Reconstruction algorithm for single photon emission computed tomography and its numerical implementation

The modern imaging techniques of positron emission tomography and of single photon emission computed tomography are not only two of the most important tools for studying the functional characteristics of the brain, but they now also play a vital role in several areas of clinical medicine, including neurology, oncology and cardiology. The basic mathematical problems associated with these techniques are the construction of the inverse of the Radon transform and of the inverse of the so-called attenuated Radon transform, respectively. An exact formula for the inverse Radon transform is well known, whereas that for the inverse attenuated Radon transform was obtained only recently by R. Novikov. The latter formula was constructed by using a method introduced earlier by R. Novikov and the first author in connection with a novel derivation of the inverse Radon transform. Here, we first show that the appropriate use of that earlier result yields immediately an analytic formula for the inverse attenuated Radon transform. We then present an algorithm for the numerical implementation of this analytic formula, based on approximating the given data in terms of cubic splines. Several numerical tests are presented which suggest that our algorithm is capable of producing accurate reconstruction for realistic phantoms such as the well-known Shepp–Logan phantom

Protein and calorie restriction may improve outcomes in living kidney donors and kidney transplant recipients

Previously, we and others showed that dietary restriction protects against renal ischemia-reperfusion injury in animals. However, clinical translation of preoperative diets is scarce, and in the setting of kidney transplantation these data are lacking. In this pilot study, we investigated the effects of five days of a preoperative protein and caloric dietary restriction (PCR) diet in living kidney donors on the perioperative effects in donors, recipients and transplanted kidneys. Thirty-five kidney donors were randomized into either the PCR, 30% calorie and 80% protein reduction, or control group without restrictions. Adherence to the diet and kidney function in donors and their kidney recipients were analyzed. Perioperative kidney biopsies were taken in a selected group of transplanted kidneys for gene expression analysis. All donors adhered to the diet. From postoperative day 2 up until month 1, kidney function of donors was significantly better in the PCR-group. PCR-donor kidney recipients showed significantly improved kidney function and lower incidence of slow graft function and acute rejection. PCR inhibited cellular immune response pathways and activated stress-resistance signaling. These observations are the first to show that preoperative dietary restriction induces postoperative recovery benefits in humans and may be beneficial in clinical settings involving ischemia-reperfusion injury