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Imaging of Nuclear Magnetic Resonance spin-lattice relaxation
activation energy in cartilage
.
White Rose Research Online URL for this paper:
http://eprints.whiterose.ac.uk/132801/
Version: Supplemental Material
Article:
Foster, RJ orcid.org/0000-0002-5337-3615, Damion, RA, Ries, ME
orcid.org/0000-0002-8050-3200 et al. (4 more authors) (2018) Imaging of Nuclear
Magnetic Resonance spin-lattice relaxation activation energy in cartilage. Royal Society
Open Science, 5. 180221. ISSN 2054-5703
https://doi.org/10.1098/rsos.180221
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Imaging of Nuclear Magnetic Resonance spin-lattice relaxation activation energy in cartilage
R.J. Foster, R.A. Damion, M.E. Ries, S.W. Smye, D.G. McGonagle, D.A. Binks, A. Radjenovic
Supplementary Information
This supplementary information is associated with the publication of the same title in Royal Society: Open Science.
Sample Details
Note that only relevant medical history related to musculoskeletal diagnoses has been included
Sample Identifier Type Details Results Presented
1 G18_11 Human 86 year old female. Main manuscript
2 Bovine Bovine Approx 18month old cow. Harvested approximately within 72hours of slaughter.
Main manuscript
3 G05_11 Human 67year old female, Osteomyelitis Supplementary Information
4 G24_09 Human 65 year old female, Spinal degeneration. Supplementary Information
5 G29_10R Human 66 year old male. Supplementary Information
6 G48_11R Med Human 70 year old male Supplementary Information
7 G48_11R Lat Human 70 year old male Supplementary Information
Imaging Details
Sample Repetition times (ms) Temperatures (C)* Matrix Size Resolution (µ/pixel) 1 200, 500, 1000, 1500, 4000,
8000
9.1, 12.5, 15.8, 20.0, 25.0, 29.4, 34.5
434x256 100x100
2 Varied at different temperatures see below 128x256 70x117
3 200, 500, 1000, 1500, 2500, 4000, 8000
7.1, 12.6, 17.5, 21.5, 27.7, 34.3, 38.8
225x355 70x70
4 200, 500, 1000, 1500, 3000, 5000
10.5, 21.0, 26.9, 30.5, 38.0**
256x256 170x170
5 200, 500, 1000, 1500, 3000, 5000
7.8, 15.7, 22.0, 29.1, 36.9,
185x330 70x70
6 200, 500, 1000, 1500, 3000, 5000
7.7, 15.3, 20.9, 26.0 , 36.3
120x270 100x100
7 110, 200, 300, 500, 1000, 1500, 2000, 4000, 8000, 16000
9.1, 17.0, 24.2, 33.3, 37.8
171x342 70x70
*For all samples (except #4 see note below), the temperature was monitored by a thermocouple within the bore of the magnet, using a standard Bruker NMR configuration. The temperature was automatically monitored during the whole imaging sequence and the temperature of imaging was taking as the (arithmetically fitted) average during the imaging sequence. The error in all temperature measurements is less than ±0.1°C. When changing the temperature, samples were given a minimum of 1 hour to equilibrate at the new temperature before starting the imaging sequence.
**There was a problem with the monitoring thermocouple when imaging this sample. Temperatures were taken as the user observed temperature whilst the imaging sequence was running. The error in these temperature measurements therefore is approximately ±1°C.
Bovine Cartilage (sample 2) imaging details
Sample Temperature
(°C) TR (ms) Averages
Bovine
8.1 295, 458, 634, 824, 1033, 1263, 1519, 1808, 2139, 2528, 2999, 3595, 4407,
5692, 9000 4
14.9 100, 287, 487, 703, 937, 1193, 1475, 1790, 2144, 2551, 3029, 3608, 4340, 5340,
6924, 11040 1
22.3 213, 440, 684, 946, 1231, 1543, 1886, 2268, 2699, 3195, 3776, 4478, 5368,
6582, 8500, 13440 1
30.0 100, 370, 660, 970, 1310, 1680, 2090, 2550, 3060, 3650, 4350, 5190, 6250,
7700, 10000, 16000 2
38.1 622, 966, 1338, 1740, 2181, 2666, 3206, 3816, 4516, 5337, 6331, 7589, 9304,
T1 fitting
[image:3.595.29.532.119.745.2]A number of pixels were chosen at random throughout the cartilage to investigate whether a mono-exponential T1 fit was suitable. Mono-exponential fits were a good fit for all data, with an r2 of greater than 0.99 in all cases within the cartilage tissue.
Figure I shows T1 fits for the same pixel at each temperature imaged. Figure II shows a series of pixels chosen at random from within the cartilage body in sample #3 at 21C.
Figure I. T1 fits for the same pixel at different temperatures. Sample #4 (G24_09).
0 1 2 3 4 5
0 1000 2000 3000 4000 5000 6000 7000 8000 Si g n a l In te n si ty (a rb u n it s)
TR (s)
Model T1SatRec (User)
Equation y = y0*(1-exp(-x/T1))
Reduced Chi-Sqr
4199.1343
Adj. R-Square 0.99931
Value Standard Error
B
T1 1.31751 0.03049 y0 7438.38462 67.50094
0 1 2 3 4 5
0 1000 2000 3000 4000 5000 6000 7000 8000 Si g n a l In te n si ty (Arb U n it s)
TR (s)
Model T1SatRec (User)
Equation y = y0*(1-exp(-x/T1))
Reduced Chi-Sqr
4036.46069
Adj. R-Square 0.99932
Value Standard Error
B T1y0 7470.135821.73179 86.691220.0461
0 1 2 3 4 5
0 1000 2000 3000 4000 5000 6000 7000
Model T1SatRec (User)
Equation y = y0*(1-exp(-x/T1))
Reduced Chi-Sqr
3045.63788
Adj. R-Square 0.99942
Value Standard Error
B
T1 2.0342 0.05549
y0 7206.06908 91.71562
Si g n a l In te n si ty (a rb u n it s)
TR (s)
0 1 2 3 4 5
0 1000 2000 3000 4000 5000 6000 7000
Model T1SatRec (User)
Equation y = y0*(1-exp(-x/T1))
Reduced Chi-Sqr
6849.12341
Adj. R-Square 0.99863
Value Standard Error
B
T1 2.22324 0.10066
y0 7063.28029 155.12553
TR (s)
Si g n a l In te n si ty (a rb u n it s)
0 1 2 3 4 5
0 1000 2000 3000 4000 5000 6000 Si g n a l In te n si ty (a rb u n it s)
Model T1SatRec (User)
Equation y = y0*(1-exp(-x/T1))
Reduced Chi-Sqr
2830.38507
Adj. R-Square 0.99932
Value Standard Error
B
T1 2.50447 0.08652 y0 6709.98166 118.53875
TR (s)
10C 21C
26.9C 30.5C
Figure II T1 fits for a series of pixels chosen at random from within the cartilage at different depths. Imaging at 26.9C. Sample #4 (G24_09).
0 1 2 3 4 5
0 1000 2000 3000 4000 5000 Si g n a l In te n si ty (a rb it a ry u n it s)
TR (s)
Model T1SatRec (User)
Equation y = y0*(1-exp(-x/T1))
Reduced Chi-Sqr
2327.68962
Adj. R-Square 0.9991
Value Standard Error
B T1 1.73727 0.05343
y0 4920.67588 66.06949
0 1 2 3 4 5
0 1000 2000 3000 4000 5000 6000 7000 8000 Si g n a l In te n si ty (a rb it a ry u n it s)
TR (s)
Model T1SatRec (User)
Equation y = y0*(1-exp(-x/T1))
Reduced Chi-Sqr
1332.04997
Adj. R-Square 0.9998
Value Standard Error
B
T1 1.82849 0.02736
y0 7952.55563 53.06312
0 1 2 3 4 5
0 1000 2000 3000 4000 5000 6000 7000
Model T1SatRec (User)
Equation y = y0*(1-exp(-x/T1))
Reduced Chi-Sqr
3045.63788
Adj. R-Square 0.99942
Value Standard Error
B T1y0 7206.069082.0342 91.715620.05549
Si g n a l In te n si ty (a rb u n it s)
TR (s)
0 1 2 3 4 5
0 1000 2000 3000 4000 5000 6000 7000 Si g n a l In te n si ty (a rb it a ry U n it s)
TR (s)
Model T1SatRec (User)
Equation y = y0*(1-exp(-x/T1))
Reduced Chi-Sqr
905.89866
Adj. R-Square 0.99981
Value Standard Error
B T1y0 7069.794112.20151 55.649760.03588
0 1 2 3 4 5
0 1000 2000 3000 4000 5000 Si g n a l In te n si ty (a rb it a ry u n it s)
TR (s)
Model T1SatRec (User)
Equation y = y0*(1-exp(-x/T1))
Reduced Chi-Sqr
1623.25527
Adj. R-Square 0.99936
Value Standard Error
T1 and EA profiles for samples #3-#7
Error bars in T1 are smaller than the size of data points. Samples #1 and #2 are presented in the main manuscript. For all samples, a slice in the imaging sequence close to the centre of cartilage has been used for EA analysis. For
samples #1 - #3 and #5 - #7, this was either slice 4 or 5, in the centre of the imaging package (the exact number depended on the total number of slices used, which varied due to the physical size of the sample). These were chosen so that the slice used for analysis was well away from any effects close to the edge of the sample. The slice number used for each sample is indicated below. For sample #4, only four slices were imaged, but due to the relative larger sample size, all slices were close to the centre of the cartilage. Therefore slice 1 was chosen for analysis in this sample.
Note that the dotted lines are estimated delineations between the PBS and cartilage, and in especially between the cartilage and subchondral bone. A description of how these were estimated is given in the figure caption for Figure 2 in the main manuscript.
Samples #2, #4, #5 and #7 show small changes in T1 with position within the PBS at the highest temperatures, and sample #3 shows a greater scatter in the data at these temperatures. This is due to the fact that the samples were immersed in PBS, but due to the relative size within the imaging tube in the NMR, the surface of the PBS generated artefacts visible in the PBS at higher temperatures. Although the region of interest was chosen carefully to avoid these artefacts, there may have been some segments in the PBS that were affected. In addition, it is possible that there are some edge effects or partial volume effects at the PBS/cartilage interface. Care was taken in the choice of imaging parameters to minimise these artefacts, but it was not possible to completely remove them because the parameters were determined in order to obtain the best T1 data throughout the cartilage tissue.
However, we note that the change in T1 with position at the higher temperatures is small compared to the change in T1 with temperature, meaning that the effect on EA is small. The Arrhenius fits gave a goodness of fit, r2 of greater than 0.8 in all the random datasets sampled for visual checking of the fits.
[image:5.595.51.554.402.619.2]Sample #3 (G05_11)
Figure III T1 and EA profiles for slice #4 of sample #3 (G05_11)
-1000 0 1000 2000 3000
0 2 4 6 8 10 12 14
7.1oC
12.6oC
17.5oC
21.5oC
27.7oC
34.3oC
38.8oC
T1
(s)
Distance into cartilage (µm)
PBS Cartilage Subchondral bone
-1000 0 1000 2000 3000
0 5 10 15 20 25 30 35 40
EA
(kJ/
mo
l)
Distance into cartilage (µm)
Sample #4 (G24_09)
Figure IV T1 and EA profiles for slice #1 of sample #4 (G24_09)
[image:6.595.53.553.310.511.2]Sample #5 (G29_10R)
Figure V T1 and EA profiles for slice #4 of sample #5 (G29_10R)
Sample #6 (G48_11R Med)
Figure VI T1 and EA profiles for slice #4 of sample #6 (G48_11R Med)
-2000 -1000 0 1000 2000 3000 4000
0 1 2 3 4 5 6 7 8 9 10 11
10o
C
21o
C
27o
C
31o
C
38o
C
T1
(s)
Distance into cartilage (µm) G24_09 Slice 1
PBS Cartilage Subchondral bone
-2000 -1000 0 1000 2000 3000 4000 5
10 15 20 25 30 35
EA
(kJ/
mo
l)
Distance into cartilage (µm) PBS
G24_09 Slice 1
Cartilage Subchondral bone
-2000 -1000 0 1000 2000 3000 4000 5000 6000 7000
0 1 2 3 4 5 6 7 8
7.8oC
15.7oC
22.0oC
29.1oC
36.9oC
T1
(s)
Distance into cartilage (µm)
Subchondral bone Cartilage
PBS
-2000 -1000 0 1000 2000 3000 4000 5000 6000 7000 0
2 4 6 8 10 12 14 16 18 20
EA
(kJ/
mo
l)
Distance into cartilage (µm)
Subchondral bone Cartilage
PBS
-2000 -1000 0 1000 2000 3000 4000 5000
0 1 2 3 4 5 6 7 8
7.7oC
15.3oC
26.0oC
36.3oC
T1
(s)
Distance into cartilage (µm)
Cartilage Subchondral bone PBS
-2000 -1000 0 1000 2000 3000 4000 5000 0
5 10 15 20 25 30 35 40
EA
(kJ/
mo
l)
Distance into cartilage (µm)
Subchondral bone Cartilage
[image:6.595.53.550.569.772.2]Sample #6 (G48_11RMed) moved during imaging after the T1 imaging data was obtained at 20.9C (NB: this imaging dataset was the first collected). This dataset was therefore omitted when calculating EA profiles for this sample. The sample did not move further during the imaging session at other temperatures.
Sample #6 was fitted from DICOM images of the datasets.
[image:7.595.50.552.120.329.2]Sample #7 (G48_11R Lat)
Figure VII T1 and EA profiles for slice #3 of sample #6 (G48_11R Lat)
Due to a user error, the datasets for T1 imaging at 9.1 and 17.0C for sample #7 (G48_11RLat) were obtained with the slice packages rotated through 180 in the axial direction. The x and y positions of the slices remained the same. Upon post-processing, theT1-fitted data for each slice in the datasets at 9.1 and 17.0C were mirrored to return them to the same orientation as the datasets obtained at the other temperatures. Note that because the slice packages were rotated by 180, the slice order is reversed for 9.1 and 17.0C datasets.
Sample #7 was fitted from DICOM images of the datasets.
Exponential pre-factor analysis
The Arrhenius plots shown in Figure 3 also allow the exponential pre-factor, A, from the Arrhenius model to be
determined from the fitted intercepts. Figure VIII shows an example dataset of how T1 at 20C, EA and A vary with depth through the cartilage for sample #1 (G18_11).
Figure VIII T1, EA and exponential pre-factor, A, as a function of depth for slice #4 of sample #1 (G18_11)
The pre-factor, A, can be related to a rotational correlation time and this is an extrapolation into the inertial limit of a completely free rotor model (Carper et al, J PhysChem, 100 (1996) p4724). It must be noted though that there is an entropic term within A that is usually not considered in an Arrhenius type analysis.
-1000 0 1000 2000 3000 4000 5000
0 1 2 3 4 5 6 7 8
7.8oC
15.7oC
22.0oC
29.1oC
36.9oC
T1
(s)
Distance into cartilage (µm)
Subchondral bone Cartilage
PBS
-1000 0 1000 2000 3000 4000 5000 0
5 10 15 20 25 30
EA
(kJ/
mo
l)
Distance into cartilage (µm)
PBS Cartilage Subchondral bone
-3000 -2000 -1000 0 1000 2000 3000 4000
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
T1 data (20oC)
EA data 'A' pre-factor
T1
(s)
Distance into Cartilage (m) G18_11 (Sample #1) - slice 4
0 2 4 6 8 10 12 14 16 18 20
EA
(kJ/
mo
l)
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
A (x10
[image:7.595.171.432.516.711.2]Data and Code Accessibility
Data associated with this work are available from the Research Data Leeds repository under a CC-BY 4.0 license at https://doi.org/10.5518/270.
The data for samples #1-#5 is uploaded in raw binary format taken directly from the Bruker NMR (Paravision). The data for samples #6 and #7 is uploaded in DICOM format. These were converted from the raw binary data using Paravision 5.1 (Bruker NMR).
Data for the figures plotted both in the main manuscript and the supplementary information is also uploaded to the same location in a single Excel spreadsheet with tabs labelled for each figure.
The code used for data analysis in this study is available from the Research Data Leeds repository under a GNU LGPL 3.0 license at https://doi.org/10.5518/271.