Systematic data analysis pipeline for quantitative morphological cell phenotyping

Quantitative morphological phenotyping (QMP) is an image-based method used to capture morphological features at both the cellular and population level. Its interdisciplinary nature, spanning from data collection to result analysis and interpretation, can lead to uncertainties, particularly among those new to this actively growing field. High analytical specificity for a typical QMP is achieved through sophisticated approaches that can leverage subtle cellular morphological changes. Here, we outline a systematic workflow to refine the QMP methodology. For a practical review, we describe the main steps of a typical QMP; in each step, we discuss the available methods, their applications, advantages, and disadvantages, along with the R functions and packages for easy implementation. This review does not cover theoretical backgrounds, but provides several references for interested researchers. It aims to broaden the horizons for future phenome studies and demonstrate how to exploit years of endeavors to achieve more with less.

Gamma distribution model of diffusion MRI for evaluating the isocitrate dehydrogenase mutation status of glioblastomas

OBJECTIVE

To determine whether the γ distribution (GD) model of diffusion MRI is useful in the evaluation of the isocitrate dehydrogenase (IDH) mutation status of glioblastomas.

METHODS

12 patients with IDH-mutant glioblastomas and 54 patients with IDH-wildtype glioblastomas were imaged with diffusion-weighted imaging using 13 b-values from 0 to 1000 s/mm2. The shape parameter (κ) and scale parameter (θ) were obtained with the GD model. Fractions of three different areas under the probability density function curve (f1, f2, f3) were defined as follows: f1, diffusion coefficient (D) < 1.0×10-3 mm2/s; f2, D > 1.0×10-3 and <3.0×10-3 mm2/s; f3, D > 3.0 × 10-3 mm2/s. The GD model-derived parameters measured in gadolinium-enhancing lesions were compared between the IDH-mutant and IDH-wildtype groups. Receiver operating curve analyses were performed to assess the parameters' diagnostic performances.

RESULTS

The IDH-mutant group's f1 (0.474  ±  0.143) was significantly larger than the IDH-wildtype group's (0.347  ±  0.122, p = 0.0024). The IDH-mutant group's f2 (0.417  ±  0.131) was significantly smaller than the IDH-wildtype group's (0.504  ±  0.126, p = 0.036). The IDH-mutant group's f3 (0.109  ±  0.060) was significantly smaller than the IDH-wildtype group's (0.149  ±  0.063, p = 0.0466). The f1 showed the best diagnostic performance among the GD model-derived parameters with the area under the curve value of 0.753.

CONCLUSION

The GD model could well describe the pathological features of IDH-mutant and IDH-wildtype glioblastomas, and was useful in the differentiation of these tumors.

ADVANCES IN KNOWLEDGE

Diffusion MRI based on the γ distribution model could well describe the pathological features of IDH-mutant and IDH-wildtype glioblastomas, and its use enabled the significant differentiation of these tumors. The γ distribution model may contribute to the non-invasive identification of the IDH mutation status based on histological viewpoint.

A comparison among gamma distribution, intravoxel incoherent motion, and mono-exponential models with turbo spin-echo diffusion-weighted MR imaging in the differential diagnosis of orofacial lesions

OBJECTIVES

To compare the gamma distribution (GD), intravoxel incoherent motion (IVIM), and monoexponential (ME) models in terms of their goodness-of-fit, correlations among the parameters, and the effectiveness in the differential diagnosis of various orofacial lesions.

METHODS

A total of 85 patients underwent turbo spin-echo diffusion-weighted imaging with six b-values. The goodness-of-fit of three models was assessed using Akaike Information Criterion. We analysed the correlations and compared the effectiveness in the differential diagnosis among the parameters of GD model (κ, shape parameter; θ, scale parameter; fractions of diffusion: ƒ₁, cellular component; ƒ₂, extracellular diffusion; ƒ₃, perfusion component), IVIM model (D, true diffusion coefficient; D*, pseudodiffusion coefficient; f, perfusion fraction), and ME model (apparent diffusion coefficient, ADC).

RESULTS

The GD and IVIM models showed a better goodness-of-fit than the ME model (p < 0.05). ƒ₁ had strong negative correlations with D and ADC (ρ = -0.901 and -0.937, respectively), while ƒ₃ had a moderate positive correlation with f (ρ = 0.661). Malignant entity presented significantly higher ƒ₁ and lower D and ADC than benign entity (p < 0.0001). Malignant lymphoma had significantly higher ƒ₁ in comparison to squamous cell carcinoma (p = 0.0007) and granulation (p = 0.0075). The trend in ƒ₁ was opposite to the trend in D. Malignant lymphoma had significant lower ƒ₃ than squamous cell carcinoma (p = 0.005) or granulation (p = 0.0075).

CONCLUSIONS

The strong correlations were found between the GD- and IVIM-derived parameters. Furthermore, the GD model's parameters were useful for characterising the pathological structure in orofacial lesions.

The relationship between diffusion heterogeneity and microstructural changes in high-grade gliomas using Monte Carlo simulations

PURPOSE

Diffusion-weighted imaging (DWI) may aid accurate tumor grading. Decreased diffusivity and increased diffusion heterogeneity measures have been observed in high-grade gliomas using the non-monoexponential models for DWI. However, DWI measures concerning tissue characteristics in terms of pathophysiological and structural changes are yet to be established. Thus, this study aims to investigate the relationship between the diffusion measurements and microstructural changes in the presence of high-grade gliomas using a three-dimensional Monte Carlo simulation with systematic changes of microstructural parameters.

METHODS

Water diffusion was simulated in a microenvironment along with changes associated with the presence of high-grade gliomas, including increases in cell density, nuclear volume, extracellular volume (VF_ex), and extracellular tortuosity (λ_ex), and changes in membrane permeability (P_mem). DWI signals were simulated using a pulsed gradient spin-echo sequence. The sequence parameters, including the maximum gradient strength and diffusion time, were set to be comparable to those of clinical scanners and advanced human MRI systems. The DWI signals were fitted using the gamma distribution and diffusional kurtosis models with b-values up to 6000 and 2500 s/mm², respectively.

RESULTS

The diffusivity measures (apparent diffusion coefficients (ADC), D_gamma of the gamma distribution model and D_app of the diffusional kurtosis model) decreased with increases in cell density and λ_ex, and a decrease in P_mem. These diffusivity measures increased with increases in nuclear volume and VF_ex. The diffusion heterogeneity measures (σ_gamma of the gamma distribution model and K_app of the diffusional kurtosis model) increased with increases in cell density or nuclear volume at the low P_mem, and a decrease in P_mem. Increased σ_gamma was also associated with an increase in VF_ex.

CONCLUSION

Among simulated microstructural changes, only increases in cell density at low P_mem or decreases in P_mem corresponded to both the decreased diffusivity and increased diffusion heterogeneity measures. The results suggest that increases in cell density at low P_mem or decreases in P_mem may be associated with the diffusion changes observed in high-grade gliomas.

The Mathematics of Quasi-Diffusion Magnetic Resonance Imaging

Quasi-diffusion imaging (QDI) is a novel quantitative diffusion magnetic resonance imaging (dMRI) technique that enables high quality tissue microstructural imaging in a clinically feasible acquisition time. QDI is derived from a special case of the continuous time random walk (CTRW) model of diffusion dynamics and assumes water diffusion is locally Gaussian within tissue microstructure. By assuming a Gaussian scaling relationship between temporal (α) and spatial (β) fractional exponents, the dMRI signal attenuation is expressed according to a diffusion coefficient, D (in mm2 s−1), and a fractional exponent, α. Here we investigate the mathematical properties of the QDI signal and its interpretation within the quasi-diffusion model. Firstly, the QDI equation is derived and its power law behaviour described. Secondly, we derive a probability distribution of underlying Fickian diffusion coefficients via the inverse Laplace transform. We then describe the functional form of the quasi-diffusion propagator, and apply this to dMRI of the human brain to perform mean apparent propagator imaging. QDI is currently unique in tissue microstructural imaging as it provides a simple form for the inverse Laplace transform and diffusion propagator directly from its representation of the dMRI signal. This study shows the potential of QDI as a promising new model-based dMRI technique with significant scope for further development.

Optimized bias and signal inference in diffusion-weighted image analysis (OBSIDIAN)

PURPOSE

Correction of Rician signal bias in magnitude MR images.

METHODS

A model-based, iterative fitting procedure is used to simultaneously estimate true signal and underlying Gaussian noise with standard deviation σ g on a pixel-by-pixel basis in magnitude MR images. A precomputed function that relates absolute residuals between measured signals and model fit to σ g is used to iteratively estimate σ g . The feasibility of the method is evaluated and compared to maximum likelihood estimation (MLE) for diffusion signal decay simulations and diffusion-weighted images of the prostate considering 21 linearly spaced b-values from 0 to 3000 s/mm² . A multidirectional analysis was performed with publically available brain data.

RESULTS

Model simulations show that the Rician bias correction algorithm is fast, with an accuracy and precision that is on par to model-based MLE and direct fitting in the case of pure Gaussian noise. Increased accuracy in parameter prediction in a low signal-to-noise ratio (SNR) scenario is ideally achieved by using a composite of multiple signal decays from neighboring voxels as input for the algorithm. For patient data, good agreement with high SNR reference data of diffusion in prostate is achieved.

CONCLUSIONS

OBSIDIAN is a novel, alternative, simple to implement approach for rapid Rician bias correction applicable in any case where differences between true signal decay and underlying model function can be considered negligible in comparison to noise. The proposed composite fitting approach permits accurate parameter estimation even in typical clinical scenarios with low SNR, which significantly simplifies comparison of complex diffusion parameters among studies.

Optimal Model Mapping for Intravoxel Incoherent Motion MRI

In general, only one diffusion model would be applied to whole field-of-view voxels in the intravoxel incoherent motion-magnetic resonance imaging (IVIM-MRI) study. However, the choice of the applied diffusion model can significantly influence the estimated diffusion parameters. The quality of the diffusion analysis can influence the reliability of the perfusion analysis. This study proposed an optimal model mapping method to improve the reliability of the perfusion parameter estimation in the IVIM study. Six healthy volunteers (five males and one female; average age of 38.3 ± 7.5 years). Volunteers were examined using a 3.0 Tesla scanner. IVIM-MRI of the brain was applied at 17 b-values ranging from 0 to 2,500 s/mm². The Gaussian model, the Kurtosis model, and the Gamma model were found to be optimal for the CSF, white matter (WM), and gray matter (GM), respectively. In the mean perfusion fraction (f_p) analysis, the GM/WM ratios were 1.16 (Gaussian model), 1.80 (Kurtosis model), 1.94 (Gamma model), and 1.54 (Optimal model mapping); in the mean pseudo diffusion coefficient (D^*) analysis, the GM/WM ratios were 1.18 (Gaussian model), 1.19 (Kurtosis model), 1.56 (Gamma model), and 1.24 (Optimal model mapping). With the optimal model mapping method, the estimated f_p and D^* were reliable compared with the conventional methods. In addition, the optimal model maps, the associated products of this method, may provide additional information for clinical diagnosis.

Gamma distribution model of diffusion MRI for the differentiation of primary central nerve system lymphomas and glioblastomas

The preoperative imaging-based differentiation of primary central nervous system lymphomas (PCNSLs) and glioblastomas (GBs) is of high importance since the therapeutic strategies differ substantially between these tumors. In this study, we investigate whether the gamma distribution (GD) model is useful in this differentiation of PNCSLs and GBs. Twenty-seven patients with PCNSLs and 57 patients with GBs were imaged with diffusion-weighted imaging using 13 b-values ranging from 0 to 1000 sec/mm2. The shape parameter (κ) and scale parameter (θ) were obtained with the GD model. Fractions of three different areas under the probability density function curve (f1, f2, f3) were defined as follows: f1, diffusion coefficient (D) <1.0×10-3 mm2/sec; f2, D >1.0×10-3 and <3.0×10-3 mm2/sec; f3, D >3.0 × 10-3 mm2/sec. The GD model-derived parameters were compared between PCNSLs and GBs. Receiver operating characteristic (ROC) curve analyses were performed to assess diagnostic performance. The correlations with intravoxel incoherent motion (IVIM)-derived parameters were evaluated. The PCNSL group's κ (2.26 ± 1.00) was significantly smaller than the GB group's (3.62 ± 2.01, p = 0.0004). The PCNSL group's f1 (0.542 ± 0.107) was significantly larger than the GB group's (0.348 ± 0.132, p<0.0001). The PCNSL group's f2 (0.372 ± 0.098) was significantly smaller than the GB group's (0.508 ± 0.127, p<0.0001). The PCNSL group's f3 (0.086 ± 0.043) was significantly smaller than the GB group's (0.144 ± 0.062, p<0.0001). The combination of κ, f1, and f3 showed excellent diagnostic performance (area under the curve, 0.909). The f1 had an almost perfect inverse correlation with D. The f2 and f3 had very strong positive correlations with D and f, respectively. The GD model is useful for the differentiation of GBs and PCNSLs.

Use of multi-flip angle measurements to account for transmit inhomogeneity and non-Gaussian diffusion in DW-SSFP

Diffusion-weighted steady-state free precession (DW-SSFP) is an SNR-efficient diffusion imaging method. The improved SNR and resolution available at ultra-high field has motivated its use at 7T. However, these data tend to have severe B1 inhomogeneity, leading not only to spatially varying SNR, but also to spatially varying diffusivity estimates, confounding comparisons both between and within datasets. This study proposes the acquisition of DW-SSFP data at two-flip angles in combination with explicit modelling of non-Gaussian diffusion to address B1 inhomogeneity at 7T. Data were acquired from five fixed whole human post-mortem brains with a pair of flip angles that jointly optimize the diffusion contrast-to-noise (CNR) across the brain. We compared one- and two-flip angle DW-SSFP data using a tensor model that incorporates the full DW-SSFP Buxton signal, in addition to tractography performed over the cingulum bundle and pre-frontal cortex using a ball & sticks model. The two-flip angle DW-SSFP data produced angular uncertainty and tractography estimates close to the CNR optimal regions in the single-flip angle datasets. The two-flip angle tensor estimates were subsequently fitted using a modified DW-SSFP signal model that incorporates a gamma distribution of diffusivities. This allowed us to generate tensor maps at a single effective b-value yielding more consistent SNR across tissue, in addition to eliminating the B1 dependence on diffusion coefficients and orientation maps. Our proposed approach will allow the use of DW-SSFP at 7T to derive diffusivity estimates that have greater interpretability, both within a single dataset and between experiments.

The application of a gamma distribution model to diffusion-weighted images of the orofacial region

OBJECTIVES

This study evaluated the correlation among the diffusion-derived parameters obtained by monoexponential (ME), intravoxel incoherent motion (IVIM) and γ distribution (GD) models and compared these parameters among representative orofacial tumours.

METHODS

Ninety-two patients who underwent 1.5 T MRI including diffusion-weighted imaging were included. The shape parameter (κ), scale parameter (θ), ratio of the intracellular diffusion (ƒ₁), extracellular diffusion (ƒ₂) and perfusion (ƒ₃) were obtained by the GD model; the true diffusion coefficient (D) and perfusion fraction (f) were obtained by the IVIM model; and the apparent diffusion coefficient (ADC) was obtained by the ME model.

RESULTS

ƒ₁ had a strongly negative correlation with the ADC (ρ = -0.993) and D (ρ = -0.926). A strong positive correlation between f and ƒ₃ (ρ = 0.709) was found. Malignant lymphoma (ML) had the highest ƒ₁, followed by squamous cell carcinoma (SCC), malignant salivary gland tumours, pleomorphic adenoma (Pleo) and angioma. Both the IVIM and GD models suggested the highest perfusion in angioma and the lowest perfusion in ML. The GD model demonstrated a high extracellular component in Pleo and revealed that the T_4a+T_4b SCC group had a lower ƒ₂ than the T₂+T₃ SCC group, and poor to moderately differentiated SCC had a higher ƒ₁ than highly differentiated SCC.

CONCLUSIONS

Given the correlation among the diffusion-derived parameters, the GD model might be a good alternative to the IVIM model. Furthermore, the GD model's parameters were useful for characterizing the pathological structure.

Modeling an equivalent b-value in diffusion-weighted steady-state free precession

PURPOSE

Diffusion-weighted steady-state free precession (DW-SSFP) is shown to provide a means to probe non-Gaussian diffusion through manipulation of the flip angle. A framework is presented to define an effective b-value in DW-SSFP.

THEORY

The DW-SSFP signal is a summation of coherence pathways with different b-values. The relative contribution of each pathway is dictated by the flip angle. This leads to an apparent diffusion coefficient (ADC) estimate that depends on the flip angle in non-Gaussian diffusion regimes. By acquiring DW-SSFP data at multiple flip angles and modeling the variation in ADC for a given form of non-Gaussianity, the ADC can be estimated at a well-defined effective b-value.

METHODS

A gamma distribution is used to model non-Gaussian diffusion, embedded in the Buxton signal model for DW-SSFP. Monte-Carlo simulations of non-Gaussian diffusion in DW-SSFP and diffusion-weighted spin-echo sequences are used to verify the proposed framework. Dependence of ADC on flip angle in DW-SSFP is verified with experimental measurements in a whole, human postmortem brain.

RESULTS

Monte-Carlo simulations reveal excellent agreement between ADCs estimated with diffusion-weighted spin-echo and the proposed framework. Experimental ADC estimates vary as a function of flip angle over the corpus callosum of the postmortem brain, estimating the mean and standard deviation of the gamma distribution as 1.50 · 10 - 4  mm2 /s and 2.10 · 10 - 4  mm2 /s.

CONCLUSION

DW-SSFP can be used to investigate non-Gaussian diffusion by varying the flip angle. By fitting a model of non-Gaussian diffusion, the ADC in DW-SSFP can be estimated at an effective b-value, comparable to more conventional diffusion sequences.

Diffusion maps of Bacillus subtilis biofilms via magnetic resonance imaging highlight a complex network of channels

Bacillus subtilis microorganism when cultivated under chemically-defined conditions developed a biofilm with an unusual pattern of wrinkles on the surface. Some questions were raised about whether there was a special function of these wrinkles for the biofilm itself, since they resembled microchannels that could be involved in the transport of nutrients within the biofilm. Since the diffusion is the main mechanism for nutrient transport to biofilm from the medium, the role of these wrinkled structures in the whole diffusion within the biofilm was investigated using diffusion-weighted magnetic resonance imaging (DW-MRI). Data from these diffusion images was used to generate 2D diffusion maps which highlighted the striking channel features of the biofilm surface. The diffusion maps revealed a network of interconnected channels, with self-diffusion coefficients higher in the microchannels than in other regions of the biofilms. Polar plots made from 2D diffusion maps obtained from the plane of the biofilm show an anisotropy of the diffusion inside the microchannels, with the diffusion higher when along the principal direction of the microchannels. These results agree with the model, that the buckling of the biofilm surface from the B. subtilis creates microchannels that can enhance diffusion throughout the biofilm.

Analysis of Diffusion-weighted MR Images Based on a Gamma Distribution Model to Differentiate Prostate Cancers with Different Gleason Score

Purpose:

Prostate cancer management includes identification of clinically significant cancers that may require curative treatment. Statistical models based on gamma distribution can describe diffusion signal decay curves of prostate cancer. The purpose of this study was to evaluate the ability of parameters obtained with the gamma model in differentiating prostate cancers with different Gleason score values.

Methods:

This study included 155 patients with prostate cancer who underwent multiparametric magnetic resonance imaging prior to prostate biopsy (127 patients) or radical prostatectomy (28 patients) between January 2015 and June 2017; 159 foci of prostate cancer were included in our study. We compared cases scored as Gleason score (GS) 3 + 3 and GS ≥ 3 + 4, and analyzed cases scored as GS ≤ 3+ 4 and GS ≥ 4 + 3 based on the gamma model (Frac < 1.0, Frac < 0.8, Frac < 0.5, Frac < 0.3, and Frac > 3.0), and apparent diffusion coefficient (ADC).

Results:

Among 159 cancerous lesions in 155 patients, 13 (8.2%) were GS 3 + 3 prostate cancers, 51 (32.0%) were GS 3 + 4 prostate cancers, 30 (18.2%) were GS 4 + 3 cancers, and 65 (40.9%) were GS ≥ 4 + 4 cancers. Frac < 0.3, Frac < 0.5, Frac < 0.8, and Frac < 1.0 were significantly higher and ADC values were significantly lower in GS ≥ 4 + 3 cancers than in GS ≤ 3 + 4 cancers (P < 0.01, P < 0.01, P < 0.01, P = 0.01, and P < 0.01, respectively). With receiver operating characteristic (ROC) analysis, Frac < 0.3 and Frac < 0.5 had significantly greater area under the ROC curve for discriminating GS ≥ 4 + 3 cancers from GS ≤ 3 + 4 cancers than ADC (P = 0.03, P < 0.01, respectively).

Conclusion:

Frac < 0.3 and Frac < 0.5 showed higher diagnostic performance than ADC for differentiating GS ≥ 4 + 3 from GS ≤ 3 + 4 cancers. The gamma model may add additional value in discrimination of tumor grades.

Gamma Distribution Model in the Evaluation of Breast Cancer Through Diffusion-Weighted MRI: A Preliminary Study

BACKGROUND

The gamma distribution (GD) model is based on the statistical distribution of the apparent diffusion coefficient (ADC) parameter. The GD model is expected to reflect the probability of the distribution of water molecule mobility in different regions of tissue, but also the intra- and extracellular diffusion and perfusion components (f₁ , f₂ , f₃ fractions).

PURPOSE

To assess the GD model in the characterization and diagnostic performance of breast lesions.

STUDY TYPE

Prospective.

POPULATION

In all, 48 females with 24 benign and 33 malignant breast lesions.

FIELD STRENGTH/SEQUENCE

A diffusion-weighted sequence (b = 0-3000 s/mm² ) with a 3 T scanner.

ASSESSMENT

For each group of benign, malignant, invasive, and in situ breast lesions, the ADC was obtained. Also, θ and k parameters (scale and shape of the statistic distribution, respectively), f₁ , f₂ , and f₃ fractions were obtained from fitting the GD model to diffusion data.

STATISTICAL TESTS

Lesion types were compared regarding diffusion parameters using nonparametric statistics and receiver operating characteristic curve diagnostic performance.

RESULTS

The majority of GD parameters (k, f₁ , f₂ , f₃ fractions) showed significant differences between benign and malignant lesions, and between in situ and invasive lesions (f₁ , f₂ , f₃ fractions) (P ≤ 0.001). The best diagnostic performances were obtained with ADC and f₁ fraction in benign vs. malignant lesions (area under curve [AUC] = 0.923 and 0.913, sensitivity = 93.9% and 81.8%, specificity = 79.2% and 91.7%, accuracy = 87.7% and 86.0%, respectively). In invasive lesions vs. in situ lesions, the best diagnostic performance was obtained with f₁ fraction, which outperformed ADC results (AUC = 0.978 and 0.941, and sensitivity = 91.3% for both parameters, specificity = 100.0% and 90.0%, accuracy = 93.9% and 90.9%, respectively).

DATA CONCLUSION

This work shows that the GD model provides information in addition to the ADC parameter, suggesting its potential in the diagnosis of breast lesions. Level of Evidence 2: Technical Efficacy Stage 2 J. Magn. Reson. Imaging 2019;50:230-238.

Evaluation of fitting models for prostate tissue characterization using extended-range b-factor diffusion-weighted imaging

PURPOSE

To compare the fitting and tissue discrimination performance of biexponential, kurtosis, stretched exponential, and gamma distribution models for high b-factor diffusion-weighted images in prostate cancer.

METHODS

Diffusion-weighted images with 15 b-factors ranging from b = 0 to 3500 s/mm² were obtained in 62 prostate cancer patients. Pixel-wise signal decay fits for each model were evaluated with the Akaike Information Criterion (AIC). Parameter values for each model were determined within normal prostate and the index lesion. Their potential to differentiate normal from cancerous tissue was investigated through receiver operating characteristic analysis and comparison with Gleason score.

RESULTS

The biexponential slow diffusion fraction f_slow , the apparent kurtosis diffusion coefficient ADC_K , and the excess kurtosis factor K differ significantly among normal peripheral zone (PZ), normal transition zone (TZ), tumor PZ, and tumor TZ. Biexponential and gamma distribution models result in the lowest AIC, indicating a superior fit. Maximum areas under the curve (AUCs) of all models ranged from 0.93 to 0.96 for the PZ and from 0.95 to 0.97 for the TZ. Similar AUCs also result from the apparent diffusion coefficient (ADC) of a monoexponential fit to a b-factor sub-range up to 1250 s/mm² . For kurtosis and stretched exponential models, single parameters yield the highest AUCs, whereas for the biexponential and gamma distribution models, linear combinations of parameters produce the highest AUCs. Parameters with high AUC show a trend in differentiating low from high Gleason score, whereas parameters with low AUC show no such ability.

CONCLUSION

All models, including a monoexponential fit to a lower-b sub-range, achieve similar AUCs for discrimination of normal and cancer tissue. The biexponential model, which is favored statistically, also appears to provide insight into disease-related microstructural changes. Magn Reson Med 79:2346-2358, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Precise Inference and Characterization of Structural Organization (PICASO) of tissue from molecular diffusion

Inferring the microstructure of complex media from the diffusive motion of molecules is a challenging problem in diffusion physics. In this paper, we introduce a novel representation of diffusion MRI (dMRI) signal from tissue with spatially-varying diffusivity using a diffusion disturbance function. This disturbance function contains information about the (intra-voxel) spatial fluctuations in diffusivity due to restrictions, hindrances and tissue heterogeneity of the underlying tissue substrate. We derive the short- and long-range disturbance coefficients from this disturbance function to characterize the tissue structure and organization. Moreover, we provide an exact relation between the disturbance coefficients and the time-varying moments of the diffusion propagator, as well as their relation to specific tissue microstructural information such as the intra-axonal volume fraction and the apparent axon radius. The proposed approach is quite general and can model dMRI signal for any type of gradient sequence (rectangular, oscillating, etc.) without using the Gaussian phase approximation. The relevance of the proposed PICASO model is explored using Monte-Carlo simulations and in-vivo dMRI data. The results show that the estimated disturbance coefficients can distinguish different types of microstructural organization of axons.

Diffusion-weighted MR Imaging for the Assessment of Renal Function: Analysis Using Statistical Models Based on Truncated Gaussian and Gamma Distributions

PURPOSE

To determine the appropriateness of statistical models using the truncated Gaussian distribution and gamma distribution for diffusion signal decay, and to assess the correlation between the parameters obtained from the statistical models and estimated glomerular filtration rate (eGFR).

METHODS

Twenty-nine patients with chronic kidney disease and 21 healthy volunteers were included and classified in four groups according to eGFR (ml/min/1.73 m(2)): group 1 (90 ≤ eGFR, n = 10), group 2 (eGFR 60-90, n = 15), group 3 (eGFR 30-60, n = 17), and group 4 (eGFR < 30, n = 8). Diffusion-weighted imaging using five b-values (0, 500, 1000, 1500, and 2000 s/mm(2)) was performed. Truncated Gaussian and gamma models were compared for goodness of fit. Area fractions for the diffusion coefficient D < 1.0 × 10(-3) mm(2)/s (Frac < 1.0) and D > 3.0 × 10(-3) mm(2)/s (Frac > 3.0) obtained from the statistical model were compared among four groups. Correlation between proposed parameters and conventional apparent diffusion coefficient (ADC) with eGFR was calculated.

RESULTS

There was no significant difference in goodness of fit between the truncated Gaussian and gamma models. Frac < 1.0 and Frac > 3.0 showed good correlation with eGFR, as did ADC. Comparison between groups 1 and 2 showed that only Frac < 1.0 in both distribution models had significant differences.

CONCLUSION

Statistical models yield robust interpretation of diffusion magnetic resonance (MR) signals with relevance to histological changes in the kidney. The parameters of the statistical models, particularly Frac < 1.0, strongly correlated with eGFR.