Osteoarthritis (OA) is a degenerative disease of the joint, with an estimated prevalence of 18% in the United States [1], of which progressive cartilage disease is considered to be the most important characteristic. Magnetic resonance imaging (MRI) is considered the gold-standard for the non-invasive assessment of cartilage. Since cartilage degeneration is not reversible, a prompt diagnosis of local damage that precedes cartilage tissue loss is of crucial importance to guide early-stage treatment. The cartilage T₂ relaxation time is considered as a biomarker for early cartilage damage and degeneration, as it has been shown to be correlated with changes in several attributes of the extracellular matrix, such as its anisotropy, water content and collagen concentration [2, 3]. Most studies have so far been based on two-dimensional (2D) T₂ mapping sequences. However, due to the complex three-dimensional (3D) structure of cartilage, an isotropic 3D acquisition is required I) to perform a high-resolution quantitative analysis of cartilage T₂ value in 3D that can be reformatted in an arbitrary direction, and II) to obtain a higher signal-to-noise (SNR) ratio compared to multiple 2D acquisitions and thus a higher T₂ precision in T₂ determination. In this study, we therefore propose an isotropic 3D T₂ mapping technique that consists of separate sequential T₂-prepared 3D gradient recalled echo (GRE) images, which allows for co-registration of these separate images to account for motion. This protocol was optimized through Bloch equation simulations and a phantom study, and validated in healthy volunteers.

The pulse sequence consists of a segmented centric GRE acquisition with repetition time TR=4.2ms, echo time TE=1.76ms, 100 k-space lines per segment, segmental acquisition time=700ms and incremental adiabatic T₂ preparation (T₂prep) durations of 0, 23, 38 and 53ms. Numerical simulations of the Bloch equations were performed using Matlab (The Mathworks, Natick, MA). The goals of these simulations were: I) to find the optimal sequence parameters (RF excitation angle, number of excitations per segment) to maximize the signal per unit of time and II) to determine an empirical T₂-fitting offset to correct for T₁ relaxation [4] in the following equation:

$$S(TE_{T2prep})=S_{0}\cdot e^{\frac{TE_{T2prep}}{T_{2}}}+\delta,$$

where S₀ is the initial signal when T₂prep= 0ms and δ is the empirical offset determined through Bloch equation simulations. To calculate the T₂ map, the signal S was fitted with the above-mentioned empirical equation in each pixel. To assess the accuracy of the fixed empirical offset, the T₂ map of a custom-built agar-NiCl₂ phantom with 3 compartments was acquired with the following additional parameters: adiabatic T₂prep, voxel volume= 0.82×0.82×0.82mm³, matrix size= 208×216×112, total scan time=9min20s, RF excitation angle 15°, 2×GRAPPA acceleration. Spin-echo (SE) relaxation time mapping was then used as a reference standard to determine the T₁ (1072ms) and T₂ (33.2ms) values of the phantom at 3T (Prisma, Siemens Healthcare). Finally, a T₂ map of the knee was acquired in 6 healthy adult volunteers (4 right and 2 left, 3 male and 3 female with an average age of 29.5±4.8 years) with the same parameters as in the phantom experiments. Rigid 3D image registration followed by pixel-wise T₂-mapping was performed in Matlab and the average T₂ in regions of interest was calculated. T₂ values were reported as average ± standard deviation over all volunteers.

Bloch equation simulations resulted in an empirical offset of 0.003, which was confirmed in the phantom study (Fig. 1). The phantom study furthermore demonstrated a homogenous T₂ distribution (T2=34.3±1.4ms) in the compartment with the relaxation times that approximated cartilage (Fig. 1, outer ring), which agreed with the spin-echo reference T₂ value (33.2±0.4ms). Similarly, the T₂ maps in the volunteers resulted in T₂ values of 28.7±4.3ms and 28±2.5ms for tibial and femoral cartilage, respectively (sagittal plane, Fig. 2a, standard deviation within the region of interest less than 15%), which agrees well with the values reported in literature [5]. Moreover, the isotropic 3D T₂ mapping technique allowed the quantification of the patellar cartilage T₂ value in the axial plane (37.5±2.6ms, Fig. 2b, standard deviation within the region of interest less than 15%). The tibial and femoral cartilage layers could consistently be visualized and T₂ value could also be quantified in the coronal plane in all volunteers (Fig. 3, 4).This study successfully demonstrated that an isotropic 3D T₂ mapping is feasible for knee cartilage characterization and results in precise T₂ values.