Relaxivity and diffusion of gadolinium agents in cartilage

Authors

  • Amy Gillis,

    1. Beth Israel Deaconess Medical Center, Boston, Massachusetts
    2. Harvard MIT Division of Health Sciences and Technology, Cambridge, Massachusetts
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  • Martha Gray,

    1. Harvard MIT Division of Health Sciences and Technology, Cambridge, Massachusetts
    2. Massachussetts Institute of Technology, Cambridge, Massachusetts
    3. New England Baptist Bone and Joint Institute, Boston, Massachusetts
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  • Deborah Burstein

    Corresponding author
    1. Beth Israel Deaconess Medical Center, Boston, Massachusetts
    2. Harvard MIT Division of Health Sciences and Technology, Cambridge, Massachusetts
    • Harvard Institutes of Medicine, Room 148, 4 Blackfan Circle, Boston, MA 02115
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Abstract

Prior work indicates that the distribution of Gd(DTPA)2- (as measured by T1) is a good surrogate measure of the distribution of gycosaminoglycan (GAG) in cartilage. In addition to the measured T1 in the presence of Gd(DTPA)2-, the precision of the measurement of Gd(DTPA)2- concentration depends on the T1 without Gd(DTPA)2- (Tmath image), and the relaxivity (r) of Gd(DTPA)2- in cartilage, parameters that are influenced by cartilage composition. These parameters were measured in native and GAG-depleted cartilage in order to estimate the bounds on the values one might expect for cartilage in arbitrary states of degeneration. The range of Tmath image was 0.3 sec; the range of r was 0.6 (mM*s)-1 at 8.5 T and 1.4 (mM*s)-1 at 2 T. These data suggest that Gd(DTPA)2- will be underestimated (and GAG overestimated) if the values for Tmath image and r are assumed to be those of native cartilage. (For example, in a severe case a 90% loss of GAG would be underestimated as a 70% loss.) Gd(HPDO3A) was investigated as a nonionic “control agent” and found to have relaxivity and diffusion properties that were comparable to Gd(DTPA)2- (rGd(HPDO3A)/rGd(DTPA) ≈ 1; DGd(HPDO3A)/DGd(DTPA) ≈ 0.85). Since Gd(HPDO3A) distributes uniformly through cartilage (independent of GAG), the distribution of T1 with Gd(HPDO3A) can be used as a surrogate measure of variations in Tmath image and r, if present. From the perspective of transport, if Gd(HPDO3A) has fully penetrated the cartilage, Gd(DTPA)2- would have in the same time frame. Therefore, the data confirm the efficacy of using Gd(HPDO3A) as a “control agent” for dGEMRIC. Magn Reson Med 48:1068–1071, 2002. © 2002 Wiley-Liss, Inc.

With the development of interventions for the prevalent problem of osteoarthritis, there is a need for improved methods for evaluating cartilage structure and macromolecular content noninvasively both in vitro and in vivo. Several techniques are under development to image the glycosaminoglycan (GAG) and collagen components of cartilage (1–4). In particular, one of the techniques developed to image the GAG component of cartilage is referred to as delayed gadolinium-enhanced MRI of Cartilage, or dGEMRIC. dGEMRIC relies on the fact that GAGs have abundant carboxyl and sulfate sidechains that confer a net negative charge to the matrix. Therefore, the negatively charged agent Gd(DTPA)2- (Magnevist, Berlex Laboratories, Cedar Knolls, NJ) will distribute within the tissue in a spatially inverse relationship to the concentration of negatively charged GAG molecules. T1 in the presence of Gd(DTPA)2- is inversely related to the concentration of Gd(DTPA)2-, and hence directly related to GAG.

Quantification of the correspondence of T1 (in the presence of Gd(DTPA)2-) to GAG (or to Gd(DTPA)2- concentration) involves knowledge of the T1 of the tissue in the absence of Gd(DTPA)2- and the relaxivity of Gd(DTPA)2- in tissue. These values have been previously measured at 8.5 T and room temperature and found to be relatively independent of cartilage tissue composition (5, 6). However, a recent report demonstrates that at low field the relaxivity of Gd(DTPA)2- is dependent on solid volume fraction in several model systems (7). Therefore, the first goal of this work was to evaluate T1 without a contrast agent for cartilage and the relaxivity (r) for Gd(DTPA)2- in cartilage at 8.5 T and 2 T. Both native cartilage and GAG depleted cartilage (through trypsinization) were studied.

One method for validating dGEMRIC involves a comparison of the distribution of Gd(DTPA)2- with the distribution of a “control agent,” ProHance (Bracco Diagnostics, Princeton, NJ), a commercially available nonionic contrast agent (Gd(HPDO3A)) similar to Gd(DTPA)2-. Because of its neutral charge, Gd(HPDO3A) would be expected to distribute uniformly throughout the cartilage tissue, irrespective of the GAG distribution. In order for Gd(HPDO3A) to be used as this control agent, one must also know the relaxivity of Gd(HPDO3A) in cartilage, as well as the kinetics of Gd(HPDO3A) penetration into cartilage relative to the rate for Gd(DTPA)2-. Therefore, the relaxivity measurements described above were also done for Gd(HPDO3A) and the transport properties (diffusion) of Gd(DTPA)2- and Gd(HPDO3A) in cartilage were measured as well.

MATERIALS AND METHODS

T1 Without Contrast Agent (Tmath image) and Contrast Agent Relaxivity

Cartilage plugs for testing were obtained from the femoral condyle of calves. In order to produce GAG-depleted cartilage samples to compare with control samples, some samples were GAG-depleted using trypsin as follows: Each cylindrical cartilage core to be trypsinized was placed in 50 mL of 1:25 dilution of trypsin for 4 hr on a shaker. The cores were then rinsed with Hanks saline solution, each placed in 50 mL of Hanks saline, and then placed on a shaker for 0.5 hr in order to rinse the cores.

Four sets of cartilage plugs were prepared to test the following conditions: 1) Gd(DTPA)2- with intact cartilage; 2) Gd(DTPA)2- with GAG-depleted cartilage; 3) Gd(HPDO3A) with intact cartilage; and 4) Gd(HPDO3A) with GAG-depleted cartilage. The solutions in each case were also tested.

The cylindrical cartilage samples were prepared as 9.5 mm diameter, 4-5 mm thick plugs. For each of the four conditions to be tested, six solution concentrations were examined: Hanks saline and 0.25 mM, 0.5 mM, 1 mM, 1.5 mM, and 2 mM contrast agent in Hanks. All samples were soaked in the appropriate solution for at least 24 hr prior to testing and all samples were brought to room temperature approximately 2 hr prior to testing.

T1 measurements of all solutions and samples were tested at two different field strengths: 8.45 T (DRX system, Bruker Instruments, Billerica, MA), and at 2 T (Biospec system, Bruker Instruments) using a spin echo, inversion recovery sequence (9 TI values from 25–2000 msec for cartilage and 10 TI values from 25–3000 msec for solutions). In all cases, measurements were made at room temperature.

T1 in the absence of contrast agent (Tmath image) was measured directly for both the Gd(DTPA)2- set as well as the Gd(HPDO3A) set of samples.

The concentration of gadolinium for all cartilage samples was measured using high resolution ICP (Element Analysis, Lexington, KY).

The equation relating the gadolinium relaxivity to the concentration of a gadolinium agent and the measured T1 relaxation times is given by:

equation image(1)

where Tmath image is the T1 of the tissue without contrast agent, Tmath image is the T1 of the tissue with contrast agent and r is the gadolinium relaxivity.

r was calculated by plotting ((1/Tmath image) − (1/Tmath image)) versus gadolinium concentration, where Tmath image and Tmath image were measured, and gadolinium concentration was determined by ICP. As seen by Eq. [1], the slope of a straight line fit through the 6 data points for each case was used to obtain r. In this way, relaxivity of Gd(DTPA)2− and Gd(HPDO3A) in saline, intact cartilage and GAG depleted cartilage was calculated at 8.45 T and 2 T.

Determining Diffusion Rates of Gd(DTPA)2- and Gd(HPDO3A) in Cartilage

In order to investigate the transport and steady state distributions of Gd(DTPA)2- and Gd(HPDO3A) in cartilage, cylindrical bovine cartilage plugs (3 mm diameter, 2 mm high) were prepared. One set of plugs was frozen in Hanks saline until the day prior to testing. The other set was GAG-depleted using trypsin (as described above) and then frozen in Hanks saline prior to testing. The day before testing the samples were thawed and hydrated in Hanks saline.

A single plug to be tested was placed in a holder with the top and bottom surface covered, so that it experienced radial diffusion only. The holder was then placed in the gadolinium solution to be tested and imaged over time. Gd(DTPA)2- and Gd(HPDO3A) solutions of from 0.4–0.9 mM were tested. Cartilage cores which were GAG-depleted (n = 2 for each contrast agent) as well as intact cartilage specimens (n = 4 for Gd(DTPA)2-, n = 3 for Gd(HPDO3A)) were tested.

These plugs were imaged across the diameter (so as to visualize the diffusion profile expected to vary radially) at repeated timepoints, thereby providing T1 values of each pixel within the cartilage as a function of time. The T1 values at each pixel location within the cartilage were converted to a gadolinium concentration using Eq. [1]. The values of r and Tmath image were taken from the first part of this study. The average gadolinium concentration was obtained by summing these values over all pixels within the image slice for a given time point. This analysis was done for T1 maps at all time points collected and the data fit to the following equation that describes radial diffusion in a cylinder:

equation image(2)

Ct is the average concentration at time t, Cinfinity is the concentration of gadolinium in the plug at infinite time, a is the radius of the cartilage plug, αn are the roots of the zero-order Bessel function (the first five roots used in the fit), and D is the diffusivity. Cinfinity was obtained from the data by averaging the later data points, after equilibrium had clearly been reached. For all cases this was an average of data beyond 125 min. Diffusivity is the parameter that describes the transport of the contrast agent into cartilage and was therefore determined for both Gd(DTPA)2- and Gd(HPDO3A). All data for each contrast agent was averaged, regardless of the testing solution concentration because, as expected for these low concentrations, the diffusivity was independent of solution concentration.

RESULTS

T1 Without Contrast Agent (Tmath image) and Contrast Agent Relaxivity

The samples in the absence of contrast agent (Tmath image) yielded a range of T1 of about 0.3 sec, with trypsinized cartilage systematically higher than for native cartilage, irrespective of field strength (Table 1). In tissue, Tmath image at 8.45 T was consistently longer than at 2 T; for saline solutions, the Tmath image values at 8.45 T were roughly equivalent to those at 2 T. These values are consistent with previous reports of T1 variations for cartilage in native and degenerated states (6, 8–12).

Table 1. T1 Values Without Contrast Agent(Tmath image)
 SalineIntact cartilageTrypsinized cartilage
  1. The T1 values for saline, intact cartilage, and trypsinized cartilage, in seconds. Each category is the average and SD of two samples.

8.45 T2.75 ± 0.021.57 ± 0.031.88 ± 0.0
2.0 T2.65 ± 0.010.93 ± 0.011.19 ± 0.04

The range of r was 0.6 (mM*s)-1 at 8.5 T and 1.4 (mM*s)-1 at 2 T, in each case trypsinized samples having the lower values (Table 2). Each value for relaxivity was determined from the slope of a best-fit line relating T1 to contrast agent concentration for six independent samples. These fits all had coefficients of correlation >0.99 and a standard error of <4%.

Table 2. Gd Relaxivity Values at 8.45 and 2 T
  SalineIntact cartilageTrypsinized cartilage
  1. The values of relaxivity ((mM*sec)−1) for Gd(DTPA)2− and Gd(HPDO3A). Each relaxivity value was obtained from six samples in each condition, equilibrated in different concentration of contrast agent. The Gd concentration, as determined by ICP for each sample, was plotted against the measured T1s as in Eq. [1]. In each case, the resulting curve fit for relaxivity had an r2 value of greater than 0.99. The numbers are given as the fitted parameter for r ± the standard error of the fit.

8.5 TGd(DTPA)2−4.35 ± 0.104.70 ± 0.074.18 ± 0.14
 Gd(HPDO3A)4.05 ± 0.044.67 ± 0.114.07 ± 0.06
2 TGd(DTPA)2−4.81 ± 0.116.28 ± 0.245.18 ± 0.20
 Gd(HPDO3A)4.41 ± 0.066.51 ± 0.165.12 ± 0.10

In all cases the relaxivity of Gd(DTPA)2- and Gd(HPDO3A) were very close to each other and were not statistically different. The relaxivity was consistently lower at 8.5 T than at 2 T for all samples.

Determining the Diffusion Rates of Gd(DTPA)2- and Gd(HPDO3A) in Cartilage

The equilibrium concentrations of the contrast agents in cartilage are shown in Table 3a. The equilibrium concentration for Gd(DTPA)2- in native cartilage was much less than the bath, as expected due to the charge on the cartilage and on the contrast agent. The equilibrium concentration for Gd(DTPA)2- in trypsinized cartilage was comparable to the bath concentration, as expected due to the lack of charge in the GAG-depleted cartilage. For Gd(HPDO3A) in both intact and trypsinized cartilage, the concentrations in cartilage and bath were comparable, as expected due to the lack of charge on the contrast agent, demonstrating that Gd(HPDO3A) will distribute uniformly in cartilage.

Table 3a. C(cartilageinfinity)/C(bath)
SolutionIntact cartilageTrypsinized cartilage
  1. The final equilibrium concentration of contrast agent in cartilage (Cinfinity) normalized by the bath concentration of contrast agent. In each case, the error of the fit is shown.

Gd-DTPA2−0.40 ± 0.04 (n = 4)0.99 ± 0.01 (n = 2)
Gd(HPDO3A)1.04 ± 0.02 (n = 3)0.97 ± 0.03 (n = 2)

In terms of transport rates, the diffusivity of contrast agent in trypsinized cartilage was slightly higher than control, consistent with previous work on the diffusivity of water in cartilage (13). The diffusivity of Gd(DTPA)2- was slightly higher, but within the same range, as that of Gd(HPDO3A) for both intact and trypsinized cartilage. (None of these differences reached statistical significance.) The standard errors of the fits were consistently less than 10% (ranging from 0.08 × 10-6 to 0.23 × 10-6 cm2/sec for diffusivities on the order of 1.5–2 × 10-6 cm2/sec). The slight differences demonstrated in these 11 samples between Gd(DTPA)2- and Gd(HPDO3A) demonstrate that the two contrast agents are well matched for studies which require the penetration of contrast agent into cartilage.

DISCUSSION

The underlying objective of the studies here was to examine several factors that could potentially confound the approach used by our group and others to calculate GAG concentration from Tmath image measured in tissue equilibrated in fluid containing Gd(DTPA)2-. To that end, we measured T1 without contrast agent (Tmath image), relaxivity (r), and diffusivity (D) in native and trypsinized young bovine cartilage, with the native and trypsinized states intended to be one set of models for two “extremes” one might see in normal vs. severely GAG degenerated tissues.

By assuming that the T1 in the presence of Gd(DTPA)2- corresponds to GAG concentration, one is implicitly assuming that Tmath image and r are constants in the system of interest (see Eq. [1]). However, a recent report by Stanisz and Henkelman (7) demonstrated that r is dependent on solid volume fraction. The experiments described here confirm that both Tmath image and relaxivity are dependent on field strength and cartilage composition. The variation among samples of differing composition is much larger than the within-sample variation, indicating that the differences between samples cannot be explained simply on the basis of measurement noise. Therefore, one must consider these potential confounds when comparing studies at different field strengths and when analyzing heterogeneous cartilage. However, these studies also demonstrate that the range over which Tmath image and r vary is fairly modest even though the native and trypsin-depleted models have relatively extreme differences with respect to GAG composition. Furthermore, as described in more detail below, our data suggest that the confounding effect of variations in Tmath image and r can be assessed by measuring T1 in tissue equilibrated with the nonionic “control agent.”

The measurements of Tmath image and r in this study are within 15% of the relaxivities measured previously for Gd(DTPA)2- at 8.45 T (5). These data are also consistent with the data of Stanisz and Henkelman (7) at 1.5 T, demonstrating higher relaxivity as solid volume fraction increased.

Operationally, we would like to ignore the compositional dependence of Tmath image and r since it would avoid time-consuming, sometimes impractical measurements of these parameters. If the value for native cartilage is used for Tmath image and r at the given field strength, each assumption would lead to an underestimation of the Gd(DTPA)2- concentration, and hence an overestimation of GAG. Consider, for example, a case where a region of tissue had 90% GAG loss. The dGEMRIC technique, analyzed using Tmath image and r measured for native cartilage, would predict a 75% GAG loss. Although this analytical approach decreases the accuracy of measurement of GAG concentration and distribution, for many applications this degree of precision presently exceeds what is needed for meaningful interpretation. Furthermore, assuming that native tissue would be at one end of the spectrum in the MR parameter, the errors would be consistent in underestimating the GAG present, and thus one should still be able to identify and track a depleted region with confidence.

It is important to note that these conclusions are based on experiments performed at room temperature, using calf cartilage, and with one intervention of trypsin degradation leading to an almost complete loss of GAG. (In the studies presented here, GAG in the control cartilage was 73 ± 2.9 mg/ml, whereas in the trypsinized cartilage it was 7 ± 13 mg/ml.) Thus, it is not clear the degree to which these results can be generalized to other systems or to situations in which the cartilage “abnormalities” might be more subtle. These and other data suggest that r will be bounded between a high seen for intact, normal cartilage and a low seen for saline, although it is not possible to predict differences within that range from these data. If this tissue-dependent variability might be of interest or concern, one practical strategy for estimating the variability is suggested by our data. Since Gd(HPDO3A) had similar relaxivities to Gd(DTPA)2- under all conditions (ratio of r for Gd(DTPA)2- to r for Gd(HPDO3A) ranges from 0.97–1.02), and given that it is expected to equilibrate in cartilage for all cartilage conditions (see transport studies), an apparent heterogeneous distribution of Gd(HPDO3A) would signify a distribution of r across the sample. Notably, in earlier studies in humans with apparent lesions seen with Gd(DTPA)2-, the T1 seen with Gd(HPDO3A) was uniform (9), suggesting that in humans the compositional dependent variation in r with these GAG lesions was not significant.

Our data confirm the hypothesis that Gd(HPDO3A) can be used as an in vivo control agent to ensure that the contrast agent has fully penetrated the cartilage. This confirmation derives from two conclusions. First, the equilibrium concentration of Gd(HPDO3A) is independent of GAG concentration (Table 3), and thus should be the same everywhere if the agent has fully penetrated. Second, the transport rates for Gd(HPDO3A) are comparable to those of Gd(DTPA)2- (Table 3). Although the diffusivity of Gd(HPDO3A) is slightly slower than that of Gd(DTPA)2- (for both native and GAG-depleted cartilage), that small difference in diffusivity yields penetration time differences small relative to the observation times employed in dGEMRIC clinical studies. Furthermore, if we are assured that full penetration is reached with Gd(HPDO3A), then for the same time point we can also be confident that full penetration has been reached with Gd(DPTA)2-. On the other side, Gd(HPDO3A) will wash out more slowly, but since clinical studies are done closer to injection time than washout time, the former is of more interest since washout times are on the order of several hours (14).

Table 3b. Diffusivity (× 10−6 cm2/sec)
SolutionIntact cartilageTrypsinized cartilage
  1. The fitted diffusivity value for the Gd contrast agents in cartilage. The numbers are given as mean ± SD of the fitted diffusion coefficient for the number of samples listed. The standard deviation of the fit for individual samples ranged from 0.08 to 0.23 × 10−6 cm2/sec.

Gd-DTPA2−1.84 ± 0.12 (n = 4)2.08 ± 0.34 (n = 2)
Gd(HPDO3A)1.55 ± 0.22 (n = 3)1.83 ± 0.01 (n = 2)

In summary, prior work indicates that the distribution of Gd(DTPA)2- as measured by the distribution of T1 is a good surrogate measure of the distribution of GAG in cartilage. The precision of the measurement of Gd(DTPA)2- concentration depends on the T1 without Gd(DTPA)2- (Tmath image) and the relaxivity of Gd(DTPA)2- in cartilage, parameters that are influenced by cartilage composition. The data here suggest that the dependence of Tmath image and relaxivity on tissue GAG composition is relatively small, but does lead to an underestimation of Gd(DTPA)2- (overestimation of GAG). Thus, in evaluating regions of cartilage that appear to be GAG-depleted by dGEMRIC, the GAG depletion is possibly more severe than predicted. Gd(HPDO3A) was investigated as a nonionic “control agent” to the Gd(DTPA)2- studies; the relaxivity of Gd(HPDO3A) was the same as Gd(DTPA)2- under all conditions. Therefore, since Gd(HPDO3A) distributes uniformly in cartilage, the distribution of T1 with Gd(HPDO3A) can be used as a surrogate measure of variations in Tmath image and r, if present. The diffusivity of Gd(HPDO3A) in cartilage was 15% lower than the diffusivity of Gd(DTPA)2-, demonstrating that if Gd(HPDO3A) has fully penetrated the cartilage, Gd(DTPA)2- would have in the same time frame. Therefore, the data confirm the efficacy of using Gd(HPDO3A) as a “control agent” for dGEMRIC, something that may be desirable in situations where there is a question of nonuniformity of Tmath image or r, or a question of whether Gd(DTPA)2- has fully penetrated the cartilage.

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