Table of contents

Volume 39

Number 1, 1 January 1994

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PAPERS

1

, and

In order to measure in vivo resistivity of tissues in the thorax, the possibility of combining anatomical data extracted from high-resolution images with multiple-electrode impedance measurements, a priori knowledge of the range of tissue resistivities, and a priori data on the instrumentation noise is assessed in this study. A statistically constrained minimum-mean-square error estimator (MIMSEE) that minimizes the effects of linearization errors and instrumentation noise is developed and compared to the conventional least-squares error estimator (LSEE). The MIMSEE requires a priori signal and noise information. The statistical constraint signal information was obtained from a priori knowledge of the physiologically allowed range of regional resistivities. The noise constraint information was obtained from a priori knowledge of the linearization error and the instrumentation noise. The torso potentials were simulated by employing a three-dimensional canine torso model. The model consists of four different conductivity regions: heart, right lung, left lung, and body. It is demonstrated that the statistically constrained MIMSEE performs significantly better than the LSEE in determining resistivities. The results based on the torso model indicate that regional resistivities can be estimated to within 40% accuracy of their true values by utilizing a statistically constrained MIMSEE, even if the instrumentation noise is comparable to the measured torso potentials.

19

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Total-body irradiation (TBI) is a therapy modality that is being used with increasing frequency, in conjunction with chemotherapy, for patients undergoing bone-marrow transplantation. At the Ottawa Regional Cancer centre a technique has been developed for the delivery of TBI to patients prior to bone-marrow transplantation. In this technique patients are treated on a mobile couch at approximately 195 cm SSD with a field size of 66.5 cm wide by 57 cm long. A computer-controlled stepping motor drives the patient couch at a user-selectable speed. The total dose delivered to the patient is a function of couch velocity, field size and patient separation. Treatment times are of the order of 10 min for each of the anterior and posterior fields for a 400 cGy fraction. It has been found that the conventional central axis tissue maximum ratio (TMR) and percentage depth dose (PDD) functions are not appropriate for describing dose delivered during dynamic treatment. To this end the authors have developed dynamic TMR and PDD functions. Extensive measurements have been performed in an anthropomorphic water phantom to determine the dose distributions in three dimensions and the efficacy of polymethyl methacrylate (PMMA) beam spoilers as a replacement for anterior and lateral bolus. It has been found that 2.4 cm PMMA spoilers do provide full skin dose and negate the requirement for lateral bolus. This TBI procedure is simple, rapid and appears to be well tolerated by the patients. 55 patients have been treated since the introduction of this technique in 1991.

37

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General analytical expressions are derived for the required motion of the collimator leaves to achieve a desired energy fluence distribution or collimator opening density in the patient in the shortest possible time. By simplification of the general expressions the equations of motion have been derived for both the shrinking field and the curtain shutter techniques with the associated approximations clearly quantified. The mechanical limitations on leaf motion, caused by the finite velocity and acceleration, are taken into account. It is shown that almost any desired energy fluence distribution can be created even when the limitations on velocity and acceleration are considered. The basic rule with the curtain shutter technique is that when the energy fluence gradient along the direction of motion of the leaves is positive, the leading leaf should move at maximum speed and the lagging leaf should modulate the field. In regions where the gradient is negative the lagging leaf should instead move at full speed and the leading leaf should modulate the field. The overall treatment time is then proportional to the total increment in energy fluence of opening density between consecutive minima and maxima. For energy fluence profiles with numerous high peaks the treatment time may therefore increase considerably over that for conventional uniform dose delivery. However, in general the treatment time is prolonged by a factor of about two compared to a traditional uniform treatment. Obviously the method developed here for multileaf collimators is also suitable for simple block collimators.

63

and

A method is presented to predict beam profiles and outputs for wedged asymmetric fields defined by independent collimator jaws allowing fast generation of beam profiles whilst requiring very little additional data to that already used by most treatment planning systems in generating symmetric field isodoses. Symmetric field data are modified by the use of wedged primary off-centre ratios (POCRs) which are obtained from in air measurements of the largest possible wedged field. Beam hardening occurring within the flattening filter and wedge is taken into account by the use of attenuation coefficients measured under each wedge and used to generate the wedged POCR at depth. A full investigation into the comparison between measured and calculated profiles was performed which demonstrates favourable agreement across the whole of the asymmetric field including the penumbra.

75

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The photon emission of tissue was measured after radiotherapy with various doses of fission neutrons. Spectral analyses of the decay rates resulted in data for the exchange of sodium and chlorine between the irradiated tissue and the whole body. In 12 cases the authors found that about three fifths of Na and Cl exchange rapidly between the extravascular and vascular liquids with a turnover half-life of 13+or-2 min. Slowly exchangeable or nonexchangeable fractions are deposited in the soft tissue. New defined mass exchange rates for Na and Cl amount to an average of 0.8 mval min-1 kg-1 of soft tissue. The turnover of the electrolytes in tissue with large tumours is about twice that in tissues with small metastasis. Depending on dose, radiotherapy led in all cases to distinct variations of the metabolism. A maximum of the exchange of Cl combined with a minimum of Na occurs at about 85 Gy of conventional or at 10 Gy of lead-filtered fission neutron radiation. These results show directly for the first time the local response of the electrolyte metabolism to therapy.

91

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Three published inverse treatment planning algorithms for physical optimization of external beam radiotherapy are compared. All three algorithms attempt to minimize a quadratic objective function of the dose distribution. It is shown that the algorithms are based on the common framework of Newton's method of multidimensional function minimization. The approximations used within this framework to obtain the different algorithms are described. The use of these algorithms requires that the number of weights of elemental dose distributions be equal to the number of sample points taken in the dose volume. The primary factor in determining how the algorithms are implemented is the dose computation model. Two of the algorithms use pencil beam dose models and therefore directly optimize individual pencil beam weights, whereas the third algorithm is implemented to optimize groups of pencil beams, each group converging upon a common point. All dose computation models assume that the irradiated medium is homogeneous. It is shown that the two different implementations produce similar results for the simple optimization problem of conforming dose to a convex target shape. Complex optimization problems consisting of nonconvex target shapes and dose limiting structures are shown to require a pencil beam optimization method.

107

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The authors develop a method to predict the energy deposition in tumours undergoing ultrasound-hyperthermia treatments. Energy depositions are calculated using an exact, analytic solution to the problem of ultrasound scattering from a spherical tumour. The biological tissues are modelled as solid, lossy elastic media so that (i) transverse-wave modes, in addition to longitudinal-wave modes, are considered, and (ii) mode coupling is fully accounted for during the scattering. The model tumour is of arbitrary size and no restrictions are placed on its material parameters relative to the surrounding tissue. Simpler analytic results are given for tumours that differ in densities and rigidities only slightly from the surrounding tissue. The authors briefly discuss how the above analysis could be extended to more complex systems, i.e., irregularly shaped tumours.

133

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Changes in tissue electrical conductivity in the low radiofrequency range due to tissue temperature coefficients (TCs), approximately 2% degrees C-1, have been investigated by others as a noninvasive means of determining tissue temperature changes during the application of therapeutic hyperthermia. However, the occurrence of additional changes in conductivity due to non-TC effects, for example, from heat-induced oedema, or changes in cellular volume or membrane characteristics, can result in incorrect temperature determination based solely on the TC. The authors (i) present estimates of the errors that will occur in temperature mapping using electrical impedance measurements if non-TC effects are ignored, using examples of excised and in vivo EMT6 tumours, (ii) present a method of differentiating the onset of non-TC effects from TC effects using conductance measurements, thereby allowing for use of the re method until the onset of non-TC effects, and (iii) suggest a means of using conductance measurements to monitor the course of hyperthermia treatments, without the use of temperature information, based on hyperthermia-induced cellular changes.

145

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Three-dimensional (3D) structure is one of the main factors influencing the mechanical behaviour of cancellous bone. To analyse the trabecular bone structure nondestructively the authors used a peripheral QCT system and applied a special thin-slice technique to create high-resolution volumetric data sets serving as a basis for something they would like to call noninvasive bone biopsy. In order to obtain binary data sets, the mineralized bone in the CT volume was separated from bone marrow and muscle tissue with the help of a sophisticated 3D segmentation algorithm based on the analysis of directional derivatives, which are computed from a locally approximated fit function of the original CT volume. Binary volumes including either a solid representation of trabecular plates and rods or a topological representation of the cancellous bone architecture were acquired. Such volumes can be processed nondestructively and, even more important, repetitively. By using a surface reconstruction algorithm based on interpolating triangulation it was possible to visualize the 3D surface of the trabecular bone structure. The results showed that surface representation and visualization in combination with a multiple thin-slice measuring technique are valuable tools in studying 3D bone architecture. In the future, the noninvasive bone biopsies will be evaluated by means of 3D mechanical analysis incorporating finite element modelling and direct morphological investigations of the cancellous bone architecture for a better prediction of bone strength as an index for fracture risk or osteoporosis.

165

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The importance of correcting a small centre-of-rotation displacement ( approximately 1 mm) in single-photon-emission computed tomography (SPECT) using high-resolution pinhole collimation is demonstrated. A filtered backprojection (FBP) algorithm is derived for a pinhole geometry that has a displaced centre-of-rotation. The centre-of-rotation displacement, or mechanical shift (MS), is the displacement of the midplane of the pinhole collimator from the rotation centre. It is characterized by two orthogonal components: the shift eta of the midplane of the pinhole collimator along the direction of the axis of rotation, and the distance tau between the midline of the pinhole collimator and the axis of rotation. This algorithm is fast and corrects the centre-of-rotation displacement directly by incorporating this displacement into the algorithm. This new algorithm is evaluated using both a three-line source and a micro-SPECT cold rod phantom. The results demonstrate that the pinhole FBP With mechanical shift correction is able to correct the 'doughnut'-type artifacts caused by the mechanical shift and restore the expected system resolution.

177

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Describes a simple method for measuring the 'differential pathlength' of photons in a scattering medium utilizing the spectral absorption features of water. Determination of this differential pathlength is a prerequisite for quantifying chromophore concentration changes measured by near-infrared spectroscopy (NIRS), and the method proposed here achieves this without the need for time- or frequency-resolved measurements. The quantification of tissue chromophore concentration measurements is a major goal in NIRS research, allowing, for example, the noninvasive measurement of blood flow and volume in the brain and other organs. The authors present the results of validation experiments performed on tissue phantoms comparing the differential path estimates yielded by water absorption and time-resolved measurements, finding that the weak water absorption feature at 820 nm can yield a differential path estimate in addition to the main feature at 975 nm. The authors also present results from in vivo studies in which they find that whilst the 820 nm feature is measured with lower accuracy for a given light flux than the 975 nm feature, it is intrinsically a more accurate differential path estimator. Studies on the adult forearm showing differences between time-resolved and water absorption differential path estimates suggest that the measurement of both could aid in quantifying NIRS signals in heterogeneous tissues.

NOTES

197

The Monte Carlo method was used to optimize a polarized photon source for the X-ray fluorescence analysis of platinum and other heavy metals in vivo. The source consisted of a 140 kVp, 25 mA X-ray tube with the photons plane-polarized by 90 degrees scattering. The use of plane-polarized photons results in a significant reduction in background when the fluorescent radiation is measured along the direction of polarization. A Monte Carlo computer programme was written to simulate the production and interaction of polarized photons in order to determine the optimal polarizing material and dimensions, together with beam width and geometrical arrangement of source, polarizer and beam collimators. Calculated photon energy distributions are compared with experimental data to test the validity of the model. The best configuration of the polarization system for the in vivo analysis of platinum consisted of a 20 mm Cu polarizing block with a secondary collimator subtending a 0.1 radian angle at the polarizer.

207

and

The aim of this study was the experimental characterization of the PRESS technique for image-guided in vivo 1H NMR spectroscopy, as implemented on a commercially available 1.5 T NMR whole-body system. Three characterization parameters were defined and evaluated in test object measurements: selection efficiency, suppression efficiency and contamination. The characterization parameters were evaluated in different experimental conditions. The profile of signal intensity across the volume of interest (VOI) was investigated. The results show that the characterization parameters are slightly affected by the echo time, while they are not affected by changes in the repetition time. When the VOI is co-extensive with the inner cube of the test object the suppression efficiency is good but the selection efficiency is not very high. Contamination is affected by the synthesizer frequency offset, while the selection efficiency is quite stable. Contamination effects become significant in case of 90 degrees pulse maladjustment.