Unique Compact Representation of Magnetic Fields using Truncated Solid Harmonic Expansions

Precise knowledge of magnetic fields is crucial in many medical imaging applications like magnetic resonance imaging or magnetic particle imaging (MPI) as they are the foundation of these imaging systems. For the investigation of the influence of field imperfections on imaging, a compact and unique representation of the magnetic fields using real solid spherical harmonics, which can be obtained by measuring a few points of the magnetic field only, is of great assistance. In this manuscript, we review real solid harmonic expansions as a general solution of Laplace's equation including an efficient calculation of their coefficients using spherical t-designs. We also provide a method to shift the reference point of an expansion by calculating the coefficients of the shifted expansion from the initial ones. These methods are used to obtain the magnetic fields of an MPI system. Here, the field-free-point of the spatial encoding field serves as unique expansion point. Lastly, we quantify the severity of the distortions of the static and dynamic fields in MPI by analyzing the expansion coefficients.Comment: 25 page

Video Compressive Sensing for Dynamic MRI

We present a video compressive sensing framework, termed kt-CSLDS, to accelerate the image acquisition process of dynamic magnetic resonance imaging (MRI). We are inspired by a state-of-the-art model for video compressive sensing that utilizes a linear dynamical system (LDS) to model the motion manifold. Given compressive measurements, the state sequence of an LDS can be first estimated using system identification techniques. We then reconstruct the observation matrix using a joint structured sparsity assumption. In particular, we minimize an objective function with a mixture of wavelet sparsity and joint sparsity within the observation matrix. We derive an efficient convex optimization algorithm through alternating direction method of multipliers (ADMM), and provide a theoretical guarantee for global convergence. We demonstrate the performance of our approach for video compressive sensing, in terms of reconstruction accuracy. We also investigate the impact of various sampling strategies. We apply this framework to accelerate the acquisition process of dynamic MRI and show it achieves the best reconstruction accuracy with the least computational time compared with existing algorithms in the literature.Comment: 30 pages, 9 figure

Automatic Individual Arterial Input Functions Calculated From PCA Outperform Manual and Population-Averaged Approaches for the Pharmacokinetic Modeling of DCE-MR Images

[EN] Background: To introduce a segmentation method to calculate an automatic arterial input function (AIF) based on prin- cipal component analysis (PCA) of dynamic contrast enhanced MR (DCE-MR) imaging and compare it with individual manually selected and population-averaged AIFs using calculated pharmacokinetic parameters. Methods: The study included 65 individuals with prostate examinations (27 tumors and 38 controls). Manual AIFs were individually extracted and also averaged to obtain a population AIF. Automatic AIFs were individually obtained by applying PCA to volumetric DCE-MR imaging data and finding the highest correlation of the PCs with a reference AIF. Variability was assessed using coefficients of variation and repeated measures tests. The different AIFs were used as inputs to the pharmacokinetic model and correlation coefficients, Bland-Altman plots and analysis of variance tests were obtained to compare the results. Results: Automatic PCA-based AIFs were successfully extracted in all cases. The manual and PCA-based AIFs showed good correlation (r between pharmacokinetic parameters ranging from 0.74 to 0.95), with differences below the manual individual variability (RMSCV up to 27.3%). The population-averaged AIF showed larger differences (r from 0.30 to 0.61). Conclusion: The automatic PCA-based approach minimizes the variability associated to obtaining individual volume- based AIFs in DCE-MR studies of the prostate.Sanz Requena, R.; Prats-Montalbán, JM.; Marti Bonmati, L.; Alberich Bayarri, A.; García Martí, G.; Pérez, R.; Ferrer Riquelme, AJ. (2015). Automatic Individual Arterial Input Functions Calculated From PCA Outperform Manual and Population-Averaged Approaches for the Pharmacokinetic Modeling of DCE-MR Images. Journal of Magnetic Resonance Imaging. 42:477-487. doi:10.1002/jmri.24805S47748742Leach, M. O., Brindle, K. M., Evelhoch, J. L., Griffiths, J. R., Horsman, M. R., Jackson, A., … Workman, P. (2005). The assessment of antiangiogenic and antivascular therapies in early-stage clinical trials using magnetic resonance imaging: issues and recommendations. British Journal of Cancer, 92(9), 1599-1610. doi:10.1038/sj.bjc.6602550Tofts, P. S., & Kermode, A. G. (1991). Measurement of the blood-brain barrier permeability and leakage space using dynamic MR imaging. 1. Fundamental concepts. Magnetic Resonance in Medicine, 17(2), 357-367. doi:10.1002/mrm.1910170208Parker, G. J. M., Roberts, C., Macdonald, A., Buonaccorsi, G. A., Cheung, S., Buckley, D. L., … Jayson, G. C. (2006). Experimentally-derived functional form for a population-averaged high-temporal-resolution arterial input function for dynamic contrast-enhanced MRI. Magnetic Resonance in Medicine, 56(5), 993-1000. doi:10.1002/mrm.21066Meng, R., Chang, S. D., Jones, E. C., Goldenberg, S. L., & Kozlowski, P. (2010). Comparison between Population Average and Experimentally Measured Arterial Input Function in Predicting Biopsy Results in Prostate Cancer. Academic Radiology, 17(4), 520-525. doi:10.1016/j.acra.2009.11.006Loveless, M. E., Halliday, J., Liess, C., Xu, L., Dortch, R. D., Whisenant, J., … Yankeelov, T. E. (2011). A quantitative comparison of the influence of individual versus population-derived vascular input functions on dynamic contrast enhanced-MRI in small animals. Magnetic Resonance in Medicine, 67(1), 226-236. doi:10.1002/mrm.22988Shukla-Dave, A., Lee, N., Stambuk, H., Wang, Y., Huang, W., Thaler, H. T., … Koutcher, J. A. (2009). Average arterial input function for quantitative dynamic contrast enhanced magnetic resonance imaging of neck nodal metastases. BMC Medical Physics, 9(1). doi:10.1186/1756-6649-9-4Wang, Y., Huang, W., Panicek, D. M., Schwartz, L. H., & Koutcher, J. A. (2008). Feasibility of using limited-population-based arterial input function for pharmacokinetic modeling of osteosarcoma dynamic contrast-enhanced MRI data. Magnetic Resonance in Medicine, 59(5), 1183-1189. doi:10.1002/mrm.21432Rijpkema, M., Kaanders, J. H. A. M., Joosten, F. B. M., van der Kogel, A. J., & Heerschap, A. (2001). Method for quantitative mapping of dynamic MRI contrast agent uptake in human tumors. Journal of Magnetic Resonance Imaging, 14(4), 457-463. doi:10.1002/jmri.1207Singh, A., Rathore, R. K. S., Haris, M., Verma, S. K., Husain, N., & Gupta, R. K. (2009). Improved bolus arrival time and arterial input function estimation for tracer kinetic analysis in DCE-MRI. Journal of Magnetic Resonance Imaging, 29(1), 166-176. doi:10.1002/jmri.21624Shi, L., Wang, D., Liu, W., Fang, K., Wang, Y.-X. J., Huang, W., … Ahuja, A. T. (2013). Automatic detection of arterial input function in dynamic contrast enhanced MRI based on affinity propagation clustering. Journal of Magnetic Resonance Imaging, 39(5), 1327-1337. doi:10.1002/jmri.24259Kim, J.-H., Im, G. H., Yang, J., Choi, D., Lee, W. J., & Lee, J. H. (2011). Quantitative dynamic contrast-enhanced MRI for mouse models using automatic detection of the arterial input function. NMR in Biomedicine, 25(4), 674-684. doi:10.1002/nbm.1784Li, X., Welch, E. B., Arlinghaus, L. R., Chakravarthy, A. B., Xu, L., Farley, J., … Yankeelov, T. E. (2011). A novel AIF tracking method and comparison of DCE-MRI parameters using individual and population-based AIFs in human breast cancer. Physics in Medicine and Biology, 56(17), 5753-5769. doi:10.1088/0031-9155/56/17/018Fedorov, A., Fluckiger, J., Ayers, G. D., Li, X., Gupta, S. N., Tempany, C., … Fennessy, F. M. (2014). A comparison of two methods for estimating DCE-MRI parameters via individual and cohort based AIFs in prostate cancer: A step towards practical implementation. Magnetic Resonance Imaging, 32(4), 321-329. doi:10.1016/j.mri.2014.01.004Lin, Y.-C., Chan, T.-H., Chi, C.-Y., Ng, S.-H., Liu, H.-L., Wei, K.-C., … Wang, J.-J. (2012). Blind estimation of the arterial input function in dynamic contrast-enhanced MRI using purity maximization. Magnetic Resonance in Medicine, 68(5), 1439-1449. doi:10.1002/mrm.24144Roberts, C., Little, R., Watson, Y., Zhao, S., Buckley, D. L., & Parker, G. J. M. (2010). The effect of blood inflow andB1-field inhomogeneity on measurement of the arterial input function in axial 3D spoiled gradient echo dynamic contrast-enhanced MRI. Magnetic Resonance in Medicine, 65(1), 108-119. doi:10.1002/mrm.22593Jackson, J. E. (1991). A Use’s Guide to Principal Components. Wiley Series in Probability and Statistics. doi:10.1002/0471725331Prats-Montalbán, J. M., Sanz-Requena, R., Martí-Bonmatí, L., & Ferrer, A. (2013). Prostate functional magnetic resonance image analysis using multivariate curve resolution methods. Journal of Chemometrics, 28(8), 672-680. doi:10.1002/cem.2585Eyal, E., Bloch, B. N., Rofsky, N. M., Furman-Haran, E., Genega, E. M., Lenkinski, R. E., & Degani, H. (2010). Principal Component Analysis of Dynamic Contrast Enhanced MRI in Human Prostate Cancer. Investigative Radiology, 45(4), 174-181. doi:10.1097/rli.0b013e3181d0a02fTofts, P. S. (1997). Modeling tracer kinetics in dynamic Gd-DTPA MR imaging. Journal of Magnetic Resonance Imaging, 7(1), 91-101. doi:10.1002/jmri.1880070113Donahue, K. M., Burstein, D., Manning, W. J., & Gray, M. L. (1994). Studies of Gd-DTPA relaxivity and proton exchange rates in tissue. Magnetic Resonance in Medicine, 32(1), 66-76. doi:10.1002/mrm.1910320110Taylor, J. S., & Reddick, W. E. (2000). Evolution from empirical dynamic contrast-enhanced magnetic resonance imaging to pharmacokinetic MRI. Advanced Drug Delivery Reviews, 41(1), 91-110. doi:10.1016/s0169-409x(99)00058-7Port, R. E., Knopp, M. V., & Brix, G. (2001). Dynamic contrast-enhanced MRI using Gd-DTPA: Interindividual variability of the arterial input function and consequences for the assessment of kinetics in tumors. Magnetic Resonance in Medicine, 45(6), 1030-1038. doi:10.1002/mrm.1137Dale, B. M., Jesberger, J. A., Lewin, J. S., Hillenbrand, C. M., & Duerk, J. L. (2003). Determining and optimizing the precision of quantitative measurements of perfusion from dynamic contrast enhanced MRI. Journal of Magnetic Resonance Imaging, 18(5), 575-584. doi:10.1002/jmri.10399Garpebring, A., Brynolfsson, P., Yu, J., Wirestam, R., Johansson, A., Asklund, T., & Karlsson, M. (2012). Uncertainty estimation in dynamic contrast-enhanced MRI. Magnetic Resonance in Medicine, 69(4), 992-1002. doi:10.1002/mrm.24328Onxley, J. D., Yoo, D. S., Muradyan, N., MacFall, J. R., Brizel, D. M., & Craciunescu, O. I. (2014). Comprehensive Population-Averaged Arterial Input Function for Dynamic Contrast–Enhanced vMagnetic Resonance Imaging of Head and Neck Cancer. International Journal of Radiation Oncology*Biology*Physics, 89(3), 658-665. doi:10.1016/j.ijrobp.2014.03.006Chen, Y.-J., Chu, W.-C., Pu, Y.-S., Chueh, S.-C., Shun, C.-T., & Tseng, W.-Y. I. (2012). Washout gradient in dynamic contrast-enhanced MRI is associated with tumor aggressiveness of prostate cancer. Journal of Magnetic Resonance Imaging, 36(4), 912-919. doi:10.1002/jmri.23723Vos, E. K., Litjens, G. J. S., Kobus, T., Hambrock, T., Kaa, C. A. H. de, Barentsz, J. O., … Scheenen, T. W. J. (2013). Assessment of Prostate Cancer Aggressiveness Using Dynamic Contrast-enhanced Magnetic Resonance Imaging at 3 T. European Urology, 64(3), 448-455. doi:10.1016/j.eururo.2013.05.045Yang, C., Karczmar, G. S., Medved, M., Oto, A., Zamora, M., & Stadler, W. M. (2009). Reproducibility assessment of a multiple reference tissue method for quantitative dynamic contrast enhanced-MRI analysis. Magnetic Resonance in Medicine, 61(4), 851-859. doi:10.1002/mrm.21912McGrath, D. M., Bradley, D. P., Tessier, J. L., Lacey, T., Taylor, C. J., & Parker, G. J. M. (2009). Comparison of model-based arterial input functions for dynamic contrast-enhanced MRI in tumor bearing rats. Magnetic Resonance in Medicine, 61(5), 1173-1184. doi:10.1002/mrm.21959Orton, M. R., d’ Arcy, J. A., Walker-Samuel, S., Hawkes, D. J., Atkinson, D., Collins, D. J., & Leach, M. O. (2008). Computationally efficient vascular input function models for quantitative kinetic modelling using DCE-MRI. Physics in Medicine and Biology, 53(5), 1225-1239. doi:10.1088/0031-9155/53/5/005Heisen, M., Fan, X., Buurman, J., van Riel, N. A. W., Karczmar, G. S., & ter Haar Romeny, B. M. (2010). The use of a reference tissue arterial input function with low-temporal-resolution DCE-MRI data. Physics in Medicine and Biology, 55(16), 4871-4883. doi:10.1088/0031-9155/55/16/01