Wu et al., 2005) for the right shoulder joint. In this bone-based shoulder coordinate system, the positive x-Axis points in the anterior, the y-axis in the superior and the z-axis in the lateral direction. The moments Mx, My and Mz turn clockwise around the +x, +y and +z axes.

This system is right-handed for a right shoulder joint. For patient S3L, who obtained her implant on the left side, all values are mirrored to the right side to make it comparable to the other patients.

Coordinate System Shoulder Joint
Implant System Shoulder Joint

Implant system

In the implant-based coordinate system of the shoulder joint, the positive z-axis coincides with the neck of the implant and points in the medial- cranial direction. x- and y-axes are in the plane perpendicular to the implant neck. Axis x points laterally and y is oriented anteriorly. Load components relative to this implant-base system may be used to test fatigue or wear of implants, for example.

Implant System Shoulder Joint

To obtain the forces and moments relative to the implant, the retroversion of the humeral head has to be known, indicated as α in the picture below. It can be measured relative to the anatomical landmarks of the epicondyles at the elbow or related to the orientation of the forearm in 90° elbow flexion as it is chosen during surgery (Hernigou et al., 2002). For some patients in OrthoLoad exact values for the retroversion to the epicondyles are available from a postoperative CT, taken for medical reasons. For the other patients a retroversion angle of 30° relative to the forearm in 90° elbow flexion was assumed as chosen by the surgeon during implantation.

The retroversion value for each patient can be found in the “Info Patient” window in OrthoLoad as the third rotation angle (picture below, right). In this example the given rotation angle of 63° corresponds to a retroversion angle of 27° (90°-63°). The other two angles are determined by the geometry of the implant and are therefore the same for all patients. The vector plot pictures (below, left) are simplified representations for better visualisation. The shown angle α is always the same and differs from the true angle in the patients.

General advice for the transformation of loads from a bone-based to an implant-based system is described here.

Implant System Shoulder Joint

Scapula system

To obtain the loads relative to the scapula, a coordinate transformation would be required, taking into account the relative movement between humerus and scapula. This requires an accurate movement analysis. Such transformations are already planned but are not yet available.

Patients

 

 

 
S1RS2RS3LS4R
S5RS6RS7RS8R

 

Table with basic information about the shoulder joint patients:

Patient Side Gender Weight [kg] Height [cm] Age at Implantation [years] Indication
S1R right m 101 186 69 Osteoartheritis
S2R right m 85 161 61 Osteoartheritis
S3L left f 72 168 70 Osteoartheritis
S4R right f 50 154 80 Osteoartheritis
S5R right f 103 163 66 Osteoartheritis
S6R right m 135 186 50 Osteoartheritis
S7R right m 89 172 68 Osteoartheritis
S8R right m 83 173 72 Osteoartheritis
             
             
 Literature:

Hernigou, P., Duparc, F., Hernigou, A., 2002. Determining humeral retroversion with computed tomography. J

Bone Joint Surg Am 84-A, 1753-1762 (http://www.ncbi.nlm.nih.gov/pubmed/12377904). Wu, G., van der Helm, F.C., Veeger, H.E., Makhsous, M., Van Roy, P., Anglin, C., Nagels, J., Karduna, A.R., McQuade, K., Wang, X., Werner, F.W., Buchholz, B., 2005. ISB recommendation on definitions of joint coordinate systems of various joints for the reporting of human joint motion–Part II: shoulder, elbow, wrist and hand. J Biomech 38, 981-992 (http://www.ncbi.nlm.nih.gov/pubmed/15844264).

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Hip Joint III

The actual hip implant (Hip III) monitor the three force components and the three moment components acting on the ceramic head of the hip joint.

Instrumented implant

Hip III with one 9-channel transmitter

This new design of a instrumented hip implant was developed to measure contact forces and the friction at the joint in vivo. A clinical proven hip implant (‘Spotorno’ design) was modified in the neck area. The stem is build by TiAl6V4 and Al2O3- Ceramic was choosen for the implant head material. The neck was widened and enhanced with a 6.2 and 10mm hole. In the hollow neck are housed six semiconductor strain gauges, an internal induction coil and the telemetry. The six strain gauges are applied at the lower part on the inner wall (10mm hole) and connected to the 9-channel transmitter. The antenna, placed under the implant head, is connected by electronically feed-through to the internal telemetry. The feed-through is welded by a laser beam into the top plate. The hollowed neck is closed by the top plate and welded with an electron beam. Therefore the internal space is hermetically closed against the body fluids.

With this implant three contact forces acting onto the implant head center and three friction moments acting between the gliding partners can be measured in vivo.

Since April 2010 ten instrumented hip joints (Hip III) were implanted in ten patients (H1L, H2R, H3L, H4L, H5L, H6R, H7R, H8L, H9L and H10R) to monitor forces and moments. No further implantations are planned.

Implant Hip III

Coordinate system

Fermur system

All forces are reported in a right-handed coordinate system of the right femur (different from hip joint type I and II). The load components are reported as Fx, Fy, Fz. The femur system is fixed at the centre of the femoral head. The femoral midline (dotted black) intersects the axis of the neck in point P1. Point P2 is defined as the deepest point of the fossa intercondylaris at the distal end of the femur. The straight connection between P1 and P2 defines the z axis of the  femur. The z axis of the coordinate system is parallel to the z axis of the femur.

The x axis of the coordinate system is defined perpendicular to z and parallel to a plane through the most dorsal parts of the condyles and points laterally. The y axis of the coordinate system is perpendicular to x and z and points ventrally.

Coordinate System ate right Femur

Implant system

In order to test fatigue or strength of the implant itself, it may sometimes be required to know the force components in an implant-based coordinate system. Axis zi of this system coincides with the shaft axis of the implant. The xi axis lies in the neck-shaft-plane. For the transformation of forces from the femur- to the implant system, three angles are required: angle Sx between the z axis of the bone and the shaft axis of the implant, angle Sy between the z axis of the bone and the shaft axis of the implant and furthermore the anteversion angle AV of the implant. These data are provided by the table in the video (“Info Patient”).

  1. Turning the system by +Sx around the – x axis
  2. Turning the system by +Sy around the – y axis 
  3. Turning the system by -Av around the + z axis

More details about this transformation are given here and in Bergmann et al. (2001) (http://www.ncbi.nlm.nih.gov/pubmed/11410170?dopt=Abstract).

Patients

H1LH2RH3LH4LH5L
H6RH7RH8LH9LH10R

Table with basic information about the patients with Hip III implants:

Patient SideGenderWeight [kg]Height [cm]Age at Implantation [years]Indication
H1L leftm7317855Coxarthrosis
H2R rightm7517261 Coxarthrosis
H3L leftm9216859 Coxarthrosis
H4L leftm8517850 Coxarthrosis
H5L leftf8716862 Coxarthrosis
H6R rightm8417668 Coxarthrosis
H7R rightm9517952 Coxarthrosis
H8L leftm8017855 Coxarthrosis
H9L leftm11818154 Coxarthrosis
H10R rightf9816253 Coxarthrosis

For the hip joint III, the forces and moments in an implant-based coordinate system are of especial interest. The torque around the shaft axis, for example, is one of the most important parameters for the stability of implant fixation. To transform the forces measured relative to the bone, as delivered by OrthoLoad, to the loads acting in the implant system, the anteversion angle AV of the implant, the CCD angle and the neck length L are required. This data is listed in the following table:

PatientAnteversion Angle AV [degree]CCD Angle [degree] Neck Length L [mm]Shaft Angle Sx [degree]Shaft Angle Sy [degree]
H1L -15.013555.62.3-2.3
H2R -13.8 135 59.34.10.6
H3L -13.8 135 55.64.0-3.0
H4L -18.9 135 63.37.5-1.7
H5L -2.3 135 55.64.0-2.3
H6R -31.0 135 55.65.8-1.7
H7R -2.4 135 63.36.3-1.7
H8L -15.5 135 59.34.6-1.7
H9L -2.3 135 59.34.60.6
H10R -9.7 135 59.61.7-1.2

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Ground reactions forces

Ground reaction forces were measured using two 6 degrees of freedom force plates (AMTI, Watertown, MA). The coordinate system is a right-handed system.

Raw data:

VARIABLE DESCRIPTION UNITS SAMPLE RATE
Fx,y,z 1/2 Ground reaction forces, forceplate 1 and 2 N 960Hz
Mx,y,z 1/2 Moments relative to the original forceplate coordinate system, forceplate 1 and 2 Nmm 960Hz

For the calculation of the center of pressure the following offsets were used. The true origins of the coordinate systems are located below the top surfaces, with a distance (zo).

Processed data

(see Comprehensive Data Sample (http://orthoload.com/comprehensive-data-sample/)):

VARIABLE DESCRIPTION UNITS SAMPLE RATE
Fgrx,y,zi Ground reaction forces, ipsilateral legN90-110 Hz
COP_x,yiCenter of pressure, relative to forceplate center, ipsilateral legmm90-110 Hz
Tz_oTorque around z-axis at CoP, ipsilateral legNm90-110 Hz

grf2f.eof data:

(Downsampled Ground Reaction Forces)

 

VARIABLE DESCRIPTION UNITS SAMPLE RATE
Fgrxi,yi,zi Ground reaction forces, ipsilateral leg N 90-110 Hz
Fgrxc,yc,zc Ground reaction forces, contralateral leg N 90-110 Hz
F Resultant joint contact force (implant) N 90-110 Hz

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Bending Moment

The resultant bending moment Mbend , acts in the middle of the femoral neck and perpendicular to the neck axis, and is calculated with the following formula:

with

The forces (Fx’, Fy’, Fz’) and moments (Mx’, My’, Mz’) are measured in the “implant coordinate system” x’, y’, z’ centered in the middle of the implant head. The force component Fx’ acts laterally, Fy’ anteriorly, and –Fz’ distally along the femur axis. The measured moment components Mx’, My’, and Mz’ turn right around the x’, y’, and z’ axes. N is the distance between the head center and the middle of the femoral neck and is equal to ½ L.

Mtne acts around the neck axis of the femur and represents the torsional loading of the neck. It is calculated by α = -45° rotation of the “bone coordinate system” around the y-axis.

Bending Moment

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Instrumented Crutches

Instrumentes Crutches

Fcont – Contralateral Crutch Force

Fipsi – Ipsilateral Crutch Force

2kN Force Transducer (KM 30z)

 

Instrumentes Crutches
Instrumentes Crutches
Technical data:
Bridge resistance:350 Ohm
Linearity error:0.1%
Hysteresis error:0.1%
Measurement amplifierBA660
Sensitivity:0.5mV/V
Bridge Voltage:5V
Output Voltage:+/-5V
Linearity error:0.02 %
fc output filter:250Hz

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Hip joint

Two different hip implants (Hip I and Hip II) monitor the three force components acting on the ceramic head of the hip joint.

Instrumented implant

Hip I with one 4-channel transmitter

Implant Hip I

The implant is made of a titanium stem and a ceramic head. A compartment, 32 mm deep and 9.5 mm wide, houses the electronic instrumentation inside the neck of the prosthesis. Three semiconductor strain gauges were applied at the lower end of the inner wall and connected to the 4-channel transmitter. Two electrical feed-throughs, welded in the top plate by electron beam, form the transmitter antenna inside the ceramic ball. After the instrumentation, the top plate is welded by laser onto the prosthetic neck, thus sealing the inner space in such a manner that it is absolutely safe against the body.

Since 1988 four instrumented hip joints (Hip I) were implanted in three patients (EBL/EBR, JBR, IBL).

 

 

 

Hip II with two 8-channel transmitters

Implant Hip II

To get more information about a potential temperature increase of hip implant after longer walking distances, an implant with a hollow shaft was instrumented with two 8-channel telemetry transmitters. A common coil in the middle of the shaft supplies power to both telemetry circuits. Inside, eight temperature sensors are arranged along the whole neck and shaft. Three strain gauges placed inside the prosthetic neck monitor the three force components which act at the centre of the ceramic ball. A fourth strain gauge measures the strain of the stem.

One telemetry transmitter is placed inside the prosthetic neck; the second device is fixed inside the hollow shaft of the implant. A 4-lead feed through is welded by laser in the top plate of the neck and forms two single loop antennas for the signal transmission.

Since 1997 five instrumented hollow shaft hip joints (Hip II) were implanted in four patients (KWL/KWR, HSR, PFL, RHR).

 

Coordinate system

Femur system

All forces are reported in a right-handed coordinate system of the left femur (different from hip joint type: Hip III). The load components are reported as -Fx, -Fy, -Fz with negative signs. Positive values therefore indicate components acting toward the femoral head.

 

Femur System Loads
Coordinate system at left Femur

 

In many previously produced >OrthoLoad videos from the hip joint the minus signs are lacking!

The femur system is fixed at the centre of the femoral head. The femoral midline (dotted black/white) intersects with the axis of the neck in point P1. This midline leaves the femur distally at point P2. Point P2 is defined as the deepest point of the fossa intercondylaris at the distal end of the femur. The straight connection between P1 and P2 defines the z axis (marked in red). Perpendicular to z and parallel to a plane through the most dorsal parts of the condyles, the x axis is defined (green) and points medially. The y axis (blue) is perpendicular to x and z and points ventrally.

Implant system

In order to test fatigue or strength of the implant itself, it may sometimes be required to know the force components in an implant-based coordinate system. Axis zi of this system coincides with the shaft axis of the implant. The xi axis lies in the neck-shaft-plane. For the transformation of forces from the femur to the implant system, two angles are required: angle S between the z axis of the bone and the shaft axis of the implant, and the anteversion angle AV of the implant. This data is provided in a table.

Because the angle S is always small, transformation of the force components can be performed with sufficient accuracy by

  • Turning the system by +AV around +z axis 
  • Turning the system by +S around the +x azis

More details about this transformation are given here and in Bergmann et al. (2001)(http://www.ncbi.nlm.nih.gov/pubmed/11410170?dopt=Abstract).

Patients

EBL/EBR (Hip I)IBL (Hip I)JBR (Hip I)
HSR (Hip II)KWL/KWR (Hip II)PFL (Hip II)RHR (Hip II)

Table with basic information about the patients with Hip I and Hip II implants:

PatientImplantSideGenderWeight [kg]Height [cm]Age at Implantation [years]Indication
EBLHip Ileft m6216883Osteoarthritis
EBRHip I rightm6216883Osteoarthritis
IBLHip I leftf8417076Osteoarthritis
JBRHip I right f4716069Femoral head necrosis
HSRHip II right m8217455Osteoarthritis
KWRHip II right m7216561Osteoarthritis
KWLHip II leftm7216561Osteoarthritis
PFLHip II leftm9817549Osteoarthritis
RHRHip II right f60N/A63Osteoarthritis

For the hip joint, the forces and moments in an implant-based coordinate system are of special interest. The torque around the shaft axis, for example, is one of the most important parameters for the stability of implant fixation. To transform the forces measured relative to the bone, as delivered by OrthoLoad, to the loads acting in the implant system, the anteversion angle AV of the implant, the CCD angle and the neck length L are required. This data are listed in the following table:

Patient Anteversion Angle AV [degree]CCD Angle [degree] Neck Length L [mm] Shaft Angle S [degree]
EBL5 135 6010
EBR5 135 6010
IBL14 135 609
JBR10 135 6010
HSR4 135 6210
KWR-2 135 629
KWL17 135 628
PFL23 135 627
RHR34135626

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Transformation of loads

Aus Orthoload Wiki

The loads (forces and moments) were measured in the implant-base coordinate system x’ y’ z’ (IBS). A force vector in the IBS is F’ = (Fx’, Fy’, Fz’), a moment vector is M’ = (Mx’, My’, Mz’). For the implant “HIP JOINT” the IBS was fixed to the left bone, for “HIP JOINT III”, “KNEE” and “SHOULDER” to the right bone. For subjects with implants at the opposite joint, the loads were first mirrored to the other side. Then they were mostly transformed to the bone-based system x y z (BBS). A force vector in the BBS is F = (Fx, Fy, Fz), a moment vector is M = (Mx, My, Mz). Only for the knee joint and the spinal implants they were left in the implant-based system x’ y’ z’.

The example shows the coordinate systems IBS and BBS of an implant of type “HIP JOINT III”. Definitions of the coordinate systems of the other implants are described in the manual under the caption “Implants”.

Relative to the BBS the implant is rotated three times in the order 1, 2, 3. The three rotation angles α1, α2, α3 are stated relative to the axes of the BBS! Their order and values are shown in the window “Info Patient” of the OrthoLoad videos:

In example 1 (implant type “HIP JOINT III”, right-sided implant) the three rotations and their order 1 2 3 are:

  1. clockwise by angle α1 = αx = +2° around axis +x
  2. clockwise by angle α2 = α= -2° around axis +y
  3. clockwise by angle α3 = α= -15° around axis +z

For this right-sided implant “HIP JOINT III”, a negative angle αz indicates an anteversion of the implant neck.

 

In example 2 (implant type “HIP JOINT III”, right-sided implant) the three rotations and their order 1 2 3 are:

  1. clockwise by angle α1 = αx = +17° around axis +z
  2. clockwise by angle α2 = α= +8° around axis +x
  3. clockwise by angle α3 = α= 0° around axis +y

For this left-sided implant an anteversion is indicated by a positive angle αz.

 

For transforming a force from the IBS x’ y’ z’ to the BBS x y z, three transformations have to be performed, using the transformation matrices T11), T22), T33). The complete transformation matrix T’ is then:

T‘ = T33) * T22) * T11) for F = T‘ * F’ (note the inverse order 3 2 1 of matrices!)

 

For transforming the loads from the BBS x y z to the IBS x’ y’ z’, this calculation has to be performed in the reverse order and with negative angles:

T = T1 (-α1) * T2(-α2) * T3(-α3) for F’ = T * F

 

Rotations around the axes x y z are performed by these matrices:

 

For example 1 the complete transformation matrices T’, T are therefore:

T‘ = Tz(-15°) * Ty (-2°) * Tx(2°)        for  F = T‘ *F

T = Tx (-2°) * Ty(+2°) * Tz(+15°)      for  F’ = T *F

 

For example 2 they are:

T’ = Ty (0°) * Tx(8°) * Tz(17°)         for F = T‘ * F

T = Tz (-17°) * Tx(-8°) * Ty(0°)       for F‘ = T * F

Transformations of the moments M and M’ are performed separately in an analogue way.

 

Measuring Units % Body Weight and Newton

In the OrthoLoad videos, the loads are mostly reported in %BW (percent of body weight) for the forces and %BW*m for the moments, except for the spine implants were they are stated in Newton. The subject’s body weight in Newton is stated in the window “Info Patient” (examples see above). To transform loads from %BW/ %BW*m to N / Nm, the forces / moments have to be multiplied by 1% of the body weight, in example 1 by 7.809 and in example 2 by 6.9.

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