Patent Application
20210373102
The present disclosure generally relates to a method of determining (i.e. measuring and calculating) the ordered water in biological tissues to reveal their specific constituents' microstructural integrities such as in articular cartilage with degenerated collagen.
The background description provided herein is for the purpose of generally presenting the context of the disclosure. Work of the presently named inventor, to the extent it is described in the background section, as well as aspects of the description that may not otherwise qualify as prior art at the time of filing, are neither expressly nor impliedly admitted as prior art against the present disclosure.
Magnetic resonance R2 imaging of ordered tissue exhibits a well-known magic angle effect that tends to overshadow pathological changes in the ordered tissue. Consequently, it is challenging to reliably diagnose early degeneration of ordered tissue (e.g., such as cartilage) in clinical practice.
Generally speaking, water is ubiquitous and it is not as uniform as it appears in living systems. Many highly structured (i.e., highly ordered) tissues can be found in the human body, including peripheral nerves, white matter, skeletal and myocardial muscles, tendons and articular cartilage. Magnetic resonance (MR) imaging of these specialized tissues exhibits a well-known orientation-dependent phenomenon, referred to as magic angle effect, predominantly in transverse R2 relaxation measurements. In the last two decades, the compositional MR imaging has received great attention in characterizing early cartilage degeneration secondary to osteoarthritis (OA), a common joint disease affecting mostly an aging population and young athletes after surgical treatments on anterior cruciate ligament (ACL) injuries.
One of the hallmark features of OA is a progressive loss of cartilage and no disease-modifying drug is available to date. Hence, it is especially critical to have an effective noninvasive imaging means to detect early cartilage degradation in order to prevent further adverse OA progression with potentially new therapeutic interventions or simply regular diet modifications. To this end, a number of advanced MR imaging techniques have been developed, two of which in particular have been investigated extensively in clinical studies, i.e. water proton R2 (1/T2) and longitudinal R1ρ (1/T1ρ) relaxation in a rotating frame.
To date, the biophysical mechanisms underlying R2 and R1ρ relaxations, induced by water and structural protein interactions on relatively slow time scales, had been controversial despite being widely used and a growing body of clinical evidence is shedding light on which structural protein has been probed. More than 50 years ago, Berendsen discovered that water bound to collagen triple-helix secondary structures give rise to an orientation-dependent MR resonance doublet splitting and then proposed that bound water form a chainlike structure along collagen fibers in hydrated cartilage. This orientation-dependent MR phenomenon was later rediscovered by Fullerton et al. in clinical MR imaging of tendon and then investigated in-depth by others with high-field and high-resolution microcopy MR imaging techniques on various cartilage samples, some of which were enzymatically degraded to deplete a specific structural protein such as collagen (CA) or proteoglycan (PG). The reported relaxation measurements from these CA− and/or PG− depleted samples revealed that the water-CA interactions in terms of residual dipolar coupling (RDC) is the dominant relaxation mechanism in clinical R2 and R1ρ studies in which the static magnetic fields B0 are usually less than or equal to 3T.
It was not without any contention regarding this dominant relaxation mechanism, and the chemical exchange (CHEX) effect in terms of water-PG interactions was also considered, and great effort has been made to enhance clinical imaging data acquisitions and standardize the pulse sequences across different imaging systems. However, no convincing clinical evidence has yet been demonstrated to corroborate the proposed mechanism. On the contrary, many clinical and experimental studies have provided substantial data to substantiate RDC as the prevailing relaxation mechanism. For instance, Xia et al. showed that the measured R2 at 7T on canine cartilage specimens decreased about 10-20% after PG depletion when the samples were orientated at the magic angle (i.e. RDC=0). Had these measurements been carried out at 3T instead of 7T, the reported decreases in R2 due to PG− depletion would have been reduced to a few percent, implying that the CHEX effect will not significantly contribute to R2 and R1ρ at 3T.
Retrospectively, it was Mlynarik et al. who provided indisputable evidence to unravel the above-mentioned controversy. He concluded that R2 and R1ρ in clinical studies (B0≤3T) were mainly induced by RDC resulting from the slow anisotropic motion of water molecules restricted in the collagen matrix. In a recent comprehensive study of relaxation anisotropy on bovine patellar cartilage samples at 9.4T, a very large number of MR relaxation metrics had been investigated in-depth and anisotropic R2 was found to be the most sensitive metric to cartilage degenerative alterations. In order to effectively and efficiently extract this potential relaxation parameter, a novel approach based on a single T2W sagittal image, referred to as anisotropic R2 of collagen degeneration (ARCADE), was proposed as an alternative to a time-consuming and much involved composite relaxation metric R2-R1ρ, which had been demonstrated to measure only an incomplete anisotropic R2 in clinical studies.
Although good progress has been made so far in measuring anisotropic R2 in standard clinical studies without significantly lengthening scanning time, it is still challenging to make the reliable diagnosis of early cartilage degeneration because of the well-known magic angle effect. This grave situation has been clearly highlighted in a recent study, showing that the changes in R2 and R1ρ values due to the magic angle effect could be several times more than that caused by cartilage degeneration. As a result, the potential of the compositional MR imaging as a biomarker for cartilage degeneration has been compromised particularly for the diagnostic purpose. Therefore, it is crucial to develop a novel method to overcome the magic angle effect and yet to retain the intrinsic sensitivity of anisotropic R2. Currently, a few initial attempts have been made to uncouple the magic angle effect; unfortunately, the most important sensitivity to the underlying microstructural changes was also lost in those proposed methods by either lengthening echo-time (TE) or utilizing T1 relaxation (e.g. in MT sequence) that is not specific to any involved constituents in cartilage extracellular matrix (ECM).
Water proton magnetic relaxation is not only one principal factor governing an exquisite and diverse soft-tissue contrast in clinical MR imaging, but also one powerful tool for studying in detail the structural and dynamical information about water molecules in various biological systems. In this regard, the field-dependent longitudinal relaxation R1ρ dispersion in a rotating frame has been revealed to provide a unique insight into water-macromolecule interactions. To some extent, R1ρ can be viewed as transverse relaxation R2 under the influence of a spin-lock (SL) RF pulse, and it is sensitive exclusively to low-frequency water molecular interactions. As early as 1970s, R1ρ had been used to investigate pathophysiological changes in biological tissues. About 20 years later, the first R1ρ imaging study of articular cartilage to characterize osteoarthritis (OA) was reported, and since then, considerable efforts have been made to develop and standardize R1ρ mapping methodology across primary MR scanner platforms in clinical environments.
R1ρ mapping of articular cartilage has been motivated by the diagnostic and research-based utility of a noninvasive and sensitive imaging method, which could detect early cartilage degeneration in the absence of advanced macroscopic changes apparent on standard anatomical MR imaging. When R1ρ was first proposed as a promising MR biomarker for characterizing changes in proteoglycan (PG) content—a major biochemical component in articular cartilage, the specificity of R1ρ changes to PG alterations was unclear and this topic has remained a point of controversy. For instance, two early studies from the 2000s did not support the concept that R1ρ itself could be a sensitive biomarker of PG in OA cartilage, and, to date, a large amount of clinical data has been in agreement with the findings from these two landmark studies.
It has been suggested that R1ρ dispersion rather than R1ρ itself was sensitive to early cartilage degeneration, and the proposed composite relaxation metric R2-R1ρ has substantiated this concept. As previously shown, R2-R1ρ is merely a two-point R1ρ dispersion in which R2 is basically an R1ρ acquired with the SL RF strength ω1/2π=0, and R1ρ is normally measured with ω1/2π=500 Hz. Most importantly, a theoretical framework of R1ρ dispersion has been outlined for highly structurally-ordered tissues such as articular cartilage, and the observed R1ρ dispersion can be associated directly with those water molecules contained within the triple-helix interstices from collagen microstructure. Thus, R1ρ dispersion can be potentially exploited as a specific MR biomarker to detect early collagen degeneration in joint OA or collagen accumulation in some tissue fibrosis.
In order to utilize R1ρ dispersion imaging in clinical studies, a reliable acquisition protocol that does not significantly lengthen imaging time is required. Currently, the developed 3D MAPSS sequence can be considered as the state-of-the-art R1ρ mapping of knee cartilage, and it is being promoted as a standard across different MR scanners. This dedicated R1ρ mapping strategy was established from the widely used magnetization-prepared turbo-FLASH sequence in which RF phase cycling and tailored excitation angles were employed to mitigate the potential imaging artifacts. These imaging artifacts could be respectively induced during the SL preparation by non-uniform B0 and B1 fields, and during imaging readout by transient magnetization evolution towards steady-state (i.e. T1 relaxation effect).
Although R1ρ can be accurately quantified with 3D MAPSS, the scan time is doubled when compared with a standard albeit inaccurate R1ρ mapping with no RF phase cycling. Furthermore, this advanced 3D MAPSS sequence was initially designed for R1ρ mapping (i.e. with one ω1/2π) but not for R1ρ dispersion (i.e. with multiple ω1/2π). Thus, it is unclear to what extent the prepared SL magnetization will be compromised by 3D MAPSS particularly when ω1/2π becomes relatively small.
The various SL schemes reported in the literature have not been tailored to R1ρ dispersion but rather optimized for some specific R1ρ mapping scenarios using an extreme ω1/2π at higher B0 fields.
In one embodiment, a computer-implemented method is provided. The computer-implemented method comprises: acquiring, by a processor, a magnetic resonance image of an ordered tissue; measuring, by a processor, based on the magnetic resonance image of the ordered tissue, an R1ρ dispersion of the ordered tissue; deriving, by a processor, R2a(α) and τb(α) for the ordered tissue based on the measured R1ρ dispersion of the ordered tissue; calculating, by a processor, an orientation-independent order parameter S for the ordered tissue, using the following equation:
and determining, by a processor, based on the orientation-independent order parameter S for the ordered tissue, a level of degeneration of the ordered tissue.
In another embodiment, a system is provided. The system comprises a magnetic resonance imaging (MRI) device configured to capture a magnetic resonance image of an ordered tissue; one or more processors; and one or more memories storing instructions. The instructions, when executed by the one or more processors, cause the one or more processors to: measure, based on the magnetic resonance image of the ordered tissue, an R1ρ dispersion of the ordered tissue; derive R2a(α) and τb(α) for the ordered tissue based on the measured R1ρ dispersion of the ordered tissue; calculate an orientation-independent order parameter S for the ordered tissue, using the following equation:
and determine, based on the orientation-independent order parameter S for the ordered tissue, a level of degeneration of the ordered tissue.
In still another embodiment, a tangible, non-transitory computer-readable medium is provided. The tangible, non-transitory computer-readable medium stores executable instructions that, when executed by at least one processor of a computing device, cause the computing device to: acquire a magnetic resonance image of an ordered tissue; measure, based on the magnetic resonance image of the ordered tissue, an R1ρ dispersion of the ordered tissue; derive R2a(α) and τb(α) for the ordered tissue based on the measured R1ρ dispersion of the ordered tissue; calculate an orientation-independent order parameter S for the ordered tissue, using the following equation:
and determine, based on the orientation-independent order parameter S for the ordered tissue, a level of degeneration of the ordered tissue.
Table 1 illustrates partitioned transverse relaxation R2 absolute (1/s) and relative (%) rates, average orientation-dependent R1ρ dispersion parameters τb
(μs) and
R2a(θ)
(1/s), and derived order parameters S (10−3) in the deep zone from four bovine patellar cartilage specimens at 9.4T. Note, θMA(°) and τex (μs) represent respectively an orientation with a minimal R2 and a chemical exchange correlation time. All data are reported as mean±standard deviation.
Table 2 illustrates average measured and modeled R1ρ dispersion parameters in the femoral, tibial and patellar cartilage from one live human knee. All data are reported as mean±standard deviation.
Table 3 illustrates tailored spin-lock RF durations (“spin-lock time” or “TSL”) and strengths or powers (PWR, i.e. ω1/2π) for the constant magnetization preparations (Mprep) used in quantitative R1ρ dispersion imaging protocol. Note that these specific values were determined assuming R2i=R2a20 (1/s) and τb=300 (μs).
Table 4 illustrates simulated noisy R1ρ dispersion quantification under influences of various SNR, with (+) and without (−) an internal reference. The key input model parameters were given as follows: R2i=R2a=20 (1/s) and =τb=300 (μs), and simulations were performed for different prepared R1ρ magnetization (Mprep). The group of “All” includes all three Mprep groups, i.e. 50%+60%+70%. Note that an order parameter S (10−3) of 2.052 can be determined herein given the values of R2a and τb.
Table 5 illustrates quantitative dispersion with (+) and without (−) an internal reference (REF1) for two radially-segmented ROIs (i.e. SZ and DZ of the tibial cartilage) from the first subject's left knee. Note that the “All” group includes all three Mprep groups, i.e. 50%+60%+70%, and the fitting results for DZ are displayed in
Table 6 illustrates quantitative dispersion (=60%) of all knees (n=6), with the second subject (i.e. S2L01 and S2L02) and the third subject having their left knees re-scanned 3 months later. In Table 6, “L” means left; “R” means right; and “S” means subject.
Table 7 illustrates repeated synthetic and measured (=500 Hz) for the second and third subjects. In Table 7, “DZ” means deep zone; “Exp” means experimental or measured; “Syn” means synthetic; and “SZ” means superficial zone.
The present disclosure provides systems and methods for analyzing ordered tissue to calculate an orientation-independent order parameter S that is sensitive to the collagen microstructural integrity in cartilage.
This orientation-dependent order parameter S may be utilized to characterize the degeneration of ordered tissue, such as cartilage, in clinical settings. A theoretical framework for developing this orientation-independent order parameter S was formulated based on R1ρ dispersion coupled with an oversimplified molecular reorientation model, where anisotropic R2 (i.e. R2a(θ)) becomes proportional to correlation time τb(θ) and an orientation-independent order parameter S can thus be established. This new methodology was corroborated on the publicly available orientation-dependent (θ=n*15°, n=0-6) R1ρ dispersion (ω1/2π=0, 0.25, 0.5. 1.0. 2.0 kHz) of bovine cartilage samples at 9.4T and R1ρ dispersion (ω1/2π=0.125, 0.25, 0.5, 0.75, 1.0 kHz) on one live human knee at 3T.
The τb(θ) derived from orientation-dependent R1ρ dispersion demonstrated a significantly high correlation (r=0.89+0.05, P<0.05) with the corresponding R2a(θ) on cartilage samples, and a moderate correlation (r=0.51, P<0.01) was found in human knee. The average order parameter S (10−3) from bovine cartilage was almost two times larger than that from human knee, i.e. 3.90±0.89 vs. 1.80±0.05.
The order parameters derived from R1ρ dispersion measurements are largely orientation-independent and thus lend strong support to the outlined theoretical framework. The promising results from this study could have great clinical implications in expanding the compositional MR imaging beyond its current applications.
The present disclosure further provides an efficient and robust R1ρ dispersion mapping of human knee cartilage using tailored spin-locking in an optimized 3D turbo-FLASH sequence.
That is, a new spin-lock (“SL”) method has been proposed for quantitative R1ρ dispersion of human knee articular cartilage (
The differently prepared Mprep evolution towards steady-state during turbo-FLASH imaging readout can be translated into a varying k-space filtering effect, resulting in a biased R1ρ. An image will be completely free of such systematic errors only if the k-space filter remains constant for all k-space lines. One approach to achieving this goal is to tailor Mprep into a narrow range; however, this reduced dynamic range in Mprep could inevitably introduce additional uncertainty in determining R1ρ when fitting the near constant R1ρ-weighting to an exponential relaxation decay model.
In particular, the present disclosure provides an efficient and robust R1ρ dispersion imaging protocol for human knee cartilage clinical studies. Specifically, the present disclosure provides a novel method to prepare a near constant Mprep by tailoring both SL RF duration (TSL) and ω1/2π, and the limited dynamic range in Mprep will be expanded by exploiting extra information derived from the magic angle (MA) location or when ω1/2π=∞. Hence, the present disclosure provides an efficient and robust method for quantitative R1ρ dispersion imaging of human knee articular cartilage. Advantageously, this method allows comparable image quality to be obtained with about a 30% reduction in scan time compared to standard R1ρ mapping.
Systems and Methods for Analyzing Ordered Tissue to Calculate an Orientation-Independent Order Parameter S that is Sensitive to the Collagen Microstructural Integrity in Cartilage
The transverse relaxation R2 of water proton in cartilage is largely induced by a dominant intramolecular dipolar interaction (R2dd) and an increasing chemical exchange effect (R2ex) as the static magnetic field B0 increases. Specifically, R2dd stems from preferentially orientated water in collagen, where the bound water is fixed by two hydrogen bonds connecting with neighboring chains in triple-helix interstices. As a result, an effective <H—H> dipolar interaction vector tends to align along the principal axis of collagen fibers as shown in
These three contributions to R2 can be categorized into different two groups, depending on their orientation dependences or the time scales of water-protein interactions. For instance, R2a(θ) is orientation-dependent in contrast to R2i and R2ex. In the meantime, R2ex and R2a(θ) are only sensitive to slow time scale interactions and thus can be suppressed in R1ρ measurements depending on the spin-lock RF strength (ω1) and the relevant correlation time (τb) and chemical exchange time (τex) for CA− and GAG− water interactions as given in EQUATION 2.
Note, τex−1 is redefined here as the average, instead of the sum, of the rate constants of the forward (kAB) and reverse (kBA) reactions. Apparently, R1ρ will turn respectively into R2 or R2i when ω1 is absent or sufficiently strong (i.e. ω1>>τb−1 and τex−).
When it becomes significant, R2ex can be further separated from R2dd based on either the former's B02 dependence or the latter's orientation dependence. R2ex is normally quantified with pApBΔω2(2πex), with pA/B and Δω representing molecular fractions and an angular chemical shift difference in and between A (—OH in water) and B (—OH in GAG) states. On the other hand, R2a(θ) can be written as R2a3 cos2 θ−1
2/4, with an angle θ formed between B0 (+Z) and an effective residual dipolar interaction vector ({right arrow over (OA)}) along a principal axis ({right arrow over (n)}) in collagen fibers as depicted in
Regarding the water-CA interactions responsible for R2a(θ), it seems more realistic and revealing to characterize {right arrow over (OA)} in a dynamic picture using an axially symmetric molecular reorientation model as shown in 3 cos2 θ−1
in R2a(θ) will be mathematically transformed into
3 cos2 β−1
(3 cos2 α−1)/2, where angle brackets
. . .
indicate a time or an ensemble average. As a result, R2a(θ) can be quantified by two different terms that are grouped in two pairs of curly brackets in EQUATION 3.
The first term contains a scaled dipolar interaction constant Sd, with a scaling factor S defined as 3 cos2 β−1
/2 and d a constant of √{square root over (3/10)}(μ0/4π) (γ2hr−3), e.g. d=1.028*105 (s−1) with a distance r of 1.59 (Å) between two proton nuclei in water. In literature, S was referred to as an order parameter—a measure of water molecular reorientation restrictions. For instance, S could have become zero had the bound water been orientated randomly in collagen. The second term is directly related to the well-known magic angle effect, where the correlation time τ⊥ characterizes a much slower molecular reorientation (i.e. τ⊥>>τ∥) about an axis perpendicular to {right arrow over (n)}, and is considered to be associated with different processes of breaking and reforming the hydrogen bonds mediated by the bound water in collagen triple-helix interstices. For this oversimplified model, only one correlation time τ⊥ is adequate to characterize the bound water anisotropic molecular motion.
It is noteworthy that EQUATION 3 can be derived by simplifying a general form of anisotropic R2 equation by assuming an axially symmetric model for a preferential water orientation in collagen. It is also worth pointing out that the rotational axis ({right arrow over (n)}) relative to B0 (i.e. α) could be arbitrarily manipulated; however, the intrinsic bound water's bonding property β or S should not be altered in the orientation-dependent MR relaxation studies on cartilage. This observation basically suggests that R2a(α) should be proportional to τb(α) regardless of collagen orientations, with τb(α) representing τ⊥(1−3 cos2 α)2/4. As a result, an orientation-independent order parameter S can be calculated using EQUATION 4 if R2a(α) and τb(α) could be derived from R1ρ relaxation dispersion.
The uncertainty in S can also be determined if the measurement errors in R2a(α) and τb(α) are available using the standard error propagation formulas. Note, the different orientation symbol (α vs. θ) is irrelevant in EQUATION 4.
Seven orientation-dependent R2(θ) and standard R1ρ (θ, ω1) dispersion (θ≈n*15°, n=0-6; ω1/2π=0.25. 0.5. 1.0. 2.0 kHz) measurements on bovine patellar cartilage-bone samples (n=4) were performed at 9.4T by others, and the corresponding relaxation depth-profiles were publicly available and used in this study. More details can be found in the original publication.
One human volunteer's right knee was studied with R1ρ (1/T1ρ) dispersion in the sagittal plane using a 16-ch T/R knee coil on a research-dedicated Philips 3T MR scanner. 3D T1ρ-weighed images with varying spin-lock (a) times (TSL=1, 10, 20, 30 and 40 ms) were acquired with a SL-prepared T1-enhanced 3D TFE pulse sequence, where five SL RF pulse strengths (ω1/2π=0.125, 0.25, 0.5, 0.75, 1.0 kHz) were used for different R1ρ mappings. The acquired voxel size was 0.40*0.40*3.00 mm3 and interpolated to 0.24*0.24*3.00 mm3 in the final reconstructed images. Total scan duration was about 45 minutes.
The orientation-depth maps of R2(θ) and R1ρ(θ, ω1) were reproduced using a slightly modified matlab script provided in the original study, with a linear interpolation replaced by a spline version to avoid undefined profiles on the map edges. This study focused only on the deep cartilage where average relaxation rates were calculated for further analysis. The deep zone was defined within a normalized depth range between 40% and 80% from the articular surface.
The chemical exchange contribution (R2ex) was first separated based on the orientation-dependence of R2(θ) and the specific dispersion of R1ρ(θMA, ω1). In modeling R2(θ), the sample orientation θ was allowed to float within a limited range of [−30°, 30°] to account for the potential errors in positioning samples and the actual orientation deviations of collagen fibers, Then, R1ρ (θ, ω1), excluding R2ex, was fitted to a function of A+R2a(θ)/(1+4ω12τb2(θ)) for different θ, where A, R2a(θ) and τb(θ) were model parameters. Subsequently, S was derived from each pair of the fitted R2a(θ) and τb(θ) at different orientation B not close to BMA (i.e. <50° or 35°). Finally, average S and its standard deviation for each bovine patellar sample were calculated.
TABLE 1 tabulates the categorized R2 absolute (1/s) and relative (%) relaxation rates, the fitted magic angles θMA, τex (μs), the average R2a(θ)
and the average
τb
in terms of the data ellipse centroids and S for each sample. The model parameter ranges were constrained in in nonlinear χ2-based curve-fittings: R2a(θ)=[0, 300] (1/s); R2i and R2ex=[0, 30] (1/s); τex and τb=[101, 103] (μs). If the determined model parameters were equal to the predefined limits or their relative errors were large than 100%, they had been excluded for further analysis.
3D R1ρ-weighted images were first co-registered following an established protocol, and R1ρ pixel maps with different ω1/2π were produced by curve-fittings to a simple exponential decay model (two parameters). Next, the angular and radial segmentations were performed on the femoral, tibial and patellar cartilage and ROI-based three parameters (R2i, R2a(θ) and τb(θ)) were fitted using EQUATION 2 with R2ex set to zero, and average order parameter S was reported for all three cartilages in TABLE 2 including the descriptive statistics for varying R1ρ dispersion and modeling parameters as well. As described above, the ranges of the model parameters for R1ρ dispersion and the criteria in selecting the accepted fitted parameters were the same as those used in bovine cartilage samples.
The differences and correlations between any two relaxation metrics were quantified using the Student's paired t-test (a two-tail distribution) and the Pearson correlation coefficient (r), with the statistical significance considered at P<0.05. Inter-group comparisons were evaluated using box-and-whisker plots and histograms, and the potential correlations between any two parameters were visualized in scatterplots with 95% confidence level data ellipses overlaid. All measurements are shown as mean±SD unless stated otherwise. All image and data analysis were performed using in-house software developed in IDL 8.5 (Exelis Visual Information Solutions, Boulder, Colo.).
To further separate R2ex from R2i, a particular R1ρ dispersion fitting was carried out at θMA (C), resulting in the fitted R2i of 10.4±0.2 (1/s), R2ex of 5.6±0.2 (1/s) and τex of 161.7±12.9 (μs), respectively. A typical modeling of R1ρ dispersion (θ=20°), excluding R2ex, is also presented (B) with the fitted R2i of 11.3±3.3 (1/s), R2a(θ) of 86.3±5.3 (1/s) and τb(θ) of 459.0±28.7 (μs), respectively. These exemplary analyses indicate that an anisotropic R2a was the dominant (90%) contribution to R2, and R1ρ dispersion was orientation-dependent.
TABLE 1 summarizes the average R2 partitions, R1ρ dispersion modeling parameters, average τb(θ)
and average
R2a(θ)
and the derived order parameter S for each of four samples, showing that the chemical exchange effect (R2ex) contributed about 3% to R2 and the determined magic angle θMA (64.4±8.9°) deviated from an assumed 54.7°. More importantly, the derived τb(θ) demonstrated a significantly high correlation (r=0.89+0.05, P<0.05) with the corresponding R2a(θ) as predicated despite varying linear relationships for different samples as shown in
In the present disclosure, a theoretical framework to derive an orientation-independent order parameter S for the bound water in collagen through R1ρ dispersion is provided and corroborated on bovine patellar cartilage samples at 9.4T and one live human knee at 3T. The proposed order parameter S can be considered as an intrinsic MR probe reflecting the microstructural integrity of highly organized tissues. Since the developed method is not only limited to cartilage, it could be extended to other structured tissues in clinical studies. For example, R1ρ dispersion has been used for characterizing myocardial fibrosis and the relaxation mechanisms underlying the proposed novel non-contrast cardiac magnetic resonance (CMR) index could be elucidated if using the similar approaches as discussed in the present disclosure.
The present disclosure describes the first attempt to separate the magic angle effect from MR relaxation measurements and yet to retain the most relevant water bonding information in highly organized tissue. To date, the compositional MR relaxation study on ordered tissue was only useful for longitudinal investigations in which the magic angle effect would be automatically decoupled if the tissue at the same location is considered. With the proposed method, however, it is possible to make the reliable diagnosis on the focal degenerative changes relative to other intact cartilage on the same knee, which could have a great impact on the diagnosis of early cartilage degeneration in clinical practice.
Five different correlation times are generally required to adequately characterize an anisotropic molecular motion according to the classical NMR relaxation theory; however, the number of these correlation times can be reduced to three if an axially symmetric model is assumed. In this scenario, the three pertinent correlation times will be constructed from two independent ones (e.g. τ∥ and τ⊥) that characterize the molecular reorientations about and perpendicular to the axially symmetric rotational axis. If an additional assumption is made such that τ⊥>>τ∥, as discussed in the present disclosure, the only relevant correlation time will be the much slower one (τ⊥); in other words, an anisotropic molecular reorientation with an oversimplified axially symmetric model can be treated as a conventional isotropic molecular rotation characterized with a large effective correlation time.
Accordingly, R2 and R1ρ will become sensitive to these slow time scale molecular interactions between water and collagen but not for R1, which depends only on fast time scale molecular motions. It cannot be stressed enough that R2 (ω1/2π=0) is the most sensitive metric for the slow time scale interactions given various R1ρ relaxation dispersions. Recently, a composite relaxation R2-R1ρ was proposed as an early predictor of cartilage lesion progression, which simply states that R2 is more sensitive than R1ρ regardless of the exact relaxation mechanism for the slow time scale molecular interactions. It is also worth mentioning that the relative change rather than the absolute value of R1ρ should be used to characterize cartilage degeneration. This interpretation differs from some previous reports that R1ρ itself was considered as an important MR biomarker for early cartilage degeneration.
The collagen fibers in articular cartilage are commonly categorized into a superficial (parallel), a transitional (arcading) and a deep (perpendicular) zone based on the preferential direction of the fibers relative to cartilage surface. Had the cartilage surface been perpendicular to B0 and the collagen fibers in the deep zone been perpendicular to the cartilage surface, the minimum R2 should have been detected at the magic angle θMA of 54.7°. However, an average θMA estimated in this study was offset by about 10° from the expected value. These unexpected observations could be partially explained by either that the cartilage surface was not exactly perpendicular to B0 or that the collagen fibers were not exactly perpendicular to the cartilage surface. In either case, the routine experimental setup for relaxation measurements would become tedious if consistent results are expected from repeated scans. Nevertheless, the developed method provided in the present disclosure could make such relaxation studies less demanding as the orientation-dependent factor has been taken out of the equation in the proposed order parameter S.
Order Parameters from Normal Cartilage
In this study, the derived S from bovine patellar cartilage samples had demonstrated both intra- and inter-sample variabilities (
It is not surprising that S could be indicative of varying biomechanical properties for different cartilage, given the molecular basis of the bound water in collagen. For instance, S from an asymptomatic human knee cartilage was estimated to about 2.0*10−3 (
Order Parameters from Modified and OA Cartilage
For the very reason underlying the water bonding, the proposed order parameters could be an essential MR biomarker for early cartilage degeneration. This potential utility was documented with one R1ρ dispersion study at 9.4T on both enzymatically modified bovine patellar cartilage samples and human tibial cartilages with early and advanced OA. In that work, the derived correlation times τb was investigated and suggested as a fundamental biophysical MRI contrast. As explained in the present disclosure, τb and anisotropic R2 are not only correlated with each other but also dependent on the same geometric factor.
As a result, the corresponding order parameters S could be estimated for human OA cartilage and biochemically degraded bovine cartilage samples as shown in
A judicious design for an efficient R1ρ dispersion imaging is conceivable in future research, which can not only reduce potential involuntary motion artifacts but also facilitate the implementation of the proposed method into a routine clinical imaging protocol. One possible approach could be a constant time R1ρ dispersion in which the varied parameter would be a spin-lock RF amplitude instead of its duration. Once an efficient R1ρ dispersion protocol becomes available, other highly organized tissues (e.g. myocardium) could be explored to elucidate the relevant relaxation mechanism in the diseased state (e.g. fibrosis) and thus the specific structural protein could be clinically investigated.
The results from applying this new concept to both ex vivo and in vivo articular cartilage studies demonstrate that an orientation-independent order parameter S that is sensitive to the microstructural integrity of highly ordered tissues can be established from R1ρ dispersion. It is foreseen that the developed unique approach will broaden the current spectrum of the compositional MR imaging applications in clinical practice.
As shown in
Bloch simulations using various rotation matrices were carried out to evaluate the improved SL performance using a relatively broad range of ω1 and Δω0 suitable for human knee cartilage imaging at 3T. Specifically, ω1/2π increased evenly from 0 to 1000 Hz and Δω0/2π from 0 to 250 Hz in 101 steps to simulate spin dynamics starting from an equilibrium state. Since only the longitudinal component of the prepared magnetizations will be mapped out by the FLASH imaging sequence, the transverse components were thus excluded for further considerations. In these simulations, the nominal flip angle (FA) α and β were scaled down 90% to mimic inhomogeneity reported for human knee cartilage imaging at 3T. Also, any relaxation effects during RF flipping, refocusing and SL were not considered, i.e. α and β were treated as hard pulses.
The steady-state longitudinal magnetization (Mss) from magnetization-prepared spoiled FLASH sequence does not depend on an initial condition (Mprep), but rather is a function of the constant excitation FA of α0, repetition time TR, and longitudinal relaxation time constant, T1, of the tissue, as shown by EQUATION 5,
where M0 is the magnetization in an equilibrium state, and E1=exp (−TR/T1). The transient magnetization (MN) immediately before an excitation RF pulse, αN, could be written as EQUATION 6,
M
N
=M
SS+(Mprep−MSS)(E1 cos α0)N (6)
where Mprep is the prepared R1ρ-weighted magnetization (normalized), ranging potentially from −1 to 1 depending on the phase of the flip-back RF pulse as well as TSL and ω1/2π. Hence, an average of the measurable magnetization (
={sin α0/(N−1)}Σ0N−1MN (7)
Consequently, an optimal α0 for each Mprep could be identified given the knowledge of N, TR and T1. In this work, simulations were performed with the following parameters: TR=6.8 ms and T1=1240 ms, α0 ranging from 0° to 24° and Mprep from 0 to 100% for each N (i.e. 32, 64, 96, 128). In vivo experiments were conducted on the first subject's left knee to validate the predicted optimal FA (see below).
The signal strength in R1ρ-weighted cartilage image could be expressed by EQUATIONS 8-9, assuming a negligible chemical exchange contribution to R1ρ at 3T.
Here, R2i stands for a non-specific isotropic relaxation component, R2a(θ) for a specific anisotropic contribution and τb for the corresponding slow (˜μs-ms) reorientation correlation time for those motion-restricted water molecules in collagen. Generally, R2a(θ) is written as R2a3 cos2 θ−1
2/4, with θ an angle between the collagen fiber direction and B0; thus, R2a(θ) will become zero when θ is at the MA of 55°.
The prepared SL magnetization, Mprep=S(TSL, ω1)/S0, is determined by the user-defined parameters TSL and ω1; thus, a near constant Mprep could be generated by imultaneously increasing or decreasing both parameters, given that other related parameters (R2i, R2a and τb) are constant. Eight different combinations of TSL and ω1 values for three Mprep preparations (i.e. 50%, 60% and 70%) were listed in TABLE 3, with an assumption of R2i=R2a=20 (1/s) and τb=300 (μs).
According to EQUATION 9, R1ρ will become R2i when θ=55° or ω1=∞. This fact was exploited to increase the dynamic range for the constant Mprep preparation, where the signal derived with θ=55 could be considered as that with ω1=∞. This extra information is referred to as an internal reference (REF), i.e. REF1 for θ=55 and REF2 for ω1=∞.
Simulated Quantitative R1ρ Dispersion with Noise
Monte Carlo simulations were performed to evaluate the accuracy and precision of R1ρ dispersion quantification with and without an REF. An R1ρ dispersion profile was generated based on EQUATIONS 8-9 following the protocols listed in TABLE 3, with S0=100, R2i=R2a=20 (1/s), TSL ranging from 9 to 32 ms, ω1/2π from 0 to 1000 Hz and τb=300 (μs). As shown before (5), an orientation-independent order parameter S (10−3) can be determined given the values of R2a and τb, and it was 2.052 herein when using a constant K of 1.0561010 (s−2) in S=√{square root over ((R2a/τb)(1/1.5K))}.
Next, the simulated data were contaminated with Gaussian noise leading to 9 signal-to-noise ratios (SNRs) from 20 to 100. Here, the SNR was defined as S0/σ, with σ standing for the standard deviation (SD) of the Gaussian noise. These defined noises were generated from normally distributed random numbers with zero mean and different variance depending on SNR. The noisy R1ρ dispersion profile was generated 1000 times for each SNR with Mprep=50%, 60%, 70%, respectively. An REF data were calculated for each of eight TSL values with ω1=∞. Thus, each Mprep group would have had 16 different R1ρ-weighted datasets had the REF data been used. In order to assess to what extent a biased REF could have compromised R1ρ dispersion quantification in a realistic scenario, a noiseless dataset was prepared with S0=100, R2i=15 (1/s), R2a=20 (1/s) and τb=200, and then an erroneous REF was created using a biased R2i with a relative uncertainty (ΔR2i) ranging from −100% to +100%.
From these 1000 simulations, the mean and SD of each of the fitted R1ρ dispersion parameters were calculated. The accuracies of these estimated parameters were evaluated in terms of the root mean square error (RMSE) defined by
√{square root over (Σi=0j{(Pfiti−Ptrue)/Ptrue}2/(j−1))}*100%
where Pfiti and Ptrue were the fitted and the true (input) values, and j was 1000 in this study. Here, the SD of the fit was considered as the fitting precision.
Three consented volunteers part of an IRB-approved clinical study evaluating post-traumatic OA after anterior cruciate ligament (ACL) surgical reconstruction were recruited and their asymptomatic knees were investigated using the developed R1ρ dispersion imaging protocol (see below). The first subject had a bilateral knee scanned using Mprep of 50%, 60% and 70%, while the second and the third subjects only had a single knee imaged using Mprep of 60%. In addition, several extra R1ρ imaging scans (see below) were collected to confirm the predicted optimal FA, and to compare the derived R1ρ values with those reported in the literature. Particularly, the second and the third subjects had their knees re-imaged 3 months later using both the developed (i.e. improved) R1ρ dispersion and standard (i.e. original) R1ρ mapping protocols.
Eight constant R1ρ-weighted images for each of three Mprep preparations were acquired with an optimized 3D turbo-FLASH sequence (see
The acquisition parameters different from those listed above are as follows: ω1/2π=500 (Hz); TSL=1, 10, 20, 30, 40 (ms); SL method =“rotary-echo” (see
Comparison of R1ρ-Weighted Images with Different FA
One R1τ-weighted scan (TSL=9 ms, ω1=0) from the developed R1ρ dispersion protocol was repeated with FA of 9°, 11°, 15° and 17° on the first subject's left knee in order to compare with that from an optimum 13°.
The SNR of the developed R1ρ dispersion imaging was not measured in this study, but it was inferred from the previously acquired five repeated datasets (TSL=1 ms, ω1/2π=0) using the preliminary R1ρ dispersion protocol based on the standard mapping as aforementioned. The signal mean and SD from each of segmented ROIs in those R1ρ-weighted images were calculated and an average SNR was thus assessed respectively for the femoral, tibial and patellar cartilage compartments.
The measured R1ρ-weighted data were fitted to EQUATIONS 8-9 using a free nonlinear curve fitting IDL script based on the Levenberg-Marquardt algorithm (http://purl.com/net/mpfit). Specifically, there were two independent variables (TSL and ω1) and four model parameters (S0, R2i, R2a and τb) in this special fitting. The measurement uncertainties for these observed signals were set to unity; accordingly, the output formal 1-sigma fitting errors were scaled so that the reduced chi-squared X2 values were approximately equal to one.
The model fit parameters were constrained as follows: S0=[100, 1000]; R2i=[1, 20] (1/s); R2a=[0.5, 100] (1/s) and τb=[1, 1000] (μs), with initial values set respectively to 500, 10, 20 and 250. If fitted parameters were equal to the boundary values or their relative uncertainties exceeded 100%, these fits would be excluded from further analysis. The goodness of fit was loosely defined by R2, indicating to what extent the observed R1ρ dispersion profile could be explained by the fitted model. Paired student's t-tests were used to assess R1ρ differences obtained from between the previous R1ρ mapping methods and the proposed R1ρ dispersion protocol, with significant differences denoted by P<0.05. All measurements are shown as mean±SD unless stated otherwise, and all image and data analysis were conducted with an in-house software developed in IDL 8.5 (Harris Geospatial Solutions, Inc., Broomfield, Colo., USA).
Two key components in the SL prepared turbo-FLASH sequence are illustrated in
R2i=R2a=20 (1/s), and τb=300 (μs), where 8 black circles traced an approximately constant Mprep of 50% trajectory. The Mprep contour plots with τb=100, 200, 300 (μs) and with τb=150 (μs) and R2i=15 (1/s) are respectively displayed in
If an REF had not been reliably identified in reality, the expected (red sold line) R1ρ dispersion characterization would have been compromised (black solid line) as revealed in
For different N and initial Mprep, an optimal FA could be calculated (
The SNR of R1ρ-weighted image was estimated using previously acquired datasets (n=5); specifically, the femoral, tibial and patellar cartilage had respectively SNR of 66.5±13.6, 107.0±23.5 and 69.3±13.9. Although some original acquisition parameters (e.g. FA, voxel size and SL scheme) had been altered, the developed (i.e. improved) R1ρ dispersion imaging protocol could still generate a comparable SNR, as demonstrated by two overlaid line profiles (
It was clear that R1ρ became significantly (P<0.01) less dispersed in the superficial zone (SZ) than in the deep zone (DZ), with the least at the MA orientation; specifically, the fitted R2a(1/s), τb (μs) and S (10−3) were respectably 14.8±0.9 vs. 27.6±1.3, 205±17 vs. 104±8 and 2.13±0.11 vs. 4.07±0.19 in the SZ and DZ. Further analyses for each group were also performed and the fitted R2i, R2a, S and τb, with (+) and without (−) an REF1, are tabulated in TABLE 5.
As revealed in
An exemplary quantitative cartilage R1ρ dispersion (Mprep=60%) of the third subject's left knee is presented in
With respect to the fitted R2a and τb (
Synthetic and Measured R1ρ with ω1/2π=500 Hz
Considering the femoral DZ only from the second (
A measured (red) and a synthetic (blue) R1ρ distribution are compared in
Furthermore, the overall synthetic R1ρ from these two subjects, as tabulated in TABLE 7, was not significantly (p=0.71) different from that measured by the state-of-the-art 3D MAPSS sequence, i.e. 24.4±6.0 vs. 23.6±2.9 (1/s), suggesting that the developed R1ρ dispersion imaging protocol was also less sensitive to the transient magnetization evolution artifacts. These reported R1ρ relaxation rates would have become 41.0±10.2 vs. 42.4±5.2 (ms) if they had been expressed with T1ρ relaxation time constants (i.e. T1ρ=1/R1ρ).
This work presents an efficient and robust R1ρ dispersion imaging protocol that can provide a unique MR imaging biomarker specifically related to collagen changes in highly ordered tissues such as human knee articular cartilage in clinical studies. This new method was developed based on previous findings including R1ρ relaxation dispersion mechanism, and corroborated by in vivo knee imaging and simulation studies. The comparison results suggest that much more detailed R1ρ dispersion characterization could be attained within a similar scan duration normally used for the conventional R1ρ mapping.
Although a plethora of in vivo knee cartilage R1ρ mapping research has been performed in the past, only two quantitative R1ρ dispersion studies can be found in the literature. The functional form of R1ρ dispersion turned out to be a kind of Lorentzian function regardless of the reported relaxation mechanisms. The so-called inflection point (ωip) on R1ρ dispersion profile could be determined by setting the second derivative of such a Lorentzian function to zero, which is directly linked to the characteristically slow molecular motion time scale, i.e. 1/τb=2√{square root over (3)}*ωip based on EQUATION 9. The measured ωip values on in vivo human knee cartilage at 3T have been reported previously, and an average τb (μs) was calculated as 262±58, with a minimum and maximum of 168 and 420, respectively. These rough estimates are in good agreement with previous findings. Therefore, it was not unreasonable to select τb of 300 μs for numerical simulations and for determining the tailored TSL and ω1 values as listed in TABLE 3.
An empirical relationship between an optimal FA, θopt(°), and the number of profiles, N, was given as θopt=√{square root over (8192/N)}, assuming that Mprep was 100% and an effect of longitudinal T1 relaxation was negligible (i.e. T1=∞) during FLASH imaging readout. In the case of a finite τ1=1240 ms for cartilage and TR=6.8 ms, an optimal FA should become relatively larger to compensate for some magnetization loss due to the finite T1 relaxation.
For instance, an optimal FA (N=64, Mprep=100%.) would become 12.3° and 11.3°, respectively, with and without considering T1 relaxation. Nonetheless, an approximately quadratic decrease in θopt could still be observed when N progressively increased from 32 to 128 as shown in
Even though the acquisition time was reduced by about 30% (1:09 vs. 1:45 minutes) for one R1ρ-weighted dataset when using the developed R1ρ dispersion rather than the previous standard R1ρ mapping protocol, a comparable SNR as demonstrated in
There still exists ample room for further improvement of the developed R1ρ dispersion imaging protocol; for instance, a dramatic change on knee cartilage R1ρ dispersion profile should occur around ωip/2π=200 Hz as reported, and thus the ω1 distribution should have been tailored accordingly to maximize the sensitivity of R1ρ dispersion imaging. Moreover, the reported ω1 ranges need to be modified if MR scanner hardwire does not afford the highest SL RF strength of 1000 Hz. In this work, a dedicated 16-channel transmit/receive knee coil was employed that could generate a maximum B1 of about 27 μT, equivalent to ω1/2π=1150 Hz on the 3T MR scanner.
The theoretical basis for the developed R1ρ dispersion imaging protocol relies on the fact that R1ρ relaxation can be accounted for by two leading contributions, i.e. the non-dispersed and dispersed parts. In the case of articular cartilage as shown by EQUATION 9, these two contributions are an isotropic R2i and an anisotropic R2a, assuming a negligible chemicall exchange R2ex. This biophysical understanding of R1ρ dispersion mechanism is fully aligned with an insightful view from the literature in that small amount of water molecules hidden within the triple-helix interstices in collagen microstructure becomes mainly responsible for the observed R1ρ dispersion.
Such an insight into R1ρ relaxation mechanism not only warrants the specificity of the derived MR relaxation metrics such as R2a and S, but also provides an opportunity to exploit other valuable information without any additional scan time. In the previous and the current work, an internal reference was used to facilitate R1ρ dispersion modeling. In an ideal scenario as shown in EQUATION 9, this reference information represented by R2i should be the same whether it is determined when θ=55° (REF1) or when ω1=∞ (REF2). Nevertheless, if R2ex is included at the magic angle orientation (i.e. R2a=0) even it is insignificant in other cartilage locations (i.e. R2a>>R2ex), REF2 (i.e. R2i) would be less than REF1 (i.e. R2i+R2ex) just as appeared in 3 cos2 θ−1
2/4.
Measuring an Unbiased R1ρ with FLASH Sequence
The primary utility of 3D MAPSS was to measure an accurate R1ρ of human knee cartilage by eliminating an adverse longitudinal relaxation effect, which was manifested by a varying k-space filtering for different prepared magnetizations. Without such a dedicated attention, R1ρ could be markedly underestimated as demonstrated in a recent multi-center and multi-vendor knee cartilage R1ρ mapping study. Similarly, the current study also confirmed the previous findings as shown in
On the other hand, the overall synthetic R1ρ (ω1/2π=500 Hz) values from this study are comparable with that measured with 3D MAPPS, suggesting that the developed R1ρ dispersion imaging method is not only efficient but also robust—free from the T1 relaxation effect during FLASH imaging readout. Recently, an efficient 3D MAPSS without RF phase cycling was reported for a robust neuro R1ρ mapping using a different variable flip-angle scheduling tailored to various prepared R1ρ magnetization. This improved 3D MAPSS method would be cumbersome if it is used for R1ρ dispersion imaging, and the SL preparation has not yet been optimized. As demonstrated in
An efficient and robust R1ρ dispersion imaging protocol that is less susceptible to imaging artifacts from non-uniform B0 and B1 fields during SL preparation and from an adverse T1 relaxation effect during FLASH imaging readout has been developed. While the proposed method was developed and demonstrated on human knee articular cartilage, its application may be expanded to other biological tissues and relevant disorders, such as liver fibrosis and intervertebral disc degeneration, already being studied by standard R1ρ mapping. Continued refinement of R1ρ relaxation dispersion methodology will facilitate additional insight into pathophysiological processes, more accurate diagnoses, and better characterization of treatment efficacy in clinical joint cartilage studies.
With reference to
In the illustrated example, the computer 12 is connected to a medical imaging system 70-1. The medical imaging system 70-1 may be a stand-alone system capable of performing imaging of molecules, such as water, in biological tissue for in vivo examination. The system 70-1 may have resolution of such biological features as fibers, membranes, micromolecules, etc., wherein the image data can reveal microscopic details about biological tissue architecture, in a normal state or diseased state.
Computer 12 typically includes a variety of computer readable media that may be any available media that may be accessed by computer 12 and includes both volatile and nonvolatile media, removable and non-removable media. The system memory 16 includes computer storage media in the form of volatile and/or nonvolatile memory such as read only memory (ROM) and random access memory (RAM). The ROM may include a basic input/output system (BIOS). RAM typically contains data and/or program modules that include operating system 20, application programs 22, other program modules 24, and program data 26. The computer 12 may also include other removable/non-removable, volatile/nonvolatile computer storage media such as a hard disk drive, a magnetic disk drive that reads from or writes to a magnetic disk, and an optical disk drive that reads from or writes to an optical disk.
A user may enter commands and information into the computer 12 through input devices such as a keyboard 30 and pointing device 32, commonly referred to as a mouse, trackball or touch pad. Other input devices (not illustrated) may include a microphone, joystick, game pad, satellite dish, scanner, or the like. These and other input devices are often connected to the processing unit 14 through a user input interface 35 that is coupled to a system bus, but may be connected by other interface and bus structures, such as a parallel port, game port or a universal serial bus (USB). A monitor 40 or other type of display device may also be connected to the processor 14 via an interface, such as a video interface 42. In addition to the monitor, computers may also include other peripheral output devices such as speakers 50 and printer 52, which may be connected through an output peripheral interface 55.
Referring now to
A magnetic resonance image of an ordered tissue may be acquired (block 102). For example, the ordered tissue may be nerve tissue, white matter tissue, intervertebral disk, skeletal muscle tissue, myocardial muscle tissue, tendon tissue, cartilage tissue, or any other highly structured or highly ordered tissue in the human body.
Based on the magnetic resonance image of the ordered tissue, an R1ρ dispersion of the ordered tissue may be measured (block 104). Based on the measured R1ρ dispersion of the ordered tissue, R2a(α) and τb(α) for the ordered tissue may be derived (block 106).
An orientation-independent order parameter S for the ordered tissue may be calculated (block 108) using the following equation:
For example, a lower value for the orientation-independent order parameter S may correspond to a greater degeneration of the ordered tissue, while a higher value for the orientation-independent order parameter S may correspond to a lesser degeneration of the ordered tissue.
Based on the orientation-independent order parameter S for the ordered tissue, a level of degeneration of the ordered tissue may be determined (block 110). Moreover, in some examples, an indication of osteoarthritis in a patient associated with the ordered tissue may be determined based on the orientation-independent order parameter S for the ordered tissue. For instance, an orientation-independent order parameter S for the ordered tissue below a certain threshold value may indicate that the patient associated with the ordered tissue likely suffers from osteoarthritis.
Although the preceding text sets forth a detailed description of numerous different embodiments, it should be understood that the legal scope of the invention is defined by the words of the claims set forth at the end of this patent. The detailed description is to be construed as exemplary only and does not describe every possible embodiment, as describing every possible embodiment would be impractical, if not impossible. One could implement numerous alternate embodiments, using either current technology or technology developed after the filing date of this patent, which would still fall within the scope of the claims.
It should also be understood that, unless a term is expressly defined in this patent using the sentence “As used herein, the term ‘______’ is hereby defined to mean . . . ” or a similar sentence, there is no intent to limit the meaning of that term, either expressly or by implication, beyond its plain or ordinary meaning, and such term should not be interpreted to be limited in scope based on any statement made in any section of this patent (other than the language of the claims). To the extent that any term recited in the claims at the end of this patent is referred to in this patent in a manner consistent with a single meaning, that is done for sake of clarity only so as to not confuse the reader, and it is not intended that such claim term be limited, by implication or otherwise, to that single meaning.
Throughout this specification, unless indicated otherwise, plural instances may implement components, operations, or structures described as a single instance. Although individual operations of one or more methods are illustrated and described as separate operations, one or more of the individual operations may be performed concurrently, and nothing requires that the operations be performed in the order illustrated. Structures and functionality presented as separate components in example configurations may likewise be implemented as a combined structure or component. Similarly, structures and functionality presented as a single component may be implemented as separate components. These and other variations, modifications, additions, and improvements fall within the scope of the subject matter herein.
Additionally, certain embodiments are described herein as including logic or a number of routines, subroutines, applications, or instructions. These may constitute either software (code embodied on a non-transitory, tangible machine-readable medium) or hardware. In hardware, the routines, etc., are tangible units capable of performing certain operations and may be configured or arranged in a certain manner. In example embodiments, one or more computer systems (e.g., a standalone, client or server computer system) or one or more hardware modules of a computer system (e.g., a processor or a group of processors) may be configured by software (e.g., an application or application portion) as a hardware module that operates to perform certain operations as described herein.
In various embodiments, a hardware module may be implemented mechanically or electronically. For example, a hardware module may comprise dedicated circuitry or logic that is permanently configured (e.g., as a special-purpose processor, such as a field programmable gate array (FPGA) or an application-specific integrated circuit (ASIC) to perform certain operations. A hardware module may also comprise programmable logic or circuitry (e.g., as encompassed within a general-purpose processor or other programmable processor) that is temporarily configured by software to perform certain operations. It will be appreciated that the decision to implement a hardware module mechanically, in dedicated and permanently configured circuitry, or in temporarily configured circuitry (e.g., configured by software) may be driven by cost and time considerations.
Hardware modules can provide information to, and receive information from, other hardware modules. Accordingly, the described hardware modules may be regarded as being communicatively coupled. Where multiple of such hardware modules exist contemporaneously, communications may be achieved through signal transmission (e.g., over appropriate circuits and buses) that connect the hardware modules. In embodiments in which multiple hardware modules are configured or instantiated at different times, communications between such hardware modules may be achieved, for example, through the storage and retrieval of information in memory structures to which the multiple hardware modules have access. For example, one hardware module may perform an operation and store the output of that operation in a memory device to which it is communicatively coupled. A further hardware module may then, at a later time, access the memory device to retrieve and process the stored output. Hardware modules may also initiate communications with input or output devices, and can operate on a resource (e.g., a collection of information).
The various operations of example methods described herein may be performed, at least partially, by one or more processors that are temporarily configured (e.g., by software) or permanently configured to perform the relevant operations. Whether temporarily or permanently configured, such processors may constitute processor-implemented modules that operate to perform one or more operations or functions. The modules referred to herein may, in some example embodiments, comprise processor-implemented modules.
Similarly, in some embodiments, the methods or routines described herein may be at least partially processor-implemented. For example, at least some of the operations of a method may be performed by one or more processors or processor-implemented hardware modules. The performance of certain of the operations may be distributed among the one or more processors, not only residing within a single machine, but deployed across a number of machines. In some example embodiments, the one or more processors or processor-implemented modules may be located in a single geographic location (e.g., within a home environment, an office environment, or a server farm). In other example embodiments, the one or more processors or processor-implemented modules may be distributed across a number of geographic locations.
Unless specifically stated otherwise, discussions herein using words such as “processing,” “computing,” “calculating,” “determining,” “presenting,” “displaying,” or the like may refer to actions or processes of a machine (e.g., a computer) that manipulates or transforms data represented as physical (e.g., electronic, magnetic, or optical) quantities within one or more memories (e.g., volatile memory, non-volatile memory, or a combination thereof), registers, or other machine components that receive, store, transmit, or display information.
As used herein any reference to “one embodiment” or “an embodiment” means that a particular element, feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. The appearances of the phrase “in one embodiment” or “in some embodiments” in various places in the specification are not necessarily all referring to the same embodiment or embodiments.
Some embodiments may be described using the terms “coupled,” “connected,” “communicatively connected,” or “communicatively coupled,” along with their derivatives. These terms may refer to a direct physical connection or to an indirect (physical or communication) connection. For example, some embodiments may be described using the term “coupled” to indicate that two or more elements are in direct physical or electrical contact. The term “coupled,” however, may also mean that two or more elements are not in direct contact with each other, but yet still co-operate or interact with each other. Unless expressly stated or required by the context of their use, the embodiments are not limited to direct connection.
As used herein, the terms “comprises,” “comprising,” “includes,” “including,” “has,” “having” or any other variation thereof, are intended to cover a non-exclusive inclusion. For example, a process, method, article, or apparatus that comprises a list of elements is not necessarily limited to only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Further, unless expressly stated to the contrary, “or” refers to an inclusive or and not to an exclusive or. For example, a condition A or B is satisfied by any one of the following: A is true (or present) and B is false (or not present), A is false (or not present) and B is true (or present), and both A and B are true (or present).
In addition, use of the “a” or “an” are employed to describe elements and components of the embodiments herein. This is done merely for convenience and to give a general sense of the description. This description, and the claims that follow, should be read to include one or at least one and the singular also includes the plural unless the context clearly indicates otherwise.
Upon reading this disclosure, those of skill in the art will appreciate still additional alternative structural and functional designs for monitoring refrigerated air usage. Thus, while particular embodiments and applications have been illustrated and described, it is to be understood that the disclosed embodiments are not limited to the precise construction and components disclosed herein. Various modifications, changes and variations, which will be apparent to those skilled in the art, may be made in the arrangement, operation and details of the method and apparatus disclosed herein without departing from the spirit and scope defined in the appended claims.
The particular features, structures, or characteristics of any specific embodiment may be combined in any suitable manner and in any suitable combination with one or more other embodiments, including the use of selected features without corresponding use of other features. In addition, many modifications may be made to adapt a particular application, situation or material to the essential scope and spirit of the present invention. It is to be understood that other variations and modifications of the embodiments of the present invention described and illustrated herein are possible in light of the teachings herein and are to be considered part of the spirit and scope of the present invention.
Finally, the patent claims at the end of this patent application are not intended to be construed under 35 U.S.C. § 112(f), unless traditional means-plus-function language is expressly recited, such as “means for” or “step for” language being explicitly recited in the claims.
The present application claims priority to U.S. Provisional Patent Application No. 63/022,155, filed May 8, 2020, entitled “An Orientation-Independent Order Parameter Derived from Magnetic Resonance R1ρ Dispersion Imaging in Ordered Tissue,” the disclosure of which is incorporated herein by reference in its entirety.
This invention was made with government support under R01HD093626 awarded by the National Institutes of Health. The government has certain rights in the invention.
| Number | Date | Country | |
|---|---|---|---|
| 63022155 | May 2020 | US |
