Anders Brahme

Dosimetric Precision Requirements in Radiation Therapy

Based on simple radiobiologic models the effect of the true distribution of absorbed dose in therapy beams on the response of uniform tumor volumes are investigated. Under assumption that the dose variation in the beam is small it is shown that the response of the tumor to radiation is determined by the mean dose to the tumor volume. Quantitative expressions are also given for the loss in tumor control probability as a function of the degree of dose variations around the mean dose level. When the dose variations are large the minimum tumor dose is best related to tumor control. It is finally shown that high tumor control rates can only be achieved with a very high accuracy in dose delivery. If the normalized dose response gradient is higher than 3, as is frequently the case, the relative standard deviation of mean dose in the target volume should be less than 3 per cent to achieve an absolute standard deviation in tumor control probability of less than 10 per cent.

Optimization of stationary and moving beam radiation therapy techniques

A new approach is suggested for the optimization of stationary and more general moving beam type of irradiations. The method reverses the order of conventional treatment planning as it derives the optimum incident beam dose distributions from the desired dose distribution in the target volume. It is therefore deterministic and largely avoids the trial and error approach often applied in treatment planning of today. Based on the approximate spatial invariance of the convergent beam point irradiation dose distribution, the desired dose distribution in the target volume is analyzed in terms of the optimum density of such point irradiations. Since each point irradiation distribution is optimal for the irradiation of a given point and due to the linearity of individual energy depositions or absorbed dose contributions, the resultant point irradiation density will also generate the best possible irradiation of an extended target volume when the maximum absorbed dose at a certain distance from the target should be minimized. The optimum shape of the incident beam for each position of the gantry is obtained simply by inverse back projection of the point irradiation density on the position of the radiation source for that orientation of the incident beam.

Solution of an integral equation encountered in rotation therapy

An integral equation relating the lateral absorbed dose profile of a photon beam to the resultant absorbed dose distribution during single-turn rotating-beam therapy has been set up and solved for the case of a cylindrical phantom with the axis of rotation coinciding with the axis of symmetry of the cylinder. In the first approximation the results obtained are also valid when the axis of rotation is somewhat off-centred, even in a phantom that deviates from circular symmetry, provided the rotation is performed in both clockwise and counter clockwise directions. The calculated dose profiles indicate that improved dose uniformity can be achieved using a new type of non-linear wedge-shaped filter, which can easily be designed using the derived general analytic solution to the integral equation.

An algorithm for maximizing the probability of complication-free tumour control in radiation therapy

New radiobiological models are used to describe tumour and normal tissue reactions and to account for their dependence on the irradiated volume and inhomogeneities of the delivered dose distribution and cell sensitivity. The probability of accomplishing complication-free tumour control is maximized by an iterative algorithm. The algorithm is demonstrated by applying it to a one-dimensional (1D) tumour model but also to a more clinically relevant 2D case. The new algorithm is n-dimensional so it could simultaneously optimize the dose delivery in a 3D volume and in principle also select the ideal beam orientations, beam modalities (photons, electrons, neutrons, etc) and optimal spectral distributions of the corresponding modalities. To make calculation time reasonable, 2D-3D problems are most practical, and suitable beam orientations are preselected by the choice of irradiation kernel. The energy deposition kernel should therefore be selected in order to avoid irradiation through organs at risk. Clinically established dose response parameters for the tissues of interest are used to make the optimization as relevant as possible to the clinical problems at hand. The algorithm can be used even with a poorly selected kernel because it will always, as far as possible, avoid irradiating organs at risk. The generated dose distribution will be optimal with respect to the spatial distribution and assumed radiobiological properties of the tumour and normal tissues at risk for the kernel chosen. More specifically the probability of achieving tumour control without fatal complications in normal tissues is maximized. In the clinical examples a reduced tumour dose is seen at the border to sensitive organs at risk, but instead an increased dose just inside the tumour border is generated. The increased tumour dose has the effect that the dose fall-off is as steep as possible at the border to organs at risk.

Comparative dosimetry in narrow high-energy photon beams.

A comparison of the response of different dosimeters in narrow photon beams (phi > or = 4 mm) of 6 and 18 MV bremsstrahlung has been performed. The detectors used were a natural diamond detector, a liquid ionization chamber, a plastic scintillator and two dedicated silicon diodes. The diodes had a very small detection volume and one was a specially designed double diode using two parallel opposed active volumes with compensating interface perturbations. The characteristics of the detectors were investigated both for dose distribution measurements, such as depth-dose curves and lateral beam profiles, and for output factors. The dose rate and angular dependence of the diamond and the two diodes were also studied separately. The depth-dose distributions for small fields agree well for the diamond, the scintillator and the single diode, while the measured dose maximum for the double diode is about 1% higher and for the liquid chamber about 1% lower than the mean of the others when normalized at a depth of 10 cm. The plastic scintillator and the liquid ionization chamber detect a penumbra width that is slightly broadened due to the influence of their finite size, while the double diode may even underestimate the penumbra width due to its small size and high density. When corrected for the extension of the detector volume a good agreement with Monte Carlo calculated beam profiles was obtained for the plastic scintillator and the liquid ionization chamber. Profiles measured with the diamond show an asymmetry when positioned with the smallest dimension facing the beam, while the double diode, the scintillator and the liquid chamber measure symmetric profiles irrespective of positioning. Significant differences in the output factors were obtained with the different detectors. The natural diamond detector measures output factors close to those with an ionization chamber (less than 1% difference) for field sizes between 3 x 3 and 15 x 15 cm2, but overestimates the output factors for large fields and underestimates the output factors for the smallest field sizes. The single and double diodes overestimated the output factor for large field sizes by up to 7 and 12% respectively due to the high content of low-energy photons. The double diode, and to some extent the single diode, also showed a relative increase in response compared with the more water equivalent liquid chamber and plastic scintillator at the smallest fields where there is a lack of lateral electron equilibrium. Both the plastic scintillator and the liquid chamber also show responses that deviate from the ionization chamber for larger field sizes. The major deviations can be explained based on the characteristics of the sensitive materials and the construction of the detectors.

Development of phase-contrast X-ray imaging techniques and potential medical applications

A significant improvement over conventional attenuation-based X-ray imaging, which lacks contrast in small objects and soft biological tissues, is obtained by introducing phase-contrast imaging. As recently demonstrated, phase-contrast imaging is characterized by its extraordinary image quality, greatly enhanced contrast, and good soft tissue discrimination with very high spatial resolution down to the micron and even the sub-micron region. The rapid development of compact X-ray sources of high brightness, tuneability, and monochromaticity as well as high-resolution X-ray detectors with high quantum efficiency and improved computational methods is stimulating the development of a new generation of X-ray imaging systems for medical applications. The present paper reviews some intrinsic mechanisms, recent technical developments and potential medical applications of two-, three- and four-dimensional phase-contrast X-ray imaging. Challenging issues in current phase-contrast imaging techniques and key clinical applications are discussed and possible developments of future high-contrast and high spatial and temporal resolution medical X-ray imaging systems are outlined.

CALCULATION AND APPLICATION OF POINT SPREAD FUNCTIONS FOR TREATMENT PLANNING WITH HIGH ENERGY PHOTON BEAMS

A general dose calculation method for treatment planning with high energy photon beams, based on folding of the total energy released by primary photons per unit mass, the terma, with a fractional mean energy imparted point spread function is described. A set of point spread functions has been calculated with Monte Carlo technique for energies of primary photons between 100 keV and 20 MeV. Dose distributions have been calculated for a 6 MV bean using the method. The results clearly point out the considerably increased precision and flexibility achieved when calculating photon beam dose distributions from first principles using Monte Carlo generated point spread functions. The point spread functions calculated in this work are available on magnetic tape from the authors.

A generalized pencil beam algorithm for optimization of radiation therapy

An iterative pencil beam algorithm for optimization of multidimensional radiation therapy dose plans has been developed. The algorithm allows the use of both physical and radiobiological treatment objective functions and allows arbitrary sampling such as straight Cartesian grids with linear or nonlinear sampling functions or random sampling. The algorithm can account for and optimally combine almost all the degrees of freedom at an advanced radiotherapy clinic, such as different beam modalities and spectra, beam directions, beam fluence distributions, and time-dose fractionations. The algorithm allows for external charged and neutral beams as well as intracavitary and interstitial sources to be optimally combined. A quantity termed the generalized fluence vector is introduced, combining fluences and energy fluences from external beams as well as the radiation source densities of intracavitary and interstitial sources or external source distributions. The positivity constraint on the generalized fluence can therefore be applied directly during the optimization procedure. The convergence properties and the required iteration time of the algorithm are discussed. Several examples with combinations of photon and electron beams of different energies and directions of incidence are presented. The optimization has been made with the treatment objective to maximize the probability of achieving tumor control without causing severe complications in healthy normal tissues.

Optimal Dose Distribution for Eradication of Heterogeneous Tumors

The traditional single hit multitarget theory has been applied on the probability of eradication of an organ or a tumor and the probability for causing complications in normal tissue. This simple theory predicts a decreasing possibility to achieve uncomplicated tumor control with increasing tumor size and maintained irradiation technique, because the control curve moves to higher doses and the complication curve to lower doses as the tumor size increases. This simple result is shown to be consistent with clinically observed dose response relations for small and large tumors. The optimal dose distribution for eradication of a heterogeneous tumor is derived on the assumption that a uniform minimal recurrence probability is most advantageous for the patient. The optimal dose distribution is proportional to the spatial variation of the local D0 value and the logarithm of the tumor cell density. Various techniques to measure the density of tumor cells and the different possibilities to deliver non-uniform dose distributions to the target volume are also discussed.

Shaping of arbitrary dose distributions by dynamic multileaf collimation.

Traditionally, the shaping of non-uniform dose distributions has been performed by using wedges or compensating filters. The advent of high resolution multileaf collimators may largely eliminate the need for material attenuators for modification of the beam. This is achieved by a new technique for the shaping of arbitrary dose distributions by dynamic motion of the collimator leaves. By employing narrow elementary slit beams that correspond to the smallest possible opening of the multileaf collimator, the optimal density of such slit beams, i.e. opening density, can be determined automatically using a newly developed inversion algorithm. The present method has two major advantages (1) internal structures in the field can be created, controlled solely by steering the collimator leaves, (2) the opening density determined by the algorithm never gives rise to underdosage: this is important from a radiobiological point of view.