Measurement of Intervertebral Disc Pressure with T_1ρ MRI

Abstract

The aim of this study is to demonstrate T_1ρ MRI’s capability for measuring intervertebral disc osmotic pressure. Self-coregistered sodium and T_1ρ-weighted MR images were acquired on ex vivo bovine intervertebral discs (N = 12) on a 3 T clinical MRI scanner. The sodium MR images were used to calculate effective nucleus pulposus fixed-charge-density (mean = 138.2±27.6 mM) and subsequently osmotic pressure (mean = 0.53±0.18 atm), while the T_1ρ-weighted images were used to compute T_1ρ relaxation maps. A significant linear correlation (R=0.56, p<0.01) between nucleus pulposus fixed-charge-density and T_1ρ relaxation time constant was observed. More importantly, a significant power correlation (R=0.72, p<0.01) between nucleus pulposus osmotic pressure as predicted by sodium MRI and T_1ρ relaxation time constant was also observed. The current clinical method for assessing disc pressure is discography, which is an invasive procedure that has been shown to have negative effects on disc biomechanical and biochemical properties. In contrast, T_1ρ MRI is non-invasive and can be easily implemented in a clinical setting due to its superior signal-to-noise ratio compared to sodium MRI. Therefore, T_1ρ MRI may serve as a non-invasive clinical tool for the longitudinal evaluation of disc osmotic pressure.

INTRODUCTION

Degeneration of the intervertebral disc (IVD) is the most common cause of back-related disability among North American adults(1). More than 80% of the population will experience an episode of low back pain in their lifetime(2), with recurrence rate as high as 85%(3). Current clinical diagnosis of IVD degeneration is based on radiography and conventional proton T₁ and T₂-weighted MRI. These techniques are useful for observing morphological changes in IVD structure. However, IVD morphological changes tend to occur in the later stages of IVD degeneration(4). The earlier stage of IVD degeneration is typified by the breakdown of extracellular proteoglycan (PG) aggrecans in the nucleus pulposus (NP). As the aggrecans degrade into smaller fragments, they are more likely to diffuse out of the NP extracellular matrix and into the surrounding fluid. The loss of PG’s negatively charged GAG side chains decreases the fixed-charge-density (FCD) of the NP, resulting in the subsequent loss of sodium ions (Na⁺). Since the Na⁺ are the main extracellular solutes responsible for generating an osmotic pressure within the IVD, the aforementioned PG depletion in the IVD’s extracellular matrix leads to decreased IVD hydration and hydrostatic pressure(5,6). Both healthy and mildly degenerated IVDs have been shown to behave hydrostatically(7), and osmotic pressure in healthy IVDs linearly correlate with their hydrostatic pressure(8).

Previous studies have demonstrated that sodium MRI can accurately quantify PG concentration ([PG]) and FCD in articular cartilage under ideal Donnan equilibrium condition(9-11). A recent study has concluded a significant correlation between IVD [PG] measured using dimethylmethylene blue assay and IVD sodium concentration ([Na⁺]) measured with sodium MRI(12). More importantly, the FCD value computed from sodium MRI can be used to calculate IVD osmotic pressure according to a model developed by Urban et al.(13). While sodium MRI is specific for FCD and osmotic pressure, its low signal-to-noise ratio (SNR) significantly limits its role in in vivo applications. Recent studies on T_1ρ MRI have shown great potential for the non-invasive evaluation of [PG] in articular cartilage and in IVD(14-16). Since T_1ρ MRI targets proton nuclei as conventional MRI techniques, it has significantly higher SNR efficiency than sodium MRI, which makes T_1ρ MRI a more clinically viable technique. T_1ρ MRI is implemented as a spin-locking radiofrequency pulse cluster, which can be readily appended to a wide array of radiofrequency pulse sequences on most clinical MRI scanners. During the application of the spin-locking radiofrequency pulse, the transverse spin magnetization undergoes T_1ρ relaxation. During T_1ρ relaxation, spin-dephasing due to processes occurring at frequencies below the spin-locking amplitude is refocused. The resulting relaxation becomes sensitive to the interactions between PG molecules and motionally restricted protons, provided that the frequency of this interaction is close to the spin-locking nutational frequency (γB₁)(17). Numerous studies have already demonstrated that water T_1ρ relaxation (γB₁=0.1~10 kHz) is sensitive to the interactions between macromolecules and motionally restricted protons(18-20). Despite previous works that correlated T_1ρ relaxation and [PG] in fibrocartilage(14-16), the relationship between T_1ρ relaxation and sodium MRI remains to be investigated in a quantitative fashion in the IVDs. More importantly, T_1ρ relaxation time constant has yet to be correlated with IVD osmotic pressure, an important biomechanical property, in intact IVD samples and in a non-invasive fashion.

The current clinical method for assessing IVD pressure is discography, which is an invasive and painful procedure. In addition, discography has potential negative side effects that may warrant additional scrutiny. A previous study has shown that the needle puncture injury caused by discography has both immediate and progressive mechanical and biological consequences on the IVD(21). Therefore, there is a need for a noninvasive method to measure IVD pressure.

In this study, we demonstrated T_1ρ MRI’s clinical significance as a potential non-invasive diagnostic tool for IVD osmotic pressure by establishing a correlation between T_1ρ relaxation time constant and osmotic pressure measured via sodium MRI.

MATERIALS AND METHODS

Bovine Specimen

Four fresh whole veal lumbar spines were obtained from a local abattoir (Bierig Brothers, Vineland NJ), within a few hours of slaughter. The last three caudal IVDs of each spine sample were surgically removed. The vertebral body on each side of the IVD specimen was trimmed with a bone saw to include the endplate and approximately 1 cm of bony tissue, thus each processed IVD specimen contained a single IVD sandwiched between vertebral endplates, preserving the integrity of the motion segment. Next, the specimens were secured to a custom-made platform attached to the scanner bed, as shown in Figure 1. This platform allowed for the interchange of a pair of sodium and proton radiofrequency (RF) coils while the sample remained stationary inside the scanner bore. As a result, the same FOV was preserved between the proton and sodium MR scans, which allowed for the pixel-to-pixel quantitative comparison of sodium and proton MR images.

Figure 1.

Diagram of the imaging platform used for the self-coregistered sodium and T_1ρ MRI. The body of the platform is secured onto the MRI scanner bed using a strap. The IVDs samples are placed at the sample station at the end of imaging platform, where a Velcro strap firmly secures the IVD sample to the imaging platform. The sodium and proton birdcage RF coils can then be slipped over the IVD sample in succession, without disturbing the sample itself. Additional sandbags are placed at the base of the imaging platform to further dampen vibrations contributed by gradient activity during the imaging sessions.

Sodium MR Imaging Protocol for Bovine IVDs ex vivo

Both sodium and T_1ρ-weighted MRI were performed on a 3 T Siemens Trio MRI scanner (Siemens Medical Solutions, Erlangen, Germany) equipped with a broadband transmitter and receiver at the Hospital of the University of Pennsylvania. All experimental procedures were in accordance with IACUC regulations at our institution. First the custom-made sodium low-pass quadrature birdcage RF coil (ω_o = 32.6 MHz) was slipped over the previously mentioned imaging platform. The sodium RF coil was 17 cm in diameter and 12.5 cm long, containing 16 struts. Its two receiver ports were inductively coupled to the coil and spatially oriented 90° relative to each other. Five 10% agarose gel phantoms containing 300 mM, 250 mM, 200 mM, 150 mM, and 100 mM [Na⁺] were imaged alongside each specimen for eventual [Na⁺] calibration (Figure 2). A standard gradient-echo pulse sequence was used to acquire all sodium images. A low-resolution sodium image was acquired prior to the actual 3D sodium MR image acquisition in order to localize the desired FOV. The 3D imaging parameters were as follows: TE/TR = 6/30 ms, Ernst angle = 75.2°, FOV = 15 × 15 cm, matrix size = 128 × 128, slices = 128, slice thickness = 1.2 mm, BW = 60 Hz/Pixel, signal average = 75, imaging time = 10 hours and 14 minutes. Sodium nuclei exhibit biexponential T₂* decay, with both a short and a long T₂* component. However, the relatively long TE in this protocol minimized signal contribution from sodium’s short T₂* component. Thus the sodium signal measured in this study can be approximately modeled as a single exponential. In addition, the broadening of the point-spread-function is minimized by not acquiring sodium signal undergoing the short T₂* relaxation. The small acquisition BW was chosen to maximize the image SNR. The above parameters were chosen to obtain a minimum SNR of 15:1 for an isotropic voxel size of 1.2 mm³. T_1ρ MRI was carried out immediately after sodium MRI during the same imaging session.

Figure 2.

An axial plane sodium image of a representative IVD, surrounded by five sodium phantoms containing different [Na⁺].

Mapping [Na⁺] in Bovine IVDs

The sodium MR images were first smoothed using a 3×3×3 pixel boxcar filter. Next, the pixel-wise [Na⁺] computation based on sodium phantom signals was carried out according to the method described by Shapiro, et al(9). The sodium signals from the sample and the phantoms were corrected separately for T₁ and T₂* decays according to Equation 1.

$$S_{\text{corrected}}=\frac{\sin \left(\theta \right)\cdot (1-e^{-TR∕T_1})\cdot e^{-TE∕{T_2}^{\ast }}}{1-\cos \left(\theta \right)\cdot e^{-TR∕T_1}}\cdot S_0$$ Equation 1

In Equation 1, θ is the flip angle and S_o is the thermal equilibrium magnetization. Sodium T₁ and T₂* of the IVD and phantoms were computed using progressive saturation experiments, yielding T₁ of 22 ms and 23 ms for the IVD and phantoms, respectively. The T₂* of the IVD and phantoms were determined by varying the TE parameter, yielding T₂* of 16ms and 8ms for IVD and phantoms, respectively. After compensating for T₁ and T₂* relaxation, the average sodium signal from each phantom of known [Na⁺] was plotted on a calibration curve of [Na⁺] versus sodium signal. The slope and y-intercept of the linear fit of the calibration curve was then used to compute a 3D [Na⁺] map of the IVD.

Calculating Bovine IVD FCD and Osmotic Pressure

FCD can be directly calculated form tissue [Na⁺] measurement ([Na⁺]_t) and surrounding fluid [Na⁺] measurement ([Na⁺]_f) using a method developed by Lesperance et al.(22). The expression that relates FCD to [Na⁺]_t and [Na⁺]_f is shown in Equation 2.

$$FCD=\frac{{\left[N{a}^{+}\right]}_f^2}{{\left[N{a}^{+}\right]}_t}-{\left[N{a}^{+}\right]}_t$$ Equation 2

In the context of this study, the FCD is computed using a [Na⁺]_f value of 150 mM, which is the normal [Na⁺] level in serum fluid. Osmotic pressure was subsequently calculated from Equation 3 empirically derived by Urban et al.(13). However, the FCD value computed according to Equation 2 is an average FCD measurement of the total NP extracellular sodium. The NP extracellular sodium is in fact composed of both intrafibrillar (relative to the type II collagen fibers) and extrafibrillar water compartments. Intrafibrillar water resides in the space within the collagen fibrils, thus the PGs are excluded from the intrafibrillar volume due to their large size(23). Instead, the PGs are confined within the extrafibrillar water, where they attract the positively charged Na⁺ ions to generate the osmotic pressure necessary to resist loads. Therefore, the effective calculation of FCD should reflect the compartmentalization of Na⁺ ions to the smaller volume of the extrafibrillar water. In fact, the effective FCD (FCD_effective) is always higher than the FCD value calculated from Equation 2, assuming that the extrafibrillar water is always less than the total water content of the IVD NP tissue. With the knowledge of FCD_effective, the actual osmotic pressure of the IVD can be accurately calculated according to Equation 3.

$$P=B\cdot {\left(FC{D}_{\text{effective}}\right)}^2$$ Equation 3

In Equation 3, P is osmotic pressure in unit of atm, B is a constant of 26.6 atm/M², and FCD_effective is the FCD specific to NP extrafibrillar water. In order to compute FCD_effective from FCD calculated directly from sodium MRI, the relative fractions of intrafibrillar and extrafibrillar water compartments in the NP need to be determined first. The relationship between FCD and FCD_effective is defined in Equation 4(23).

$$FC{D}_{\text{effective}}=FCD\cdot \frac{W_{\text{total}}}{W_{\text{water}}-W_{\text{intrafibrillar}}}$$ Equation 4

In Equation 4, the FCD value calculated using Equation 2 is compensated by the ratio of the tissue’s total wet weight (W_total) and the weight of the extrafibrillar water, which is defined as the subtraction of the total water weight (W_water) by the intrafibrillar water weight (W_{intrafibrillar}). Since W_{intrafibrillar} is not easily measured directly, it is expanded in Equation 4 to form Equation 5(23).

$$FC{D}_{\text{effective}}=FCD\times \frac{W_{\text{total}}}{W_{\text{water}}-W_{\text{total}}\times {\stackrel{‒}{W}}_{\text{collagen}}\times {\stackrel{‒}{W}}_{\text{intrafibrillar}}}$$ Equation 5

In Equation 5, the W_{intrafibrillar} term from Equation 4 is expanded as the product of W_total, ${\stackrel{‒}{W}}_{\text{collagen}}$ (dry weight of collagen normalized against W_total) and ${\stackrel{‒}{W}}_{\text{intrafibrillar}}$ (weight of intrafibrillar water normalized per dry weight of collagen). A previous study has concluded that water content constitutes 80% of a healthy adult’s IVD NP(5). Therefore, W_water = 0.8 after normalizing it against W_total. NP collagen amounts to 20% of the dry weight of the NP tissue (24), which yields 0.04 for ${\stackrel{‒}{W}}_{\text{collagen}}$. At last, ${\stackrel{‒}{W}}_{\text{intrafibrillar}}$ for a healthy adult has been shown to be 0.98 g water/g collagen(25). Substituting these values back in Equation 5 and Equation 3 results in the final expression that relates osmotic pressure measurement to the FCD values measured from sodium MRI directly, as shown in Equation 6.

$$P=B\cdot {(1.314\cdot FCD)}^2$$ Equation 6

Equation 6 takes into account the contribution of intrafibrillar water to the total water volume in IVD NP.

Mapping T_1ρ Relaxation Rate in Bovine IVD

Following the sodium MR scan, the sodium coil was removed and a Siemens 8-channel proton birdcage radiofrequency coil was slipped over the imaging platform. T_1ρ MRI was carried out using a custom spin-locking prepared 3D SPGR pulse sequence. The FOV and resolution parameters were identical to those of the sodium MRI. The imaging parameters were as follows: TE/TR = 4.5/120 ms, Flip Angle = 15°, FOV = 15×15 cm, matrix size = 128×128, slices = 64, slice thickness = 1.2 mm. The small flip angle was chosen to allow both the AF and the NP longitudinal magnetizations to recover to their thermal equilibrium during the given TR, which mitigated the need to separately correct for T₁ relaxation in the AF and the NP compartments. Spin-locking preparation was applied once for every 16 phase-encodes, and the phase-encoding was centrically ordered to preserve T_1ρ weighting in the center of the k-space. T_1ρ-weighted images at four spin-locking times (TSL = 10, 20, 30, 40 ms) were collected, with a spin-locking amplitude of 500 Hz, for a total imaging time of 1 hour and 20 minutes. The highest TSL of 40 ms was limited by the SAR restriction on the clinical MRI scanner used. The FOV center and spatial resolution of the T_1ρ scans were copied directly from the previous sodium MRI scans, thus the pixel-to-pixel coregistration between the sodium and T_1ρ MR scans was maintained. A T_1ρ map was computed on a pixel-by-pixel basis from the four T_1ρ-weighted images according to Equation 7.

$$S=S_o\cdot e^{-TSL∕T_{1\rho }}$$ Equation 7

In Equation 7, S is the image signal intensity and S_o is the intensity of the thermal equilibrium magnetization.

Image Processing and Data Analysis for Bovine IVD

All sodium T_1ρ-weighted MR images were transferred to a Macbook Pro computer (Apple, Cupertino, CA) for processing and ROI analysis, which were carried out using algorithms developed with MATLAB software (Mathworks, Natick, MA). For each IVD, a single user (CW) chose a 4mm diameter circular ROI on three mid-axial slices in the T_1ρ-weighted image. The ROIs were then used to extract average [Na⁺] and T_1ρ relaxation time constant values from the self-coregistered [Na⁺] and T_1ρ maps. The average ROI FCD_effective and osmotic pressure measurements were computed from [Na⁺] using Equation 5 and Equation 6 accordingly.

Statistical Analysis

Linear regression analysis was applied to the T_1ρ relaxation time constant versus FCD_effective data. Bivariate correlation of the same data pairs was also carried out, and Pearson correlation coefficient and Spearman’s rank correlation coefficient were computed to determine if there was a direct linear relationship between T_1ρ relaxation time constant and FCD_effective in the NP regions of the IVDs. Regression analysis was applied to the T_1ρ relaxation time constant versus osmotic pressure data. However, due to the non-linear relationship between FCD_effective and osmotic pressure as shown in Equation 6, a power regression analysis was applied to the T_1ρ relaxation time constant versus osmotic pressure data instead of a linear regression analysis. Both the bivariate correlation analysis between T_1ρ relaxation time constant and FCD_effective measurements, and the power regression analysis between T_1ρ relaxation time constant and osmotic pressure data were carried out with the significance level of p<0.01.

RESULTS

Figure 3 illustrates a series of four consecutive axial slices of an IVD [Na⁺] color maps overlaid on top of their grayscale anatomical images. The center of the IVD typically has the highest [Na⁺] value around roughly 250 mM. Since the NP contains the majority of PGs in the IVD, the regions of high [Na⁺] represent the NP region. In contrast, the peripheries of the IVD [Na⁺] maps in Figure 3 indicate a much lower [Na⁺] at around 150 mM, which is close to the theoretical serum fluid level [Na⁺]. The peripheries of the IVD [Na⁺] maps represent the AF region with lower [Na⁺], due to the lack of PGs.

Figure 3.

Four consecutive axial slices of an IVD’s [Na⁺] map. Note the decrease in [Na⁺] going from the center of the NP toward the AF. Ventral side of the IVD faces up.

Figure 4 illustrates four consecutive axial slice T_1ρ maps of the same IVD for which the [Na⁺] maps are shown in Figure 3. As in the case of the [Na⁺] maps, T_1ρ appeared to be the highest in the center of the IVD, where the PG-rich NP is located. In the IVD peripheries composed of the AF, T_1ρ decreased to approximately 30% of the maximum value observed in the center of the NP. In addition, the T_1ρ maps in Figure 4 exhibit superior spatial resolution when compared to the corresponding [Na⁺] maps, which have a blurry appearance.

Figure 4.

Four consecutive axial slices of an IVD’s T_1ρ map. Note the decrease in T_1ρ going from the center of the NP toward the AF. Ventral side of the IVD faces up.

ROI analysis of the NP [Na⁺] maps and the NP T_1ρ maps yielded average FCD_effective (from Equation 5), osmotic pressure (from Equation 6), and T_1ρ relaxation time constant. T_1ρ relaxation time constants were separately compared to first the FCD_effective values and then to the osmotic pressure values. Figure 5(A) contains the scatter plot of average NP FCD_effective vs. T_1ρ relaxation time constant. The solid line marks the linear regression fit of the data points, and it shows a positive relationship between NP FCD_effective and T_1ρ relaxation time constant. A one-tailed bivariate correlation analysis of the FCD_effective vs. T_1ρ data yielded a significant Pearson correlation coefficient of 0.56 with p<0.01, as well as a significant Spearman’s rank correlation coefficient of 0.44 with p<0.01. Due to the squared relationship between FCD_effective and osmotic pressure as shown in Equation 6, a power regression analysis was applied to the osmotic pressure vs. T_1ρ relaxation time constant scatter plot in Figure 5(B), resulting in the expression relating NP T_1ρ relaxation time constant in unit of ms to IVD osmotic pressure in unit of atm, as shown in Equation 8.

$$\text{Pressure}={\left(\frac{T_{1\rho }}{1000}\right)}^{1.6}$$ Equation 8

Figure 5.

(A) A scatter plot of IVD NP FCD_effective measurement vs. the corresponding T_1ρ relaxation time constant. The solid line represents the linear regression line of the scatter plot, with a correlation coefficient of 0.56 at p<0.01. (B) A scatter plot of IVD NP osmotic pressure measurement vs. the T_1ρ relaxation time constant. A power regression fit was applied to the scatter plot, yielding a correlation coefficient of 0.72 at p<0.01.

Equation 8 was obtained with a significant correlation coefficient of 0.72 with p<0.01. Note that T_1ρ was raised to the power of 1.6 in Equation 8, in contrast to the power of 2 for the FCD_effective variable in Equation 6.

DISCUSSION AND CONCLUSIONS

The high [Na⁺] in IVD NP compared to the lower [Na⁺] in IVD AF observed from the colored [Na⁺] maps in Figure 3 is consistent with a previous study that measured IVD [Na⁺] directly and demonstrated significantly lower sodium content in the AF compared to the NP(26). In a similar fashion, the observation of elevated T_1ρ relaxation time constant in the IVD NP and a much lower T_1ρ in the IVD AF supports previous studies that concluded a positive relationship between IVD [PG] and T_1ρ relaxation time constant(16,27). In contrast to IVDs, articular cartilage has been shown to exhibit an opposite relationship between [PG] and T_1ρ relaxation time constant(14,28,29). The discrepancy between the trend of T_1ρ in articular cartilage and IVD degenerations may be due to their different possible mechanisms of degeneration. In articular cartilage degeneration, PG depletion creates space for synovial fluid infiltration, resulting in elevated T_1ρ relaxation time constant. In contrast, PG depletion in IVD leads to decreased hydration and hence decreased T_1ρ relaxation time constant.

The quadrupolar nature of sodium results in a biexponential T₂* relaxation when the rotational correlation time of sodium is long enough to not satisfy the extreme narrowing condition(30). The IVD NP Na⁺ reside in a motion-restricted macromolecular environment composed of cross-linked type II collagen fibers, which results in an increase in sodium’s rotational correlation time. Therefore, the same IVD NP sodium undergoes both short and long T₂* relaxations simultaneously. Thus the measurement of sodium signal undergoing long T₂* relaxation alone along with calibrated phantoms can be used to quantify total sodium content. This technique has been previously demonstrated by a sodium MRI study of articular cartilage, which confirmed that the FCD value computed from sodium images acquired at long TE correlated strongly with FCD value obtained from dimethylmethylene blue PG assay(9).

Moreover, FCD has been previously used to calculate the osmotic pressure of IVD and articular cartilage(13). However, the FCD value obtained from [Na⁺] measured using sodium MRI is in fact a spatially averaged value taking into account both the extrafibrillar sodium and the intrafibrillar sodium of the IVD NP. Since the PGs responsible for generating IVD osmotic pressure are restricted to the extrafibrillar space due to their large size, the FCD calculated according to the expression (Equation 2) developed by Lesperance et al. in theory would result in an underestimation of the effective FCD (FCD_effective) and subsequently an underestimation of the IVD osmotic pressure. In order to address this issue, we determined the relationship between FCD_effective and the FCD value calculated from sodium MRI using literature values of IVD NP intrafibrillar water content and collagen content. The expression of this relationship (Equation 6) was then utilized in the calculation of IVD osmotic pressure. As a result, we demonstrated that the FCD measurement computed using sodium MRI also offers a potentially useful tool for the non-invasive quantification of IVD osmotic pressure, which is an important IVD biomechanical property.

Despite sodium MRI’s promising capability in monitoring IVD NP FCD_effective and IVD osmotic pressure, it has inherently low SNR. Thus, the spatial resolution of the sodium MR scan is often lowered in combination with increased scanning time in order to compensate for its low SNR. Together both the long scanning time and low spatial resolution limit the clinical applicability of sodium MRI. The three primary factors contributing to sodium MRI’s low SNR are listed as follows, in the order of importance. The first factor is the low natural concentration of sodium in tissue. In human body, typical proton density ([H]) is around 110 M while [Na⁺] in healthy IVD is only around 250 mM. The second factor leading to low SNR of sodium MRI is sodium’s lower gyromagnetic ratio (γ=11.26 MHz/T) compared to proton’s (γ=42.57 MHz/T), which results in a smaller measurable thermal equilibrium magnetization. The third factor is the short T₂* of sodium nuclei, which causes rapid relaxation of sodium’s measurable transverse magnetization.

In comparison to sodium MRI, T_1ρ MRI yields significantly higher SNR because it targets proton nuclear spin. Moreover, T_1ρ contrast is sensitive to the interactions between protons on PG and free water protons. Free water proton spin-spin relaxation in IVD NP is partially influenced by the residual dipolar interaction between type II collagen fibers and free water protons. T_1ρ relaxation effectively refocuses the spin relaxation due to residual dipolar interaction, which renders T_1ρ relaxation relatively insensitive to collagen content and more sensitive to PG content and hydration in the IVD. A previous ex vivo IVD study has indeed demonstrated a strong correlation between IVD PG content and T_1ρ relaxation(31). However, to the best of our knowledge, there has been no previous attempt to use non-invasive MRI techniques such as sodium MRI and T_1ρ MRI to compute IVD osmotic pressure in intact IVD specimens.

From the results of our regression and bivariate correlation analyses between T_1ρ relaxation time constant value, FCD_effective, and osmotic pressure, we concluded that T_1ρ is not only linearly correlated with FCD_effective, but also correlated with osmotic pressure measurements, which has been shown to be linearly correlated with the hydrostatic pressure produced by IVDs under normal loading conditions(8). The power regression analysis of T_1ρ relaxation time constant and osmotic pressure yielded Equation 8, which showed that the osmotic pressure measurement was related to T_1ρ raised to the power of 1.6. Note in Equation 6, the FCD_effective variable was raised to the power of 2 for the calculation of osmotic pressure. Assuming a linear relationship between T_1ρ relaxation time constant and FCD_effective, as demonstrated by the significant Pearson and Spearman’s correlation coefficients of their bivariate analysis, the discrepancy between Equation 8 and Equation 6 might be attributed to the fact that Equation 6 was derived from an experiment conducted at 4 °C(13), which is significantly lower than both the body temperature as well as the room temperature at our imaging facility.

In conclusion, we demonstrated that T_1ρ MRI of IVD correlates well with FCD_effective and osmotic pressure measurements obtained from sodium MRI. Due to its non-invasive nature and high SNR, T_1ρ MRI can potentially be readily applied in clinical setting. Therefore, we have shown that T_1ρ MRI has significant potential as a non-invasive clinical tool for the evaluation of IVD osmotic pressure.