Resolution ‘Scaling Law’ in MRI of Articular Cartilage

A recent editorial review in this journal ^[1] discussed whether MRI was fulfilling its promise for molecular imaging of cartilage in osteoarthritis (OA) and related joint diseases. Many issues in the implementation of three MRI techniques (T2, T1rho, and dGEMRIC) were discussed in both clinical and high resolution environments. Although the theoretical bases of these MRI techniques are reasonably comprehensible, quantitative correlations between the values of these MRI parameters and the healthy states of the cartilage tissue have not yet been proved to be reliable and consistent in clinical trials of OA. The authors ^[1] concluded accurately that “the factors associated with cartilage degeneration may have differential and competing effects” on the values of these parameters. In this short note, we would like to participate in this discussion by exploring the influence of an additional factor, the image resolution, in MRI of cartilage, based on our limited experience in microscopic imaging of cartilage using T2 relaxation and in quantitative correlation among several microscopic imaging techniques.

Fundamental Issues in Cartilage Imaging by MRI

Before we try to elaborate on the influence of image resolution in MRI of cartilage, a seemingly trivial factor, let’s first outline some fundamental issues in our quest for better management of arthritis using the molecular imaging methods of MRI.

1. Even though articular cartilage is quite thin, its morphological structure has a distinct depth-dependent heterogeneity across its (thin) thickness. In the simplest sense, cartilage has three sub-tissue zones from the articular surface to the bone: the superficial zone, the transitional zone, and the radial zone. Each of these three zones is distinctly characterized by a different orientation of collagen fibers ^[2–4]. As a result, a bulk MRI measurement is unlikely to be useful in molecular imaging of cartilage because of the averaging of different structures. (It should be noted that MRI is an effect tool in morphological imaging of cartilage, which relates the volume / area / thickness of cartilage tissue to the clinical grade of tissue lesion ^{[5, 6]}.)

2. Articular cartilage curves as a two-dimensional surface at the ends of bones in synovial joint. The biomechanical, physical, morphological, and molecular properties of the tissue from different locations in a single joint surface can have noticeable topographic variations ^[7–14]. Therefore, identifying the precise sampling site where the measurement is done can become an important factor, especially when multiple specimens/subjects are involved in the study.

3. The earliest clinically detectable lesion tends to be localized and small (e.g., occurring near the articular surface at certain topographical locations) ^[15–17]. Therefore, any method for early detection likely needs a wide field of view to survey the surface in order to identify any localized lesion.

4. Because MRI requires a specimen to be placed in a strong magnetic field, the physical orientation of some macromolecules (eg, collagen fibers, muscle fibers) can cause the tissue to behave differently in MRI when the same tissue is oriented differently in the magnet ^[18–21]. For that reason, the physical orientation of the specimen (including human) in the magnet can become important in MRI experiments.

5. The degradation of articular cartilage leading to OA and other diseases is an insidious and continuing process, characterized at different degradation stages by different types of structural and molecular changes ^{[17, 22]}. The mechanisms of these changes exist at multiple levels, including biochemically, molecularly, ultra-structurally, and histologically. Some of these mechanisms may co-exist ‘intrinsically’ while others co-exist because of multiple molecular environments, consequently nulling and voiding any significant outcome.

The Importance of Imaging Resolution

As one can see, these fundamental issues are intricate and convoluted; the solution for one issue could be undesirable for another issue. Except for the issue of competing mechanisms, however, the influence of all other issues towards the outcome of our measurement can be minimized if we can ‘tailor’ the molecular environment within any single voxel (individual volume elements of an image). By improving the image resolution, a smaller voxel can better resolve individual sub-tissue zones, better differentiate topographical variations, better identify local tissue degradations, and better map tissue curvatures. Perhaps more importantly, a smaller voxel could simplify the molecular populations in the volume element, hence reducing the averaging effect of competing mechanisms.

In addition to several of our μMRI studies that used healthy cartilage ^{[14, 23]}, one recent μMRI study in our lab found a number of detectable changes in an animal model of early OA ^[24]. An important feature of these significant OA cartilage findings is their strong topographical dependency on the tibial surface, since they were not significant in the central locations of the tibias where there was no meniscus (i.e., the site/load dependency). To obtain these meaningful results, the transverse pixel sizes of 13.7 μm to 23.1 μm had been used in μMRI. If the resolutions of this tibial OA study were not that high, these significant findings of early lesion would likely be missed.

The ‘Scaling Law’ in Cartilage Imaging

Let’s set aside, for the moment, the immediate sighs of “How can we get a 13.7 μm resolution in clinical MRI?”, and answer a simple question: “Is this microscopic resolution a necessity in human MRI?” In these μMRI experiments of canine cartilage ^[23], the total thickness of the non-calcified tissue was about 650μm. At that resolution, one has about 50 pixels across the entire depth of non-calcified tissue; in other words, each pixel represents approximately 2% of the total thickness of the tissue. So, the question can be rephrased as, “How fast does the morphological structure (hence, molecular environment) change in articular cartilage along its depth?” Since the same pieces of tissue in these studies were also imaged by polarized light microscopy (PLM) at a much higher resolution ^[23], the thicknesses of the sub-tissue zones were known: 49.7±23.8μm for the superficial zone, 100.8±14.4μm for the transitional zone, and 472.8±31.5μm for the radial zone. One can easily see that the thinnest zone in the tissue only had about three pixels across its thickness - this 13.7 μm resolution was therefore not a luxury, but a necessity.

However, this 13.7 μm resolution was a necessity only for a thin piece of cartilage 650μm thick. If we keep the same relative dimensionality (2% thickness per image pixel) in the structural variation of articular cartilage and in cartilage imaging, since the clinically important human cartilage (from knees and hips) is much thicker, we could scale up the resolution requirement and still obtain results comparable to the microscopic studies. We would need a pixel resolution of 27.4 μm for tissue 1.3 mm thick or 41μm for tissue 2 mm thick. A pixel size of 41μm, though it is still a challenge in clinical environments, could conceivably be reachable! (It should be noted that this recommendation for clinical resolution is made purely based on the need to resolve tissue structures in imaging. A discussion of various experimental and technical consequences of this recommendation is beyond the scope of this short note.)

The Importance of Voxel Orientation when the Voxel Size is Not Isotropic

Before we rush to fine-tune our instruments, we need to understand the importance of one more parameter in MRI experiments: the size and direction of the image slice. An ideal MRI protocol for cartilage imaging should use a 3D k-space sampling with an isotropic resolution, which offers several distinct advantages over the 2D slice selection protocol ^{[6, 25–28]}. However, 3D imaging at high resolution is extremely time and computationally consuming; many MRI experiments are done in a 2D (coronal, sagittal, axial) format using the slice selection. The use of slice selection essentially tailors the shape of the individual image voxels from a ‘cube’ to a ‘pencil’. In the 13.7-μm μMRI experiments ^[23], a 1-mm slice thickness was used. So the next question is, what is the best way of orienting this pencil-shaped voxel?

For experiments that characterize the depth-dependent variations in cartilage, one can orient the short dimension of this elongated voxel to be parallel with the tissue thickness, to resolve different histological zones in high resolution. By placing the long dimension of this elongated voxel orthogonal to the radial direction, one can reduce the experimental time and improve SNR. Of course, the topographical variations over the 2D joint surface will cause some structural averaging over this long dimension, and for that one has to consider the ratio of the slice thickness over the joint size. For experiments that study other features of the tissue/tissue degradation, one might want to orient the elongated voxel in some other direction. In essence, if one can tailor the imaging voxel in such a way that the molecular environment inside this volume is the simplest and most homogenous possible, any effect due to partial volume averaging and competing mechanisms would be minimized.

Conclusion Remarks

In summary, in imaging articular cartilage using MRI, the parameter of imaging resolution can have some non-trivial effects on the outcomes of the experiment. By reducing the size of the imaging voxel, one can improve the homogeneity of the molecular environment, consequently reducing any artifacts due to partial volume averaging and/or competing mechanisms. By placing the imaging dimensions carefully, one can optimize the experiments by utilizing the symmetry of the tissue structures. By managing the relative orientation between the specimen (tissue block as well as human) and the direction of the magnetic field, one can manipulate the magic angle effect in cartilage MRI. The goal here is to simplify the molecular environment within each voxel so that the desired mechanisms become dominant.

Based on our limited experience in μMRI of cartilage using T2 relaxation, it seems that a transverse resolution of approximately 2% relative tissue depth per image pixel is a necessity, which, at the present time, poses challenges to the whole-body scanners. However, one needs to recognize that most of the clinical MRI scanners are designed as the generic version of the MRI system, with a primary target in neurological applications and body scans. Valuable information at higher resolutions and the social importance of managing joint diseases are sufficient motivations for all of us to work together to design effective MRI systems around our problem (musculoskeletal conditions) and to develop novel MRI protocols that are exquisitely sensitive to a small set of relevant events in the tissue degradation.

Finally, having a fine spatial resolution in MRI is not going to solve all issues in molecular MRI of cartilage. The competing mechanisms ^[1] intrinsically co-existing at the molecular level will pose the ultimate limit to the potential of the technology. In view of the complex molecular and ultrastructural changes due to early diseases and the interdependent relationships among concentration-structure-property-function in articular cartilage, applying multidisciplinary techniques together can discriminate among the various factors/changes and their influence on the functional integrity of cartilage as a load-bearing biological tissue, thus providing critical information towards the development of novel methods for early detection and effective monitoring of the etiology of cartilage diseases at both clinical and molecular levels.