Table of contents

Target motion is one of the major limitations of each high precision radiation therapy. Using advanced active beam delivery techniques, such as the magnetic raster scanning system for particle irradiation, the interplay between time-dependent beam and target position heavily distorts the applied dose distribution. This paper presents a simulation environment in which the time-dependent effect of target motion on heavy-ion irradiation can be calculated with dynamically scanned ion beams. In an extension of the existing treatment planning software for ion irradiation of static targets (TRiP) at GSI, the expected dose distribution is calculated as the sum of several sub-distributions for single target motion states. To investigate active compensation for target motion by adapting the position of the therapeutic beam during irradiation, the planned beam positions can be altered during the calculation. Applying realistic parameters to the planned motion-compensation methods at GSI, the effect of target motion on the expected dose uniformity can be simulated for different target configurations and motion conditions. For the dynamic dose calculation, experimentally measured profiles of the beam extraction in time were used. Initial simulations show the feasibility and consistency of an active motion compensation with the magnetic scanning system and reveal some strategies to improve the dose homogeneity inside the moving target. The simulation environment presented here provides an effective means for evaluating the dose distribution for a moving target volume with and without motion compensation. It contributes a substantial basis for the experimental research on the irradiation of moving target volumes with scanned ion beams at GSI which will be presented in upcoming papers.

In this paper two tests based on statistical models are presented and used to assess, quantify and provide positional information of the existence of bias and/or variations between planar images acquired at different times but under similar conditions. In the first test a linear regression model is fitted to the data in a pixelwise fashion, using three mathematical operators. In the second test a comparison using z-scoring is used based on the assumption that Poisson statistics are valid. For both tests the underlying assumptions are as simple and few as possible. The results are presented as parametric maps of either the three operators or the z-score. The z-score maps can then be thresholded to show the parts of the images which demonstrate change. Three different thresholding methods (naïve, adaptive and multiple) are presented: together they cover almost all the needs for separating the signal from the background in the z-score maps. Where the expected size of the signal is known or can be estimated, a spatial correction technique (referred to as the reef correction) can be applied. These tests were applied to flood images used for the quality control of gamma camera uniformity. Simulated data were used to check the validity of the methods. Real data were acquired from four different cameras from two different institutions using a variety of acquisition parameters. The regression model found the bias in all five simulated cases and it also found patterns of unstable regions in real data where visual inspection of the flood images did not show any problems. In comparison the z-map revealed the differences in the simulated images from as low as 1.8 standard deviations from the mean, corresponding to a differential uniformity of 2.2% over the central field of view. In all cases studied, the reef correction increased significantly the sensitivity of the method and in most cases the specificity as well. The two proposed tests can be used either separately or in combination and are capable of showing trends and/or the magnitude of difference between images acquired under similar conditions with high positional and statistical precision. In addition to gamma camera quality control, they could be applied to any pair (or set) of registered planar images to detect subtle changes, e.g. a set of scintigrams or conventional radiographs of a patient before, during and after treatment.

In this paper, we present a fully automatic, fast and accurate deformable registration technique. This technique deals with free-form deformation. It minimizes an energy functional that combines both similarity and smoothness measures. By using calculus of variations, the minimization problem was represented as a set of nonlinear elliptic partial differential equations (PDEs). A Gauss–Seidel finite difference scheme is used to iteratively solve the PDE. The registration is refined by a multi-resolution approach. The whole process is fully automatic. It takes less than 3 min to register two three-dimensional (3D) image sets of size 256 × 256 × 61 using a single 933 MHz personal computer. Extensive experiments are presented. These experiments include simulations, phantom studies and clinical image studies. Experimental results show that our model and algorithm are suited for registration of temporal images of a deformable body. The registration of inspiration and expiration phases of the lung images shows that the method is able to deal with large deformations. When applied to the daily CT images of a prostate patient, the results show that registration based on iterative refinement of displacement field is appropriate to describe the local deformations in the prostate and the rectum. Similarity measures improved significantly after the registration. The target application of this paper is for radiotherapy treatment planning and evaluation that incorporates internal organ deformation throughout the course of radiation therapy. The registration method could also be equally applied in diagnostic radiology.

We present an exact filtered backprojection reconstruction formula for helical cone beam computed tomography in which the pitch of the helix varies with time. We prove that the resulting algorithm, which is functionally identical to the constant pitch case, provides exact reconstruction provided that the projection of the helix onto the detector forms convex boundaries and that PI lines are unique. Furthermore, we demonstrate that both of these conditions are satisfied provided the sum of the translational velocity and the derivative of the translational acceleration does not change sign. As a special case, we show that gantry tilt can also be handled by our dynamic pitch formula. Simulation results demonstrate the resulting algorithm.

The potential for malignancy detection using dynamic infrared imaging (DIRI) has been investigated in an animal model of human malignancy. Malignancy was apparent in images formed at the vasomotor and cardiogenic frequencies of tumour bearing mice. The observation of malignancy was removed by the administration of an agent that blocks vasodilation caused by nitric oxide (NO). Image patterns similar to those that characterize malignancy could be mimicked in normal mice using an NO producing agent. Apparently DIRI allows for cancer detection in this model through vasodilation caused by malignancy generated NO. Dynamic infrared detection of vasomotor and cardiogenic surface perfusion was validated in human subjects by a comparison with laser Doppler flowmetry (LDF). Dynamic infrared imaging technology was then applied to breast cancer detection. It is shown that dynamic infrared images formed at the vasomotor and cardiogenic frequencies of the normal and malignant breast have image pattern differences, which may allow for breast cancer detection.

The impulse response of the ultrasonic transducer used for detection is crucial for photoacoustic imaging with high resolution. We demonstrate a reconstruction method that allows the optical absorption distribution of a sample to be reconstructed without knowing the impulse response of the ultrasonic transducer. A convolution relationship between photoacoustic signals measured by an ultrasound transducer and optical absorption distribution is developed. Based on this theory, the projection of the optical absorption distribution of a sample can be obtained directly by deconvolving the recorded PA signal originating from a point source out of that from the sample. And a modified filtered back projection algorithm is used to reconstruct the optical absorption distribution. We constructed a photoacoustic imaging system to validate the reconstruction method and the experimental results demonstrated that the reconstructed images agreed well with the original phantom samples. The spatial resolution of the system reaches 0.3 mm.

The iterative reconstruction algorithms employed in brain single-photon emission computed tomography (SPECT) allow some quantitative parameters of the image to be improved. These algorithms require accurate modelling of the so-called point spread function (PSF). Nowadays, most in vivo neurotransmitter SPECT studies employ pharmaceuticals radiolabelled with ¹²³I. In addition to an intense line at 159 keV, the decay scheme of this radioisotope includes some higher energy gammas which may have a non-negligible contribution to the PSF. The aim of this work is to study this contribution for two low-energy high-resolution collimator configurations, namely, the parallel and the fan beam. The transport of radiation through the material system is simulated with the Monte Carlo code PENELOPE. We have developed a main program that deals with the intricacies associated with tracking photon trajectories through the geometry of the collimator and detection systems. The simulated PSFs are partly validated with a set of experimental measurements that use the 511 keV annihilation photons emitted by a ¹⁸F source. Sensitivity and spatial resolution have been studied, showing that a significant fraction of the detection events in the energy window centred at 159 keV (up to approximately 49% for the parallel collimator) are originated by higher energy gamma rays, which contribute to the spatial profile of the PSF mostly outside the 'geometrical' region dominated by the low-energy photons. Therefore, these high-energy counts are to be considered as noise, a fact that should be taken into account when modelling PSFs for reconstruction algorithms. We also show that the fan beam collimator gives higher signal-to-noise ratios than the parallel collimator for all the source positions analysed.

The performances of three recently published leaf sequencing algorithms for step-and-shoot intensity-modulated radiation therapy delivery that eliminates tongue-and-groove underdosage are evaluated. Proofs are given to show that the algorithm of Que et al (2004 Phys. Med. Biol.49 399–405) generates leaf sequences free of tongue-and-groove underdosage and interdigitation. However, the total beam-on times could be up to n times those of the sequences generated by the algorithms of Kamath et al (2004 Phys. Med. Biol.49 N7–N19), which are optimal in beam-on time for unidirectional leaf movement under the same constraints, where n is the total number of involved leaf pairs. Using 19 clinical fluence matrices and 100 000 randomly generated 15 × 15 matrices, the average monitor units and number of segments of the leaf sequences generated using the algorithm of Que et al are about two to four times those generated by the algorithm of Kamath et al.

The results of a recent study on the limiting uncertainties in the measurement of photon radiation dose with MOSFET dosimeters are reported. The statistical uncertainty in dose measurement from a single device has been measured before and after irradiation. The resulting increase in 1/f noise with radiation dose has been investigated via various analytical models. The limit of uncertainty in the ubiquitous linear trend of threshold voltage with dose has been measured and compared to two nonlinear models. Inter-device uncertainty has been investigated in a group of 40 devices, and preliminary evidence for kurtosis and skewness in the distributions for devices without external bias has been observed.

The EGSnrc Monte Carlo system has been used to calculate the dose distributions from ¹²⁵I radioactive seeds (model 6711). The results showed that the agreement between EGSnrc and the American Association of Physicists in Medicine Task Group Report 43 (AAPM-TG43) dosimetry protocol is generally within ±15% for radial distances less than 1.0 cm in both the transverse axis and longitudinal axis of the source. For radial distances between 1.0 and 2.5 cm the agreement between Monte Carlo simulations and the AAPM-TG43 dosimetry protocol is within ±20%. In the longitudinal axis of the source the difference between Monte Carlo simulations and the AAPM-TG43 dosimetry is up to 40% for radial distances greater than 2.5 cm. The agreement between the EGSnrc/Monte Carlo simulation and the AAPM-TG43 dosimetry protocol improved significantly when recently published data of the anisotropic function were implemented (Weaver 1998 Med. Phys.25 2271–8). The difference between Monte Carlo simulations and the AAPM-TG43 dosimetry protocol is not more than ±10% in the transverse axis of the source up to a radius of 2.5 cm. The EGSnrc Monte Carlo simulation and the AAPM-TG43 with the Weaver anisotropic data were also used to investigate the differences in the dose distribution caused by small differences in the construction of individual seeds (Sloboda and Menon 2000 Med. Phys.27 1789–99). The results show that a change in length of the silver rod containing the ¹²⁵I radioactive material of 0.14 mm does not affect the dose distribution significantly in the transverse and longitudinal axes but a change of 0.13 mm in the thickness of the welded end of the encapsulation affected the dose significantly in the longitudinal axis of the source.

EGSnrc Monte Carlo simulation was used to investigate dose perturbation effects in prostate seed implant brachytherapy using ¹²⁵I radioactive seeds used in implant brachytherapy. Dose perturbation effects resulting from the seed mutual attenuation in a prostate seed implant consisting of 27 seeds were investigated. The results showed that for ¹²⁵I seeds implanted into the prostate at 1.00 cm, 0.75 cm and 0.50 cm apart (uniform spacing), the dose perturbation effects are up to 10%. The volume of the target occupied by the 10% dose difference between the full Monte Carlo simulation and the single seed superposition model decreases with increasing seed spacing. Despite the differences between the Monte Carlo simulation and the simple superposition, there was no significant change in the dose volume histogram for 1 cm and 0.75 cm seed spacing. However, there was a significant change in the dose volume histogram when the seed spacing was 0.5 cm. An analysis of the external volume index (EI), coverage index (CI) and homogeneity index (HI) also showed that there is no difference in these indexes for the 1.00 cm and 0.75 cm seed spacing between the simple superposition model and the full Monte Carlo simulation. Compared to the full Monte Carlo simulations, the simple superposition model overestimated EI, CI and HI by 7%, 5% and 4% respectively for the 0.50 cm seed spacing.

It is desirable to reduce range ambiguities in treatment planning for making full use of the major advantage of heavy-ion radiotherapy, that is, good dose localization. A range verification system using positron emitting beams has been developed to verify the ranges in patients directly. The performance of the system was evaluated in beam experiments to confirm the designed properties. It was shown that a ¹⁰C beam could be used as a probing beam for range verification when measuring beam properties. Parametric measurements indicated the beam size and the momentum acceptance and the target volume did not influence range verification significantly. It was found that the range could be measured within an analysis uncertainty of ±0.3 mm under the condition of 2.7 × 10⁵ particle irradiation, corresponding to a peak dose of 96 mGyE (gray-equivalent dose), in a 150 mm diameter spherical polymethyl methacrylate phantom which simulated a human head.

Since prostatic carcinoma is usually multifocal within the prostate, effective photodynamic therapy (PDT) of prostatic carcinoma is expected to require the photochemical destruction of the entire organ. Accurate light dosimetry will be essential to avoid damage to proximal sensitive tissue such as the rectum. The prostate will be illuminated using interstitial cylindrical fibreoptic light sources and, because of the limited transparency of prostate tissue, these sources will be mounted in a parallel array analogous to the source array used in brachytherapy. Both source spacing and the light delivered to each source will control light dosimetry from a parallel array of fibreoptic sources implanted into tissue. Clinical PDT will require dose planning in order to determine the position and illumination of each source prior to treatment, but unfortunately few methods of predicting light fluence from cylindrical interstitial sources currently exist. In this paper, a novel light fluence model is used to predict tissue transillumination resulting from cylindrical interstitial sources. The cylindrical source is modelled as a finite array of infinitesimal small sources using Christian Huygens' famous single-slit diffraction model. We show that this source model when combined with a robust derivation of fluence in a spherical geometry using diffusion theory, accurately predicts fluence levels from a single cylindrical source in a variety of media. This method is found to retain its accuracy near the sources. With a simple extension, this fluence model is used to predict the light fluence levels from an array of three sources and the predicted fluence is found to compare favourably with experimental data.

Advances in photodynamic therapy (PDT) treatment for prostate cancer can be achieved either by improving selectivity of the photosensitizer towards prostate gland tissue or improving the dosimetry by means of individualized treatment planning using currently available photosensitizers. The latter approach requires the ability to measure, among other parameters, the fluence rate at different positions within the prostate and the ability to derive the tissue optical properties. Here fibre optic probes are presented capable of measuring the fluence rate throughout large tissue volumes and a method to derive the tissue optical properties for different volumes of the prostate. The responsivity of the sensors is sufficient to detect a fluence rate of 0.1 mW cm⁻². The effective attenuation coefficient in the canine prostate at 660 nm is higher at the capsule (2.15 ± 0.19 cm⁻¹) than in proximity of the urethra (1.84 ± 0.36 cm⁻¹). Significant spatial and temporal intra- and inter-canine variability in the tissue optical properties was noted, highlighting the need for individualized monitoring of the fluence rate for improved dosimetry.

The efficient delivery of intensity modulated radiation therapy (IMRT) depends on finding optimized beam intensity patterns that produce dose distributions, which meet given constraints for the tumour as well as any critical organs to be spared. Many optimization algorithms that are used for beamlet-based inverse planning are susceptible to large variations of neighbouring intensities. Accurately delivering an intensity pattern with a large number of extrema can prove impossible given the mechanical limitations of standard multileaf collimator (MLC) delivery systems. In this study, we apply Cimmino's simultaneous projection algorithm to the beamlet-based inverse planning problem, modelled mathematically as a system of linear inequalities. We show that using this method allows us to arrive at a smoother intensity pattern. Including nonlinear terms in the simultaneous projection algorithm to deal with dose–volume histogram (DVH) constraints does not compromise this property from our experimental observation. The smoothness properties are compared with those from other optimization algorithms which include simulated annealing and the gradient descent method. The simultaneous property of these algorithms is ideally suited to parallel computing technologies.

The lateral and longitudinal distributions of absorbed dose of broad and narrow light ion beams in water are investigated. An analytical algorithm based on the generalized Fermi–Eyges theory is developed and used to calculate the effects of multiple scattering and range straggling on the dose distribution of light ion beams in water. A first-order Gaussian multiple scattering and energy loss straggling approach is generally sufficiently accurate for describing the lateral and longitudinal spread of the Bragg peak and the associated energy deposition distribution of therapeutic light ion beams at ranges of clinical interest. Nuclear reactions are not taken into account in this study. The analytical algorithm given in the present study allows an accurate description of the radial spread and the range straggling of light ions traversing matter. A verification of this approach by comparing with experimental data, Monte Carlo methods and other analytical techniques will be presented in a forthcoming paper.

As the magnetic field of widely used MR scanners is one of the strongest magnetic fields to which people are exposed, the biological influence of the static magnetic field of MR scanners is of great concern. One magnetic interaction in biological subjects is the magnetic torque on the magnetic moment induced by biomagnetic substances. The red blood cell is a major biomagnetic substance, and the blood flow may be influenced by the magnetic field. However, the underlying mechanisms have been poorly understood. To examine the mechanisms of the magnetic influence on blood viscosity, we measured the time for blood to fall through a glass capillary inside and outside a 1.5 T MR scanner. Our in vitro results showed that the blood viscosity significantly increased in a 1.5 T MR scanner, and also clarified the mechanism of the interaction between red blood cells and the external magnetic field. Notably, the blood viscosity increased depending on blood oxygenation and the shear rate of the blood flow. Thus, our findings suggest that even a 1.5 T magnetic field may modulate blood flow.

Images acquired from an electronic portal imaging device are aligned with digitally reconstructed radiographs (DRRs) or other portal images to verify patient positioning during radiation therapy. Most of the currently available computer aided registration methods are based on the manual placement of corresponding landmarks. The purpose of the paper is twofold: (a) the establishment of a methodology for patient set-up verification during radiotherapy based on the registration of electronic portal images, and (b) the evaluation of the proposed methodology in a clinical environment. The estimation of set-up errors, using the proposed methodology, can be accomplished by matching the portal image of the current fraction of the treatment with the portal image of the baseline treatment (reference portal image) using a nearly automated technique. The proposed registration method is tested on a number of phantom data as well as on data from four patients. The phantom data included portal images that corresponded to various positions of the phantom on the treatment couch. For each patient, a set of 30 portal images was used. For the phantom data (for both transverse and lateral portal images), the maximum absolute deviations of the translational shifts were within 1.5 mm, whereas the in-plane rotation angle error was less than 0.5°. The two-way Anova revealed no statistical significant variability both within observer and between-observer measurements (P > 0.05). For the patient data, the mean values obtained with manual and the proposed registration methods were within 0.5 mm. In conclusion, the proposed registration method has been incorporated within a system, called ESTERR-PRO. Its image registration capability achieves high accuracy and both intra- and inter-user reproducibility. The system is fully operational within the Radiotherapy Department of 'HYGEIA' Hospital in Athens and it could be easily installed in any other clinical environment since it requires standardized hardware specifications and minimal human intervention.

This work proposes a compact dichromatic imaging system for the application of the K-edge digital subtraction technique based on a conventional x-ray tube and a monochromator system. A quasi-monochromatic x-ray beam at the energy of iodine K-edge is produced by Bragg diffraction on a mosaic crystal. Two thin adjacent beams with energies that bracket the K-edge discontinuity are obtained from the diffracted beam by means of a proper collimation system. They are then detected using an array of Si detectors. A home-made phantom is used to study the image quality as a function of iodine concentration. Signal and signal-to-noise ratio analysis has also been performed. The results are compared with theoretical expectations.

Truncated singular value decomposition (TSVD) is an effective method for the deconvolution of dynamic contrast enhanced (DCE) MRI. Two robust methods for the selection of the truncation threshold on a pixel-by-pixel basis—generalized cross validation (GCV) and the L-curve criterion (LCC)—were optimized and compared to paradigms in the literature. GCV and LCC were found to perform optimally when applied with a smooth version of TSVD, known as standard form Tikhonov regularization (SFTR). The methods lead to improvements in the estimate of the residue function and of its maximum, and converge properly with SNR. The oscillations typically observed in the solution vanish entirely, and perfusion is more accurately estimated at small mean transit times. This results in improved image contrast and increased sensitivity to perfusion abnormalities, at the cost of 1–2 min in calculation time and hyperintense clusters in the image. Preliminary experience with clinical data suggests that the latter problem can be resolved using spatial continuity and/or hybrid thresholding methods. In the simulations GCV and LCC are equivalent in terms of performance, but GCV thresholding is faster.

An acardiac twin is a severely malformed monochorionic twin fetus that lacks most organs, particularly a heart. It grows during pregnancy, because it is perfused by its developmentally normal co-twin (called the pump twin) via a set of placental arterioarterial and venovenous anastomoses. The pump twin dies intrauterine or neonatally in about 50% of the cases due to congestive heart failure, polyhydramnios and prematurity. Because the pathophysiology of this pregnancy is currently incompletely understood, we modified our previous haemodynamic model of monochorionic twins connected by placental vascular anastomoses to include the analysis of acardiac twin pregnancies. We incorporated the fetoplacental circulation as a resistance circuit and used the fetal umbilical flow that perfuses the body to define fetal growth, rather than the placental flow as done previously. Using this modified model, we predicted that the pump twin has excess blood volume and increased mean arterial blood pressure compared to those in the acardiac twin. Placental perfusion of the acardiac twin is significantly reduced compared to normal, as a consequence of an increased venous pressure, possibly implying reduced acardiac placental growth. In conclusion, the haemodynamic analysis may contribute to an increased knowledge of the pathophysiologic consequences of an acardiac body mass for the pump twin.

Optimized radiographic techniques for clinical images of chest, skull and pelvis using conventional single-phase, three-phase and high-frequency x-ray units for a standard patient have been developed. Optimization of image contrast and optical density was obtained by using a homogeneous phantom (PEP) and an Anderson Rando anthropomorphic phantom. Image quality was evaluated by nine radiologists in independent analyses, leading to the choice of the optimized technique. A course of action to implement and validate these techniques in other radiographic systems has also been introduced. A realistic-analytic phantom (RAP) was constructed to certify the validation process. The optimized radiographic technique was implemented in the routine of our home hospital radiodiagnostic routine, enabling a reduction in patient doses around 25, 14 and 72%, respectively, for chest, skull and pelvis exams when compared with the previously used techniques. In addition, a corresponding reduction in the x-ray tube load of 68, 14 and 62% for the respective mentioned exams has been observed. In conclusion, implemented optimal techniques can lead to a reduction in the rate of film rejection, thus contributing to a better risk–benefit relationship for the patient and cost–benefit for the radiodiagnostic facility.

Quantitative indices of radionuclide uptake in an object of interest provide a useful adjunct to qualitative interpretation in the diagnostic application of radionuclide imaging. This note describes a new measure of total uptake of an organ, the specific uptake size index (SUSI). It can either be related in absolute terms to the total activity injected or to the specific activity in a reference region. As it depends on the total activity in the object, the value obtained will not depend on the resolution of the imaging process, as is the case with some other similar quantitative indices. This has been demonstrated in an experiment using simulated images. The application of the index to quantification of dopamine receptor SPECT imaging and parathyroid–thyroid subtraction planar scintigraphy is described. The index is considered to be of potential value in reducing variation in quantitative assessment of uptake in objects with applications in all areas of radionuclide imaging.

A new accurate Monte Carlo code for IMRT dose computations, MCDE (Monte Carlo dose engine), is introduced. MCDE is based on BEAMnrc/DOSXYZnrc and consequently the accurate EGSnrc electron transport. DOSXYZnrc is reprogrammed as a component module for BEAMnrc. In this way both codes are interconnected elegantly, while maintaining the BEAM structure and only minimal changes to BEAMnrc.mortran are necessary. The treatment head of the Elekta SLiplus linear accelerator is modelled in detail. CT grids consisting of up to 200 slices of 512 × 512 voxels can be introduced and up to 100 beams can be handled simultaneously. The beams and CT data are imported from the treatment planning system GRATIS via a DICOM interface. To enable the handling of up to 50 × 10⁶ voxels the system was programmed in Fortran95 to enable dynamic memory management. All region-dependent arrays (dose, statistics, transport arrays) were redefined. A scoring grid was introduced and superimposed on the geometry grid, to be able to limit the number of scoring voxels. The whole system uses approximately 200 MB of RAM and runs on a PC cluster consisting of 38 1.0 GHz processors. A set of in-house made scripts handle the parallellization and the centralization of the Monte Carlo calculations on a server. As an illustration of MCDE, a clinical example is discussed and compared with collapsed cone convolution calculations. At present, the system is still rather slow and is intended to be a tool for reliable verification of IMRT treatment planning in the case of the presence of tissue inhomogeneities such as air cavities.

Induced activity due to photonuclear reactions produced in the vacuum window of the accelerating wave-guide, the x-ray target and the beam-flattening filter of an 18 MV Siemens KDS linac has been studied. Measurements were performed using a high-purity portable germanium detector. Radioisotopes such as ¹⁹⁶Au, ⁵⁷Co, ⁶⁰Co and other traces were detected one week after the last clinical use of the linac.

High resolution micro-CT images are often corrupted by ring artefacts, prohibiting quantitative analysis and hampering post processing. Removing or at least significantly reducing such artefacts is indispensable. However, since micro-CT systems are pushed to the extremes in the quest for the ultimate spatial resolution, ring artefacts can hardly be avoided. Moreover, as opposed to clinical CT systems, conventional correction schemes such as flat-field correction do not lead to satisfactory results. Therefore, in this note a simple but efficient and fast post processing method is proposed that effectively reduces ring artefacts in reconstructed μ-CT images.

We present a concise overview of the modified Beer–Lambert law, which has been extensively used in the literature of near-infrared spectroscopy (NIRS) of scattering media. In particular, we discuss one form of the modified Beer–Lambert law that is commonly found in the literature and that is not strictly correct. However, this incorrect form of the modified Beer–Lambert law still leads to the correct expression for the changes in the continuous wave optical signal associated with changes in the absorption coefficient of the investigated medium. Here we propose a notation for the modified Beer–Lambert law that keeps the typical form commonly found in the literature without introducing any incorrect assumptions.