Piotr Kozlowski


Relevant Thesis-Based Degree Programs


Graduate Student Supervision

Doctoral Student Supervision

Dissertations completed in 2010 or later are listed below. Please note that there is a 6-12 month delay to add the latest dissertations.

Bi-convex model based reconstruction methods for magnetic resonance elastography (2023)

Magnetic resonance elastography (MRE) is a biomechanical imaging tool that reconstructs the tissue elasticity map by capturing tissue displacement with magnetic resonance imaging (MRI). MRE has the unique advantage of capturing all three directional displacement components with a moveable and deep field of view. In addition, MRE offers the functionality to incorporate other MRI contrast seamlessly to extend MRE for advanced biomechanical models. However, MRE is limited by its long scanning time, low signal-to-noise ratio, and low resolution. This thesis focuses on iterative model-based reconstruction techniques with structured sparsity for faster MRE acquisition and robust elastogram reconstruction. A new optimization technique for elastogram reconstruction is proposed using the bi-convexity of the elastodynamic model and the alternating direction method of multipliers (ADMM). The proposed optimization technique allows easy integration of structured sparsity and is robust to noise and initialization. Four elastography reconstruction methods were implemented in this thesis with different models and regularization prior: (a) scalar 2D shear wave model (2D-ERBA), (b) scalar 3D shear wave model (3D-ERBA), (c) vector 3D elastodynamic wave model (ERSA), and (d) multifrequency vector 3D elastodynamic wave model (MERSA). The former two elastography reconstruction methods used a sparsity prior to the shear modulus, while the latter used sparsity prior on both shear modulus and displacement. These methods were extensively validated for in silico, in vitro, and in vivo datasets and compared with state-of-the-art methods. Experiments showed that MERSA provides higher robustness to noise, higher robustness to wavelength-to-voxel ratio, and higher accuracy for both elasticity and viscosity. A comparison study of diagnostic performance in detecting liver disease of scalar 2D shear wave model, scalar 3D shear wave model, and vector 3D elastodynamic wave model with MERSA implementation concludes the reconstruction part of this thesis. A bi-convex optimization-based displacement regularized compressed sensing (DRCS) method is proposed for fast MRE acquisition. The proposed method uses separate sparsity prior on the magnitude, phase and displacement to recover the MR signal from a highly undersampled k-space. We compare the performance of DRCS with other compressed sensing methods for highly undersampled data from in silico, in vitro and in vivo datasets.

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Measurement of the arterial input function from radial MR projections (2020)

Dynamic Contrast-Enhanced MRI (DCE-MRI) data may be used to non-invasively investigate the health status of tissue. The technique requires that the concentration of a contrast agent vs. time curve is known in both the tissue of interest and in a blood vessel feeding the tissue - commonly referred to as the arterial input function (AIF). Physiologically relevant parameters are extracted through Pharmacokinetic modeling, though the accuracy is known to be highly sensitive to the quality of the acquired data. It is difficult to get a good measurement of the AIF in pre-clinical studies in mice due to their small body size and limited number of vessels of a sufficient size. As a result, several groups use a population averaged curve from the literature. This curve does not account for inter or intra-individual differences, and impacts the accuracy of the fit parameters.We propose a new projection-based measurement that measures the AIF from a single trajectory in k-space, which provides a temporal resolution equal to the repetition time (TR). This AIF is measured in the mouse tail due to the simpler geometry void of highly enhancing organs nearby. The projection-based AIF is advantageous as it allows for the acquisition of DCE data, in the tissue of interest, between measurements without affecting the temporal resolution of either data set. We set up a dual coil experimental platform that acquires AIF data at the mouse tail and DCE data at the tumour. Our technique allows for data optimization at both locations, without restricting the temporal or spatial resolutions of the AIF or DCE data. It may be applied to any pre-clinical study using mice or rats.

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A new multiparametric MRI protocol for diagnosis of prostate cancer (2017)

In this thesis, a new magnetic resonance imaging (MRI) quantitative T2 mapping technique, called Luminal water imaging (LWI), has been developed and used for non-invasive detection and grading of prostatic tumours. Using this technique, we measured what we hypothesized to be the fractional amount of water content of luminal spaces in prostate, and called it Luminal Water Fraction, LWF. Based on the differences in tissue composition and fractional amount of luminal space between malignant and normal prostatic tissues and between tumors of different grades, we hypothesized that the measurements of LWF could be used for the detection and grading of prostatic tumours. To verify these hypotheses, we performed two patient studies in which we compared MR measurements of LWI with whole-mount histology. In the first study, we evaluated the correlation between LWF and the percentage area of luminal space in the prostatic tissue. The results of this study demonstrated that LWF is significantly and strongly correlated with the percentage area of luminal space in the prostatic tissue. In the second study, we investigated the feasibility of LWI in the detection and grading of prostate cancer. The results of this study showed that LWI provides high accuracy both in the detection and grading of prostatic tumours. After verifying our hypotheses, we performed a detailed comparison between the diagnostic accuracy of LWI and the more established MRI techniques: Dynamic Contrast-Enhanced (DCE) and Diffusion-Weighted MRI (DW-MRI). The results of this pilot study showed that LWI alone performs better than DCE, DW-MRI, or their combination, in the detection of prostatic tumours and also in correlation with GS. Based on the results of this study, we proposed a guideline for making a more efficient, abbreviated multi-parametric MRI protocol for the diagnosis of prostate cancer.Finally, as a side project, we explored some potential areas of improvement in DCE-MRI by investigating the impact of temporal resolution on the accuracy of DCE-MRI in detection of prostatic tumours. Our results showed that within a certain range of temporal resolutions, the diagnostic accuracy of DCE-MRI would be independent of the temporal resolution.

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Validation and optimization of myelin water imaging in a preclinical model of spinal cord injury (2017)

Myelin content is an important marker for neuropathology; however, direct imaging of myelin is difficult. Consequently, quantitative T2 based myelin water imaging measures myelin content indirectly by probing the property of the surrounding water. Typically, a lengthy multi-echo spin-echo sequence is used to obtain decay curves that are fitted to produce T2 distributions. In white matter, two peaks are observed, one with short and one with long T2 associated with water trapped between the myelin lipid bilayers and intra/extracellular water. The ratio of myelin water peak to the entire distribution is called the myelin water fraction (MWF) and correlates well the myelin content. This thesis has two parts. The first half deals with the use of compressed sensing (CS) to accelerate the lengthy sequence used in myelin water imaging. The CS CPMG sequence was implemented in 2D utilizing group-sparse reconstruction in order to take advantage of the correlation between echoes. Simulated undersampling and real undersampling experiments were performed. It was found that acceleration up to 2× was possible without impacting MWF map quality, wherever adequate SNR was available. This is followed by a brief investigation into 3D CS CPMG, where similar results were achieved.The second part of the thesis focuses on myelin water imaging in the presence of myelin debris. Because MWF is associated with the water trapped in between the myelin lipid bilayers, the reading depends heavily on myelin morphology. I compared MWF to transmission electron microscopy (TEM) derived myelin fraction using a rat injury model at normal (normal myelin), 3 weeks post-injury (a large amount of myelin debris), and 8 weeks post-injury (myelin debris partially cleared). I found that myelin water fraction correlated strongly with the amount of myelin lipid bilayers in both intact myelin and myelin debris. From the TEM images, it appears that myelin debris consists of areas of either normally spaced myelin or large watery spaces. No significant difference was found in myelin period among the three groups.

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Master's Student Supervision

Theses completed in 2010 or later are listed below. Please note that there is a 6-12 month delay to add the latest theses.

Combining inhomogeneous magnetization transfer and myelin water imaging at 9.4T (2023)

Myelin is an important biomarker for neurodegenerative diseases such as multiple sclerosis. It is for this reason that there has been a concerted effort to enhance myelin imaging techniques. Two established methods in this pursuit are myelin water imaging (MWI) and inhomogeneous magnetization transfer (ihMT). Combining these approaches has the potential to further elucidate the microenvironment surrounding myelin. In this study, the viability of this joint method is investigated on a 9.4 Tesla magnetic resonance imaging (MRI) scanner, focusing on pulse sequence implementation and optimizations. The method is then applied to a cohort of 17 formalin-fixed rat spinal cord samples, collected at various stages post-injury: six controls, five at 3 weeks post-injury, and six at 8 weeks post-injury, with the aim to gain insight on the myelin degradation process. Specifically, data with various levels of dipolar relaxation (T₁D) filtering was acquired, selecting for protons experiencing predominantly dipolar coupling, such as those within myelin. These datasets were then subjected to fitting within an expanded 4-pool model framework to extract T₁D for myelin and non-myelin semisolids, as an indirect measure of myelin content. It was discovered that the 9.4T scanner’s high field strength rendered the T₂ value of myelin water too short to be resolved under standard imaging conditions, despite advantages in improved resolution and SNR. This led to truncated myelin water peaks within the T₂ distributions, consequently distorting area estimates under these curves. Additionally, it impeded the scanner’s ability to detect the impact of dual saturation pulses on the myelin water compartment, thereby obstructing subsequent analyses such as determining T₁D. This work underscores the importance of considering field strength when pursuing myelin imaging, highlighting the need for exploration at lower field strengths to harness the full diagnostic potential of this method.

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Development of MR image analysis with machine learning to enhance T2W images with luminal water imaging for prostate cancer (2022)

Luminal water imaging (LWI) is a novel quantitative MRI technique developed to aid with prostate cancer diagnosis. The results of LWI have shown significance in relating its derived parameters to the Gleason score, indicating its usefulness with prostate cancer grading. However, LWI parameters cannot show anatomical information on which radiologists rely for diagnosis. To address the lack of anatomic detail and to allow for LWI to become clinically feasible, a method for enhancing anatomical T2-Weighted (T2W) images with luminal water parametric maps is proposed. In addition to enhancing images, a U-Net model is implemented to automatically segment the prostate region and peripheral zone in T2W images. Results indicate that LWI-enhanced T2W images can provide better image contrast when compared to T2W images alone. Automatic segmentation shows a Dice coefficient score of 91.93% and 75.05% accuracy for the whole-prostate and peripheral zone segmentation, respectively. With automatic segmentation and an LWI enhancement routine, anatomical T2W images can be quickly processed to provide better cancer image diagnostics to radiologists in a clinical setting.

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Comparison of combinations of various levels of GraSE and compressed sensing on luminal water imaging measurements in MRI (2020)

Several methods have been developed to decrease scanning times including gradient-and-spin echo (GraSE) imaging, and compressed sensing. One of the benefits of both techniques is that they can decrease scan time to varying degrees by changing the GraSE factor or sampling level.An electronic phantom was created to model a single slice multi-echo magnetic resonance imaging (acquisitions using different GraSE factors, sampling levels, and signal-to-noise ratios (SNRs). The image included two types of prostatic tissue, peripheral zone and transitional zone, both with the signal composed of two different T2 decay values. LWI analysis was applied to the resulting images and the resulting T2 decay values and luminal water fraction (LWF) measurements were compared with a modeled multi-echo spin echo sequence without noise. The results of comparing the error with the theoretical scan times suggest that if scan times are comparable, the errors will be comparable. As the SNR decreased preference shifted towards using lower GraSE when possible.Next a celery phantom was scanned because it shows two T2 components with values similar to those found in an in-vivo prostate. 3D GraSE Images were acquired with different GraSE factors and had simulated undersampling to various degrees. Measurements of the reconstructions were compared to the fully sampled GraSE factor 3 images and agreed with the previous result that similar scan times lead to similar errors, showing no preference for a higher or lower GraSE factor.Lastly one patient had 3D multi-echo GraSE images taken of their prostate. Images had a simulated undersampling of various levels and reconstructions were compared to the fully sampled GraSE factor 3 images. Again, similar scan times resulted in similar error measurements.For the celery and human prostate scans, selected combinations of GraSE factor and sampling levels were simulated with one hundred different sampling schemes each in order to observe the variability due to the chosen sampling scheme. Following our method of fully sampling the central 33% of k-space and randomly sampling the remainder, the results strongly suggest that different sampling schemes of the same level have little effect on the resulting LWF and T2 measurements.

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Frequency shift mapping in spinal cord models of white matter demyelination (2016)

The behavior of MR phase and frequency in demyelination and damage in central nervous tissue white matter arises not only from traditionally associated bulk susceptibility changes, but also from changes to its tissue microstructure. A recently proposed generalized Lorentzian model of microstructure-related magnetic susceptibility effects predicts an increase in MR frequency due to damage in myelin in MS lesions. The same model also predicts reduction in MR frequency due to axonal degeneration. Here, we investigate the effect of both myelin and axonal damage through transection of white matter fibers in the dorsal column of rat cervical spinal cord. This injury generates secondary damage consisting of neurodegeneration along nerve tracts bilateral to the transection site, producing cases of Wallerian and retrograde degeneration free of excessive hemorrhage and inflammation. High-resolution frequency maps of degenerating tracts were correlated with histopathology for axons, myelin, degenerated myelin, and macrophages. Damage to myelin sheaths is prominent in Wallerian degeneration, where we observe strong correlations with increasing frequency up to 8 weeks post-injury. Retrograde degeneration, which consists predominantly of axonal damage, produces decreased frequency shift over time. The MR frequency shifts are sensitive to the effects of macrophage in filtration and debris clearance, which vary with white matter fiber density and affect rates of degeneration. We demonstrate how MR frequency can successfully characterize injury in rat spinal cord white matter in a manner consistent with predictions outlined by the Generalized Lorentzian Approximation Model, and conclude that these results suggest potential applications of MR frequency to supplement or replace current clinical techniques, such as myelin water and diffusion weighted imaging, as a non-invasive and quantitative method of assessing white matter damage in CNS.

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In-vivo 3T and ex-vivo 7T diffusion tensor imaging of pro state cancer: correlation with histology (2012)

Diffusion Tensor Imaging has been successfully applied in prostate cancer diagnosis (Kozlowski et al., 2010). It has been well established that the water Apparent Diffusion Coefficient has a lower value in the prostate carcinomas when compared to normal prostatic tissue (Bashar, 2002; Gürses et al., 2008; Kozlowski et al., 2010; Manenti et al., 2007; Pickles et al., 2005; Sato et al., 2005; Xu et al., 2009). However, fractional anisotropy values in prostatic carcinoma have been reported to be higher (Gürses et al., 2008), lower (Manenti et al., 2007), and unchanged(Xu et al., 2009) when compared to the prostate’s normal peripheral zone. Preliminary data from a study involving diffusion tensor imaging measurements in prostate glands, in-vivo and ex-vivo following radical prostatectomy, is presented. Histology whole mount slides were registered to T2 weighted images and diffusion parametric maps using a mutual information voxel intensity registration algorithm using software developed in-house. Regions of interest which included the normal peripheral zone, the normal peripheral zone with enlarged glands, and tumours were taken into account for this study. The tumours were highlighted and graded with the Gleason score grading system by a specialized pathologist. Values of the apparent diffusion coefficient and the fractional anisotropy parameters were calculated. Monte-Carlo simulations of the behaviour of the fractional anisotropy with respect to the value of the apparent diffusion coefficient, the signal to noise ratio, and the b-value of the Stejskal-Tanner equation were performed. The results show lower values of the apparent diffusion coefficient for regions of tumours for the ex-vivo and in-vivo cases. Values of the fractional anisotropy in the prostate carcinomas are slightly higher ex-vivo than in-vivo, which may be explained by the dependence of the fractional anisotropy on partial volume effects and noise. These preliminary results show that the fractional anisotropy does not show significant differences between normal and cancerous tissue, strongly suggesting that it is not likely to contribute significantly to the diagnostic capabilities of diffusion tensor imaging in prostate cancer.

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