Gd-DPTA-2 Diffusion Kinetics in Cartilage are Concentration Independent
Jonathan David Freedman1, Kayelynn Bernier2, Brian Snyder2, Mark Grinstaff1.
1
Boston University, Boston, MA, USA, 2Beth Israel Deaconess Medical Center, Boston, MA, USA.
Disclosures:
J.D. Freedman: None. K. Bernier: None. B. Snyder: None. M. Grinstaff: None.
Introduction: Articular cartilage is the hydrated tissue that provides a smooth, nearly frictionless surface that evenly distributes
applied loads across articular joints. It is comprised of 68-85% water, 10-20% collagen, and 5-10% glycosaminoglycans (GAGs).
Collagen fibrils provide the structural framework that contains the extracellular matrix (ECM). GAGs confer the fixed negative
charge density (FCD) responsible for the retention of water by the ECM, thereby creating a porous structure where applied loads
are supported by pressurization of entrapped interstitial water. Loss of GAG is an early hallmark of osteoarthritis (OA). Delayed
Gadolinium Enhanced Magnetic Resonance Imaging of Cartilage (dGEMRIC), using the anionic contrast agent Gd-DPTA-2 ,
injected intravenously or intra-articularly, has been shown to measure the loss of GAG that accounts for the changes in the
mechanical performance of articular cartilage accompanying OA. Since Gd-DPTA-2 acts as a negatively charged anionic probe, it is
repelled by the negatively charged GAGs comprising the ECM and according to Donnan equilibrium theory equilibrates in inverse
proportion to the GAG concentration of the tissue. Determining the appropriate time required for Gd-DPTA-2 to reach
equilibrium in the cartilage is important for consistent clinical and research applications since measurement of the T1 relaxation
time before Gd-DPTA-2 equilibrium is reached will lead to incorrect calculations of GAG content.
Clinical protocols require the patient to walk or move the joint to be evaluated for ~30 minutes after injection of Gd-DPTA-2
(convection) before the MRI scan is obtained 1.5-3hrs after injection. Depending on the circulating blood volume, the time
constant for partitioning of Gd-DPTA-2 into the synovial fluid and/or through the subchondral bone into the cartilage, as well as
the intrinsic GAG concentration and porosity of the cartilage itself, the effective concentration of Gd-DPTA-2 will vary between
patients. Therefore the purpose of this study was to determine the extent that the rate of diffusion of Gd-DPTA-2 into the
cartilage ECM depends on the concentration of Gd-DPTA-2 in the circulating blood.
The rate of diffusion as a function of the concentration of the contrast agent can be modeled by a 1st order differential
equation: d Phi/dt = C(A[Gd]bath - Phi); where A is a partition coefficient and [Gd]bath is constant. The solution to this differential:
Phi=A[Gd]bath(1-e-t/tau) suggests that the time to equilibrium (1-e-t/tau) is independent of the concentration of the contrast agent in
the circulating blood. To test the hypothesis that the time for Gd-DPTA-2 to reach diffusion equilibrium in cartilage is
independent of the circulating concentration of Gd-DPTA-2, we measured empirically the time for Gd-DPTA-2 to reach diffusion
equilibration in bovine osteochondral plugs as a function of the concentration of the Gd-DPTA-2 bath (10, 25, 50, 75, 100 mM) in
which the osteochondral plugs were submerged.
Methods: Bovine osteochondral plugs (7mm diameter; n =15) were cored from the tibia and femur of freshly slaughtered 1-2
year old cows. The outer margin of each osteochondral plug was sealed with cyanoacrylate. The plugs were kept hydrated in
solutions containing protease inhibitors and antibiotics throughout the experiment. Gd-DPTA-2 solutions of 10, 25, 50, 75, and
100 mM were made by dilution and balanced to 400±10mOsm with sodium chloride. For each of the five concentrations of GdDPTA-2 , three plugs each were immersed in a 50 mL bath of Gd-DPTA-2 and imaged sequentially over time (i.e. at baseline and
after immersion for 1, 3, 6, 9, 12, 18, 24, 48 hours) using a Scanco μCT 40 (Brüttisellen, Switzerland) at 36μm isotropic resolution
(70kVp, 114μA, 300 ms). The image files were converted to DICOM format and post processed to create object maps of the
cartilage at baseline and at subsequent time points using a voxel registration module (AnalyzeDirect, Overland Park, KS). The
concentration of Gd-DPTA-2 that diffused into the cartilage as a function of time and the concentration of the Gd-DPTA-2 bathing
solution was fit to Phi=A[Gd]bath(1-e-t/tau) using a curve fitting tool (MathWorks, Natick, MA). The coefficients of determination
of the fit relationships were evaluated and the dependence of the concentration of the diffused Gd-DPTA-2 into the cartilage
over time as a function of the initial concentration of the Gd-DPTA-2 bathing solution was evaluated by ANCOVA.
Results: The diffusion kinetics for each of the different concentrations of Gd-DPTA-2 (n=3 cartilage plugs/concentration) were fit
to Phi=A[Gd]bath(1-e-t/tau) (Figure 1), the partition coefficient A and time constant tau are given in Table 1. Diffusion of the
10mM concentration of Gd-DPTA-2 into the cartilage by μCT showed a change of <100 HU, which is near the detection limit of
the instrument and therefore the signal to noise ratio of the data was insufficient for robust analysis. For 25, 50, 75 & 100mM
concentrations, A and tau values were not significantly different for the different concentrations of Gd-DPTA-2 (A: F=0.123,
p=0.944; tau: F=0.399, p=0.758). The average value (±SD) of A was 0.38±0.02 and the overall average value (±SD) of tau was
1.45±0.30 hours.
Discussion: In order for the dGEMRIC technique to accurately measure GAG content, the contrast agent must reach equilibrium
within the tissue. Literature examples show the time required to reach equilibrium ranging from 30 minutes to over 29 hours
(Table 2). One possibility is that concentration of the contrast agent plays a role in the time required to reach equilibrium. In this
study we tested this hypothesis at different concentrations ranging from 25mM to 100mM Gd-DPTA-2. Our empirical results
agree with the analytical model and suggest that time for Gd-DPTA-2 to reach equilibrium in the cartilage (i.e. tau value) is
independent of the concentration of the contrast agent (p=0.758). Since the cartilage was cored from the distal femur of young
healthy cows where the cartilage GAG content is quite high and relatively homogeneous it follows that the partition coefficient
should be similar as well (p=0.944). In this experiment, the cartilage and solution were minimally agitated, so accelerated
diffusion by convection was not a factor.
Clinically and in-vivo it is likely that the time required for the contrast agent to reach equilibrium is dependent upon variables
other than concentration gradient of the circulating Gd-DPTA-2. Factors such as the porosity of the subchondral bone, and
perfusion of the synovium will affect the concentration of Gd-DPTA-2 that the cartilage is exposed to at its superficial and deep
zones. Furthermore, the time required for Gd-DPTA-2 to reach equilibrium in the cartilage will most depend on the relative
porosity and GAG content of the cartilage itself.
Significance: Accurate measurements of GAG content by dGEMRIC require that the contrast agent is fully equilibrated within the
cartilage. By varying the concentrations of contrast agent in ex vivo bovine cartilage samples, we demonstrated that the
concentration of the circulating Gd-DPTA-2 solution to influence diffusion equilibrium in the cartilage is minimal and that other
factors intrinsic to the properties of the cartilage itself may be the source of the variability in Gd-DPTA-2 diffusion among
patients.
Acknowledgments:
References: test
Table 1. Diffusion kinetics statistics for fit to Phi=A[Gd]bath(1-e-t/tau).
Concentration
A
tau
R2
25mM
0.3771
1.679
0.9435
50mM
0.3956
1.496
0.9726
75mM
0.3775
1.715
0.9531
100mM
0.3932
1.404
0.9663
Table 2. Literature examples of Gd-DPTA-2 diffusion into cartilage.
Literature Value of Diffusion Time (Hours)
Reference
0.5-1.5 (hip)
Burstein D et al.
2-3 (knee)
Burstein D et al.
1.5-3
Tiderius CJ et al.
>18
Salo et al
8-12 hours
Kallioniemi et al
>29
Silvast et al
ORS 2014 Annual Meeting
Poster No: 0371