Table of contents

Photodynamic therapy (PDT) uses light-activated drugs to treat diseases ranging from cancer to age-related macular degeneration and antibiotic-resistant infections. This paper reviews the current status of PDT with an emphasis on the contributions of physics, biophysics and technology, and the challenges remaining in the optimization and adoption of this treatment modality. A theme of the review is the complexity of PDT dosimetry due to the dynamic nature of the three essential components—light, photosensitizer and oxygen. Considerable progress has been made in understanding the problem and in developing instruments to measure all three, so that optimization of individual PDT treatments is becoming a feasible target. The final section of the review introduces some new frontiers of research including low dose rate (metronomic) PDT, two-photon PDT, activatable PDT molecular beacons and nanoparticle-based PDT.

Based on the concept of differentiated backprojection (DBP) (Noo et al2004 Phys. Med. Biol.49 3903, Pan et al 2005 Med. Phys.32 673, Defrise et al 2006 Inverse Problems22 1037), this paper shows that the solution to the interior problem in computed tomography is unique if a tiny a priori knowledge on the object f(x, y) is available in the form that f(x, y) is known on a small region located inside the region of interest. Furthermore, we advance the uniqueness result to obtain more general uniqueness results which can be applied to a wider class of imaging configurations. We also develop a reconstruction algorithm which can be considered an extension of the DBP-POCS (projection onto convex sets) method described by Defrise et al (2006 Inverse Problems22 1037), where we not only extend this method to the interior problem but also introduce a new POCS algorithm to reduce computational cost. Finally, we present experimental results which show evidence that the inversion corresponding to each obtained uniqueness result is stable.

Small animal SPECT imaging systems have multiple potential applications in biomedical research. Whereas SPECT data are commonly interpreted qualitatively in a clinical setting, the ability to accurately quantify measurements will increase the utility of the SPECT data for laboratory measurements involving small animals. In this work, we assess the effect of photon attenuation, scatter and partial volume errors on the quantitative accuracy of small animal SPECT measurements, first with Monte Carlo simulation and then confirmed with experimental measurements. The simulations modeled the imaging geometry of a commercially available small animal SPECT system. We simulated the imaging of a radioactive source within a cylinder of water, and reconstructed the projection data using iterative reconstruction algorithms. The size of the source and the size of the surrounding cylinder were varied to evaluate the effects of photon attenuation and scatter on quantitative accuracy. We found that photon attenuation can reduce the measured concentration of radioactivity in a volume of interest in the center of a rat-sized cylinder of water by up to 50% when imaging with iodine-125, and up to 25% when imaging with technetium-99m. When imaging with iodine-125, the scatter-to-primary ratio can reach up to approximately 30%, and can cause overestimation of the radioactivity concentration when reconstructing data with attenuation correction. We varied the size of the source to evaluate partial volume errors, which we found to be a strong function of the size of the volume of interest and the spatial resolution. These errors can result in large (>50%) changes in the measured amount of radioactivity. The simulation results were compared with and found to agree with experimental measurements. The inclusion of attenuation correction in the reconstruction algorithm improved quantitative accuracy. We also found that an improvement of the spatial resolution through the use of resolution recovery techniques (i.e. modeling the finite collimator spatial resolution in iterative reconstruction algorithms) can significantly reduce the partial volume errors.

Scanned particle beams and target motion interfere. This interplay leads to deterioration of the dose distribution. Experiments and a treatment planning study were performed to investigate interplay. Experiments were performed with moving radiographic films for different motion parameters. Resulting dose distributions were analyzed for homogeneity and dose coverage. The treatment planning study was based on the time-resolved computed tomography (4DCT) data of five lung tumor patients. Treatment plans with margins to account for respiratory motion were optimized, and resulting dose distributions for 108 different motion parameters for each patient were calculated. Data analysis for a single fraction was based on dose–volume histograms and the volume covered with 95% of the planned dose. Interplay deteriorated dose conformity and homogeneity (1-standard deviation/mean) in the experiments as well as in the treatment-planning study. The homogeneity on radiographic films was below ≈80% for motion amplitudes of ≈15 mm. For the treatment-planning study based on patient data, the target volume receiving at least 95% of the prescribed dose was on average (standard deviation) 71.0% (14.2%). Interplay of scanned particle beams and moving targets has severe impact on the resulting dose distributions. Fractionated treatment delivery potentially mitigates at least parts of these interplay effects. However, especially for small fraction numbers, e.g. hypo-fractionation, treatment of moving targets with scanned particle beams requires motion mitigation techniques such as rescanning, gating, or tracking.

Whole brain radiation therapy (WBRT) is the standard treatment for patients with brain metastases, and is often used in conjunction with stereotactic radiotherapy for patients with a limited number of brain metastases, as well as prophylactic cranial irradiation. The use of open fields (conventionally used for WBRT) leads to higher doses to the brain periphery if dose is prescribed to the brain center at the largest lateral radius. These dose variations potentially compromise treatment efficacy and translate to increased side effects. The goal of this research was to design and construct a 3D 'brain wedge' to compensate dose heterogeneities in WBRT. Radiation transport theory was invoked to calculate the desired shape of a wedge to achieve a uniform dose distribution at the sagittal plane for an ellipsoid irradiated medium. The calculations yielded a smooth 3D wedge design to account for the missing tissue at the peripheral areas of the brain. A wedge was machined based on the calculation results. Three ellipsoid phantoms, spanning the mean and ± two standard deviations from the mean cranial dimensions were constructed, representing 95% of the adult population. Film was placed at the sagittal plane for each of the three phantoms and irradiated with 6 MV photons, with the wedge in place. Sagittal plane isodose plots for the three phantoms demonstrated the feasibility of this wedge to create a homogeneous distribution with similar results observed for the three phantom sizes, indicating that a single wedge may be sufficient to cover 95% of the adult population. The sagittal dose is a reasonable estimate of the off-axis dose for whole brain radiation therapy. Comparing the dose with and without the wedge the average minimum dose was higher (90% versus 86%), the maximum dose was lower (107% versus 113%) and the dose variation was lower (one standard deviation 2.7% versus 4.6%). In summary, a simple and effective 3D wedge for whole brain radiotherapy has been developed. The wedge gives a more uniform dose distribution than commonly used techniques. Further development and shape optimization may be necessary prior to clinical implementation.

If an electromagnetic field is incident normally onto a perfectly conducting ground plane, the field is reflected back into the domain. This produces a standing wave above the ground plane. If a person is present within the domain, absorption of the field in the body may cause problems regarding compliance with electromagnetic guidelines. To investigate this, the whole-body averaged specific energy absorption rate (SAR), localised SAR and ankle currents in the voxel model NORMAN have been calculated for a variety of these exposures under grounded conditions. The results were normalised to the spatially averaged field, a technique used to determine a mean value for comparison with guidelines when the field varies along the height of the body. Additionally, the external field values required to produce basic restrictions for whole-body averaged SAR have been calculated. It was found that in all configurations studied, the ICNIRP reference levels and IEEE MPEs provided a conservative estimate of these restrictions.

We compared the stability and discriminatory power of different methods of determining cardiac magnetic field map (MFM) orientation within the context of coronary artery disease (CAD). In 27 healthy subjects and 24 CAD patients, multichannel magnetocardiograms were registered at rest. MFM orientation was determined during QT interval using: (a) locations of the positive and negative centres-of-gravity, (b) locations of the field extrema and (c) the direction of the maximum field gradient. Deviation from normal orientation quantified the ability of each approach to discriminate between healthy and CAD subjects. Although the course of orientation was similar for all methods, receiver operating characteristic analysis showed the best discrimination of CAD patients for the centre-of-gravity approach (area-under-the-curve = 86%), followed by the gradient (84%) and extrema (76%) methods. Consideration of methodological and discriminatory advantages with respect to noninvasive diagnosis of CAD suggests that the centres-of-gravity method is the most suited one.

Plastic scintillator fibre optic dosimeters (FODs) have advantages for both brachytherapy and external beam radiotherapy applications. Convenient real-time monitoring and diagnosis of such dosimeters are desirable because of changes in the optical circuit that may arise in use. In this paper, we propose and demonstrate a real-time method using ultraviolet light emitting diodes (LED) to stimulate the scintillator and to diagnose failures of FODs. Key aspects of the LED FOD dosimetry design are investigated, enabling the design of a stable and accurate real-time monitoring dosimetry system. We demonstrate experimentally that the real-time monitoring FOD system is convenient to be used to monitor FOD dosimeters and to diagnose their failures resulted from different mechanisms.

This paper describes the implementation of neutron-stimulated emission computed tomography (NSECT) for non-invasive imaging and reconstruction of a multi-element phantom. The experimental apparatus and process for acquisition of multi-spectral projection data are described along with the reconstruction algorithm and images of the two elements in the phantom. Independent tomographic reconstruction of each element of the multi-element phantom was performed successfully. This reconstruction result is the first of its kind and provides encouraging proof of concept for proposed subsequent spectroscopic tomography of biological samples using NSECT.

Treatment planning calculations for proton therapy require an accurate knowledge of radiological path length, or range, to the distal edge of the target volume. In most cases, the range may be calculated with sufficient accuracy using kilovoltage (kV) computed tomography (CT) images. However, metal implants such as hip prostheses can cause severe streak artifacts that lead to large uncertainties in proton range. The purposes of this study were to quantify streak-related range errors and to determine if they could be avoided by using artifact-free megavoltage (MV) CT images in treatment planning. Proton treatment plans were prepared for a rigid, heterogeneous phantom and for a prostate cancer patient with a metal hip prosthesis using corrected and uncorrected kVCT images alone, uncorrected MVCT images and a combination of registered MVCT and kVCT images (the hybrid approach). Streak-induced range errors of 5–12 mm were present in the uncorrected kVCT-based patient plan. Correcting the streaks by manually assigning estimated true Hounsfield units improved the range accuracy. In a rigid heterogeneous phantom, the implant-related range uncertainty was estimated at <3 mm for both the corrected kVCT-based plan and the uncorrected MVCT-based plan. The hybrid planning approach yielded the best overall result. In this approach, the kVCT images provided good delineation of soft tissues due to high-contrast resolution, and the streak-free MVCT images provided smaller range uncertainties because they did not require artifact correction.

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a widely used technique for assessing tissue physiology. Spoiled gradient echo (SPGR) pulse sequences are one of the most common methods for acquisition of DCE-MRI data, providing high temporal and spatial resolution with strong T₁-weighting. Conversion of SPGR signal to concentration is briefly reviewed, and a new closed-form expression for concentration measurement uncertainty for finite signal-to-noise ratio (SNR) and baseline scan time is derived. This result is applicable to arbitrary concentration-dependent relaxation rate and is valid over the same domain as the theoretical SPGR signal equation. Expressions for the lower and upper bounds on measurable concentration are also derived. The existence of a concentration- and tissue-dependent optimal flip angle that minimizes concentration uncertainty is demonstrated and it is shown that, for clinically relevant pulse sequence parameters, this optimal flip angle is significantly larger than the corresponding Ernst angle. Analysis of three pulse sequences from the DCE-MRI literature shows that optimization of flip angle using the methods discussed here leads to potential improvements of 10–1166% in effective SNR over the 0.5–5.0 mM concentration range with minimal or no loss of measurement accuracy down to 0.1 mM. In vivo data from three study patients provide further support for our theoretical expression for concentration measurement uncertainty, with predicted and experimental estimates agreeing to within ±30%. Equations for concentration bias resulting from biases in flip angle and from pre-contrast relaxation time and contrast relaxivity (both longitudinal and transverse) are also derived in closed-form. The resulting equations show the potential for significant contributions to bias in concentration measurement arising from even relatively small mis-specification of flip angle and/or pre-contrast longitudinal relaxation time, particularly at high contrast concentrations.

A planning study was carried out on a cohort of CT datasets from breast patients scanned during different respiratory phases. The aim of the study was to investigate the influence of different air filling in lungs on the calculation accuracy of photon dose algorithms and to identify potential patterns of failure with clinical implications. Selected respiratory phases were free breathing (FB), representative of typical end expiration, and deep inspiration breath hold (DIBH), a typical condition for clinical treatment with respiratory gating. Algorithms investigated were the pencil beam (PBC), the anisotropic analytical algorithm (AAA) and the collapsed cone (CC) from the Varian Eclipse or Philips Pinnacle planning system. Reference benchmark calculations were performed with the Voxel Monte Carlo (VMC++). An analysis was performed in terms of physical quantities inspecting either dose–volume or dose–mass histograms and in terms of an extension to three dimensions of the γ index of Low. Results were stratified according to a breathing phase and algorithm. Collectives acquired in FB or DIBH showed well-separated average lung density distributions with mean densities of 0.27 ± 0.04 and 0.16 ± 0.02 g cm⁻³, respectively, and average peak densities of 0.17 ± 0.03 and 0.09 ± 0.02 g cm⁻³. Analysis of volume–dose or mass–dose histograms proved the expected deviations on PBC results due to the missing lateral transport of electrons with underestimations in the low dose region and overestimations in the high dose region. From the γ analysis, it resulted that PBC is systematically defective compared to VMC++ over the entire range of lung densities and dose levels with severe violations in both respiratory phases. The fraction of lung voxels with γ > 1 for PBC reached 25% in DIBH and about 15% in FB. CC and AAA performed, in contrast, similarly and with fractions of lung voxels with γ > 1 in average inferior to 2% in FB and 4–5% (AAA) or 6–8% (CC) in DIBH. In summary, PBC proved to be severely defective in calculations involving lungs and particularly for cases where specific respiratory phases (e.g. DIBH) are assumed for treatment. In contrast, CC and AAA manifested a high degree of consistency against the Monte Carlo method and provided stable results over the entire range of clinically relevant densities.

Random coincidences can contribute substantially to the background in positron emission tomography (PET). Several estimation methods are being used for correcting them. The goal of this study was to investigate the validity of techniques for random coincidence estimation, with various low-energy thresholds (LETs). Simulated singles list-mode data of the MADPET-II small animal PET scanner were used as input. The simulations have been performed using the GATE simulation toolkit. Several sources with different geometries have been employed. We evaluated the number of random events using three methods: delayed window (DW), singles rate (SR) and time histogram fitting (TH). Since the GATE simulations allow random and true coincidences to be distinguished, a comparison between the number of random coincidences estimated using the standard methods and the number obtained using GATE was performed. An overestimation in the number of random events was observed using the DW and SR methods. This overestimation decreases for LETs higher than 255 keV. It is additionally reduced when the single events which have undergone a Compton interaction in crystals before being detected are removed from the data. These two observations lead us to infer that the overestimation is due to inter-crystal scatter. The effect of this mismatch in the reconstructed images is important for quantification because it leads to an underestimation of activity. This was shown using a hot–cold–background source with 3.7 MBq total activity in the background region and a 1.59 MBq total activity in the hot region. For both 200 keV and 400 keV LET, an overestimation of random coincidences for the DW and SR methods was observed, resulting in approximately 1.5% or more (at 200 keV LET: 1.7% for DW and 7% for SR) and less than 1% (at 400 keV LET: both methods) underestimation of activity within the background region. In almost all cases, images obtained by compensating for random events in the reconstruction algorithm were better in terms of quantification than the images made with precorrected data.

We study the time-dependent disintegration kinetics of tumor cells that did not survive radiotherapy treatment. To evaluate the cell disintegration rate after irradiation, we studied the volume changes of solitary lung tumors after stereotactic radiotherapy. The analysis is performed using two approximations: (1) tumor volume is a linear function of the total cell number in the tumor and (2) the cell disintegration rate is governed by the exponential decay with constant risk, which is defined by the initial cell number and a half-life T_1/2. The half-life T_1/2 is determined using the least-squares fit to the clinical data on lung tumor size variation with time after stereotactic radiotherapy. We show that the tumor volume variation after stereotactic radiotherapy of solitary lung tumors can be approximated by an exponential function. A small constant component in the volume variation does not change with time; however, this component may be the residual irregular density due to radiation fibrosis and was, therefore, subtracted from the total volume variation in our computations. Using computerized fitting of the exponent function to the clinical data for selected patients, we have determined that the average half-life T_1/2 of cell disintegration is 28.2 days for squamous cell carcinoma and 72.4 days for adenocarcinoma. This model is needed for simulating the tumor volume variation during radiotherapy, which may be important for time-dependent treatment planning of proton therapy that is sensitive to density variations.

Magnetic resonance imaging (MRI) provides a method for non-invasive characterization of cartilage composition and structure. We aimed to see whether T₁ and T₂ relaxation times are related to proteoglycan (PG) and collagen-specific mechanical properties of articular cartilage. Specifically, we analyzed whether variations in the depthwise collagen orientation, as assessed by the laminae obtained from T₂ profiles, affect the mechanical characteristics of cartilage. After MRI and unconfined compression tests of human and bovine patellar cartilage samples, fibril-reinforced poroviscoelastic finite-element models (FEM), with depthwise collagen orientations implemented from quantitative T₂ maps (3 laminae for human, 3–7 laminae for bovine), were constructed to analyze the non-fibrillar matrix modulus (PG specific), fibril modulus (collagen specific) and permeability of the samples. In bovine cartilage, the non-fibrillar matrix modulus (R = −0.64, p < 0.05) as well as the initial permeability (R = 0.70, p < 0.05) correlated with T₁. In bovine cartilage, T₂ correlated positively with the initial fibril modulus (R = 0.62, p = 0.05). In human cartilage, the initial fibril modulus correlated negatively (R = −0.61, p < 0.05) with T₂. Based on the simulations, cartilage with a complex collagen architecture (5 or 7 laminae), leading to high bulk T₂ due to magic angle effects, provided higher compressive stiffness than tissue with a simple collagen architecture (3 laminae). Our results suggest that T₁ reflects PG-specific mechanical properties of cartilage. High T₂ is characteristic to soft cartilage with a classical collagen architecture. Contradictorily, high bulk T₂ can also be found in stiff cartilage with a multilaminar collagen fibril network. By emerging MRI and FEM, the present study establishes a step toward functional imaging of articular cartilage.

Monte Carlo (MC) dose calculations are performed on patient geometries derived from computed tomography (CT) images. For most available MC codes, the Hounsfield units (HU) in each voxel of a CT image have to be converted into mass density (ρ) and material type. This is typically done with a (HU; ρ) calibration curve which may lead to mis-assignment of media. In this work, an improved material segmentation using dual-energy CT-based material extraction is presented. For this purpose, the differences in extracted effective atomic numbers Z and the relative electron densities ρ_e of each voxel are used. Dual-energy CT material extraction based on parametrization of the linear attenuation coefficient for 17 tissue-equivalent inserts inside a solid water phantom was done. Scans of the phantom were acquired at 100 kVp and 140 kVp from which Z and ρ_e values of each insert were derived. The mean errors on Z and ρ_e extraction were 2.8% and 1.8%, respectively. Phantom dose calculations were performed for 250 kVp and 18 MV photon beams and an 18 MeV electron beam in the EGSnrc/DOSXYZnrc code. Two material assignments were used: the conventional (HU; ρ) and the novel (HU; ρ, Z) dual-energy CT tissue segmentation. The dose calculation errors using the conventional tissue segmentation were as high as 17% in a mis-assigned soft bone tissue-equivalent material for the 250 kVp photon beam. Similarly, the errors for the 18 MeV electron beam and the 18 MV photon beam were up to 6% and 3% in some mis-assigned media. The assignment of all tissue-equivalent inserts was accurate using the novel dual-energy CT material assignment. As a result, the dose calculation errors were below 1% in all beam arrangements. Comparable improvement in dose calculation accuracy is expected for human tissues. The dual-energy tissue segmentation offers a significantly higher accuracy compared to the conventional single-energy segmentation.

In proton scanning systems that employ active energy variation for depth modulation, a switch of the particle energy might typically require 1–2 s. For plans comprising many energy slices, these seconds could sum up to a non-negligible fraction of the total treatment duration. We have applied the Nyquist–Shannon sampling theorem to determine an efficient spatial arrangement of Bragg peaks in a target volume. This pre-determined schedule of increasing energy spacing with higher energy allows us to reduce the number of used energy slices without compromising the physical dosimetric quality of a plan. Our results suggest that the advantage of such a simple implementation would be especially significant for larger, deep-seated tumors such as the prostate; the number of energy slices was cut by a factor of 2–6.

An optimal plan in modern treatment planning tools is found through the use of an iterative optimization algorithm, which deals with a high amount of patient-related data and number of treatment parameters to be optimized. Thus, calculating a good plan is a very time-consuming process which limits the application for patients in clinics and for research activities aiming for more accuracy. A common technique to handle the vast amount of radiation dose data is the concept of the influence matrix (DIJ), which stores the dose contribution of each bixel to the patient in the main memory of the computer. This study revealed that a bottleneck for the optimization time arises from the data transfer of the dose data between the memory and the CPU. In this note, we introduce a new method which speeds up the data transportation from stored dose data to the CPU. As an example we used the DIJ approach as is implemented in our treatment planning tool KonRad, developed at the German Cancer Research Center (DKFZ) in Heidelberg. A data cycle reordering method is proposed to take the advantage of modern memory hardware. This induces a minimal eviction policy which results in a memory behaviour exhibiting a 2.6 times faster algorithm compared to the naive implementation. Although our method is described for the DIJ approach implemented in KonRad, we believe that any other planning tool which uses a similar approach to store the dose data will also benefit from the described methods.