This paper describes a new quantitation method called AQSES for short echo time magnetic resonance spectra. This method is embedded in a software package available online from www.esat.kuleuven.be/sista/members/biomed/new/ with a graphical user interface, under an open source license, which means that the source code is freely available and easy to adapt to specific needs of the user. The quantitation problem is mathematically formulated as a separable nonlinear least-squares fitting problem, which is numerically solved using a modified variable-projection procedure. A macromolecular baseline is incorporated into the fit via nonparametric modelling, efficiently implemented using penalized splines. Unwanted components such as residual water are removed with a maximum-phase FIR filter. Constraints on the phases, dampings and frequencies of the metabolites can be imposed. AQSES has been tested on simulated MR spectra with several types of disturbance and on short echo time in vivo proton MR spectra. Results show that AQSES is robust, easy to use and very flexible.

The aim of this study was to assess the importance of deconvolution for the calculation of renal perfusion and glomerular filtration rate (GFR) on the basis of concentration-time curves as measured with perfusion MRI. Six rabbits were scanned dynamically after injection of a gadolinium chelate. Concentration-time curves were generated by manually drawing regions of interest in the aorta and the renal cortex. To remove the dependency on the arterial input function, a regularized structured total least-squares deconvolution algorithm was used to calculate the renal impulse response. This curve was fitted by the sum of two gamma variate functions, corresponding to the passage of the contrast agent in the glomeruli and the proximal convoluted tubules. Tracer kinetics models were applied to these two functions to obtain the renal perfusion and GFR.

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In this paper we develop a fast algorithm for the basic deconvolution problem. First we show that the kernel problem to be solved in the basic deconvolution problem is a so-called structured Total Least Squares problem. Due to the low displacement rank of the involved matrices, we are able to develop a fast algorithm. We apply the new algorithm on a deconvolution problem arising in a medical application in renography. By means of this example, we show the increased computational performance of our algorithm as compared to other algorithms for solving this type of structured Total Least Squares problems. In addition, Monte-Carlo simulations indicate the superior statistical performance of the structured Total Least Squares estimator compared to other estimators such as the ordinary Total Least Squares estimator.

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