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A novel concept for CT with fixed anodes (FACT): Medical imaging based on the feasibility of thermal load capacity
Physica Medica xxx (2015) 1e10
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Original paper
A novel concept for CT with fixed anodes (FACT): Medical imaging based on the feasibility of thermal load capacity Markus Kellermeier a, b, *, Christoph Bert a, b, c, Reinhold G. Müller a, b a
Department of Radiation Oncology, University Clinic Erlangen, Germany Friedrich-Alexander-University Erlangen-Nürnberg, Germany c GSI Helmholtz Centre for Heavy Ion Research, Darmstadt, Germany b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 15 July 2014 Received in revised form 19 March 2015 Accepted 20 March 2015 Available online xxx
Focussing primarily on thermal load capacity, we describe the performance of a novel fixed anode CT (FACT) compared with a 100 kW reference CT. Being a fixed system, FACT has no focal spot blurring of the X-ray source during projection. Monte Carlo and finite element methods were used to determine the fluence proportional to thermal capacity. Studies of repeated short-time exposures showed that FACT could operate in pulsed mode for an unlimited period. A virtual model for FACT was constructed to analyse various temporal sequences for the X-ray source ring, representing a circular array of 1160 fixed anodes in the gantry. Assuming similar detector properties at a very small integration time, image quality was investigated using an image reconstruction library. Our model showed that approximately 60 gantry rounds per second, i.e. 60 sequential targetings of the 1160 anodes per second, were required to achieve a performance level equivalent to that of the reference CT (relative performance, RP ¼ 1) at equivalent image quality. The optimal projection duration in each direction was about 10 ms. With a beam pause of 1 ms between projections, 78.4 gantry rounds per second with consecutive source activity were thermally possible at a given thermal focal spot. The settings allowed for a 1.3-fold (RP ¼ 1.3) shorter scan time than conventional CT while maintaining radiation exposure and image quality. Based on the high number of rounds, FACT supports a high image frame rate at low doses, which would be beneficial in a wide range of diagnostic and technical applications. © 2015 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
Keywords: CT physics Fixed anode CT FACT Thermal load capacity X-ray anode
Introduction Third-generation computed tomography (CT) scanners incorporate an X-ray tube and a detector arrangement that mechanically rotate around the patient. Current clinical CT scanners and most industrial CT scanners operate on this principle. During recent decades, volumetric CT imaging has advanced with the advent of spiral acquisition [1,2] and the progression to multidetector row CT (MDCT) scanners [3]. During continuous movement of the couch, these systems acquire sufficient information in a helical path for reconstructing images from raw projection data. An increased number of detector rows provides the advantages of thinner slices, shorter scan times, and reduced motion artefacts.
* Corresponding author. Department of Radiation Oncology, University Clinic Erlangen, Germany. E-mail address: [email protected] (M. Kellermeier).
Particularly due to the rapid increase in the number of installed detector rows, there is a desire to obtain sufficient volume coverage in the axial direction during a single rotation, in which the X-ray tube rotates around in the gantry. However, a wide X-ray beam has a number of drawbacks, such as increased scattering, overscanning, and cone-beam artefacts at large cone angles. Various approaches and novel concepts have been proposed to address different issues [4e10]. Besides, the approaches of the fourthgeneration CT and the electron beam CT (EBCT) [11] are currently not in widespread use. Recently, an inverse-geometry CT (IGCT) system was proposed to achieve a scanned volume during a single gantry rotation that was essentially free of cone-beam artefacts [12e15]. Scanning a volume during a single rotation is limited by the gantry rotation time because centrifugal force can become destructive. Taking this mechanical restriction out of a system, the maximum temperature at the focal spot of an X-ray anode poses a serious limitation for the scanning time.
http://dx.doi.org/10.1016/j.ejmp.2015.03.012 1120-1797/© 2015 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
Please cite this article in press as: Kellermeier M, et al., A novel concept for CT with fixed anodes (FACT): Medical imaging based on the feasibility of thermal load capacity, Physica Medica (2015), http://dx.doi.org/10.1016/j.ejmp.2015.03.012
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In this paper, we described a concept for CT based on a ring of stationary X-ray sources, as proposed by Foster and Müller [16e18] from our group. The investigations of possible achievable image frame rates were closely related to potential performance. In general, a number of medical applications can benefit from a high image frame rate for a volume, including cardiac imaging, CT angiography, perfusion studies, and other demanding imaging applications. The potential performance of a conventional CT is primarily limited by the thermal load capacity of the X-ray anode. Thus, we began with studies on the thermal load capacities of anode focal spots. For these studies, a CT concept was outlined that had no mechanical restrictions due to gantry movements and that allowed for a high image frame rate, which was coupled with operated rounds in the stationary X-ray source ring at doses normally used for patients. The aim of the paper is to provide a conceptual theoretical framework for CT with fixed anodes based on the feasibility of thermal load capacity. However, this paper does not cover technical feasibility of the source ring and does not consider detector performance or efficiency. Since detectors need to be developed as per their specific requirements, we used as a benchmark today's acquisition of X-ray attenuation without an adaptation to the novel concept. Furthermore, the detection properties of the currently used integration times are extrapolated linearly to small time ranges. This means that the same total energy and photon fluence per projection yields identical image quality.
Throughout these studies, we chose parameters of our design in accordance with the reference CT, which was also used as a benchmark to determine the performance of our novel concept. The operating data for this reference CT (see Table 1) were based on SOMATOM Definition, Siemens Medical Solutions, Forchheim, Germany. Using an impact angle close to the right angle to the target surface, as considered by us at 84 (anode angle of 6 ), the following approximate relation [19] applies to electrical X-ray tube power (Pel) and thermal focal spot power (Pth):
Basic concept
Simulations of the thermal loads for a single anode
The basic concept for CT with fixed anodes (FACT) is illustrated in Fig. 1. The generation of a primary X-ray beam from an X-ray tube follows the same principle that has been known for over a century. A rotating anode X-ray tube, which conventionally revolves in a gantry around an object, is replaced in FACT by a stationary source ring of fixed anodes. In the current study, 1160 fixed X-ray anodes were used, analogous to the reference CT specified in Table 1. For theoretical analysis, the beam at a single fixed anode allows being switched on and off at any frequency. The fixed anodes in the source ring were used in sequential operation. Due to the restricted exposure time for each direction, the required number of projections for typical image information was acquired using multiple gantry rounds (~20). Projection data were combined during pre- or post-processing to acquire equivalent information analogous to the principle used in the reference CT.
3D simulation models In a simulation model, each fixed anode in the source ring of FACT was usually modelled as a sandwich of a high-Z material, a body with high thermal conductivity, and a heat bath for cooling: The square body was made of copper (Cu) with a base area of 25 mm by 3.2 mm and a height of 20 mm. Towards the focal spot, the tungsten (W) target layer of 0.5 mm thickness was adjoined without contact resistance. On the opposite side of the copper body, a heat bath at 300 K for cooling was defined. Away from the heat bath for all other surface boundary conditions and for the worst case scenario, a thermal insulation was chosen (see also Fig. 2). This fixed anode model was extended to a rotating anode model analogous to the principle used for the reference CT (see Table 1). Our model of a rotating anode with a radius of 60 mm had the same sandwich configuration as the fixed anode defined above. The nonconventional use of copper as a base for a rotating disk was
1 Pth z $Pel 2
(1)
This approximation applies to both fixed anodes, used in the FACT concept, as well as the rotating anode, used in the reference CT. Preliminary simulations of energy deposition in the focal spot confirmed this approximation within a deviation of 1% for the considered acceleration voltages of 80 kV, and even of 120 kV. We thus only present the simulation results at 80 kV. Methods In the following, the thermal load capability of a single fixed anode is first studied and compared with a rotating anode. Subsequently, the fixed anode is used as an isolated and independent module in the arrangement for the FACT concept.
Figure 1. Basic concept for FACT. (a) Geometric relationships of a FACT with a single source ring and a detector ring. (b) At helical source path for FACT, compared to that of a multislice spiral CT, the reconstructed images are normally determined by pre-processing. Alternatively, the information for the reconstructed images could be combined during postprocessing, as employed in Section Medical Imaging. (Additional figures can be found in supplementary data, Fig. 1e).
Please cite this article in press as: Kellermeier M, et al., A novel concept for CT with fixed anodes (FACT): Medical imaging based on the feasibility of thermal load capacity, Physica Medica (2015), http://dx.doi.org/10.1016/j.ejmp.2015.03.012
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Table 1 Specifications used for FACT and reference CT. Symbol
Specification
FACT
Reference CT
Pel U tround N SID OFS A (Pth/A)
Electrical X-ray tube power X-ray tube voltage Gantry round time of the source Source positions per round Source-to-isocenter distance Optical focal spot Thermal focal spot area Thermal focal spot power density
Depending on (Pth/A)max 80 kV Up to 300 ms 1160 60 cm 0.7 0.9 mm2 6 mm2 (Pth/A)max is shown in Fig. 4 (a)
100 kW 80 kV 300 ms 1160 60 cm (rounded) 0.7 0.9 mm2 6 mm2 (Pth/A)const ¼ 8.6 kW/mm2
considered a useable approximation for theoretical investigations during a short-time operation. Using copper for a rotating anode model with its outstanding material property of thermal conductivity also leads to the worst case scenario for FACT, when compared with conventional clinical CTs. The material properties used in the two 3D simulation models described above are listed in Table 2. Energy deposition The energy deposition of accelerated electrons in the so-called thermal focal spot was determined based on the latest research on particle interactions included in the Monte Carlo simulation GEANT4 [20]. Within the GAMOS framework, rapid access to verified programming routines is provided [21]. All simulations were performed using GAMOS 3.0 by accessing GEANT 4.9.4.p01. The physics of low-energy interactions was described by the Livermore models [22] (also known as EEDL [23]-EPDL [24] models) and tracks were followed down to the production cut length of 10 nm or an energy of 1 eV, including rest energy deposition, below which the particles were placed under split in terms of probability. Energy was collected in 1 nm voxels. These voxels were averaged in the lateral extension to have a representative 1D distribution of energy along a penetration depth of 8 mm, in which the voxel value was four orders of magnitude less than the maximum at
Figure 2. 3D simulation model with representation of incident electron beam (e): (a) at the fixed anode model in short intervals with a given projection duration and (b) at the rotating anode model with continuous long-lasting beam. The fixed anode designed as a square body was made of copper (Cu) with a base area of 25 mm by 3.2 mm and a height of 20 mm. The tungsten (W) target layer had a material thickness of 0.5 mm. The rotating model used the same construction, but as a cylindrical body with a rotational frequency of 150 Hz and a radius of 60 mm. The thermal focal spot area, A, on the anode surface is formed by the entering electrons of equally distributed intensity. For cooling, a heat bath of 300 K has been defined. The surfaces, except for the heat bath, were considered thermally insulated.
0.4 mm. Thus, a small effect of scattering on field boundaries was eliminated when used only in the central area with half the focal spot width. Preliminary investigations showed that a deeper penetration depth did not give significantly different results in the subsequent FEM applications. The trajectories and energy of the emitted particles were registered on the target surface. Based on the differences between the primary energy of the incident electron beam and the energy of the emitted electrons and photons, we calculated the relative proportions of deposited energy in the thermal focal spot. Overall, the deposition of energy in the thermal focal spot on the tungsten target results in an increase in temperature, which could be determined from the solutions of partial differential equations.
Heat transfer Applying partial differential equations to describe the temperature profile in the X-ray anode from the deposited energy, the finite element method (FEM) was used. For this purpose, commercial software COMSOL Multiphysics (version 4.3) was applied using its standard heat transfer module for solid interfaces. For FEM simulations, the corresponding temperature-dependent data of material properties (cf. Table 2) were used from the Material Library of COMSOL Multiphysics, which was based on the Material Property Database (MPDB) from JAHM Software, Inc. The acquired depth energy distribution was evenly applied over the thermal focal spot area A (see Table 1) and scaled using the relative proportion of deposited energy. Based on a number of simulations, values for the maximum thermal power density, (Pth/A)max, were obtained. This caused an increase in temperature from 300 K to 2500 K within a certain period, which we called the projection duration (Dt). Krieger [25] indicated that, due to the vapour pressure of anode material, the favourable operating temperature of an anode is around 70% of its melting temperature (cf. Table 2) to obtain a service life at an usual expectation. This led us to the absolute upper temperature limit of 2500 K for the tungsten target layer. Bouwers [26] and Oosterkamp [27] did fundamental work on the load capacities of X-ray tubes while in operation. We used formulas based on simple modelling assumptions [28] for comparisons with our simulation results. In addition to the initial temperature, which could be estimated from values in the literature, we were interested in heat transport under various conditions in terms of both, temporal and spatial resolution. Thus, we did consider a 3D simulation model with an atomic interaction region
Table 2 Material properties used for Monte Carlo simulations and literature formulas. Symbol
Specification
Tungsten (W)
Copper (Cu)
l
Thermal conductivity Specific heat capacity Density
170 W m1 K1 138 J kg1 K1 19.25 g cm3
400 W m1 K1 385 J kg1 K1 8.92 g cm3
c
r
Melting point for W: 3695 K and Cu: 1358 K.
Please cite this article in press as: Kellermeier M, et al., A novel concept for CT with fixed anodes (FACT): Medical imaging based on the feasibility of thermal load capacity, Physica Medica (2015), http://dx.doi.org/10.1016/j.ejmp.2015.03.012
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M. Kellermeier et al. / Physica Medica xxx (2015) 1e10
in the thermal focal spot and with macroscopic dimensions with respect to the basic copper block. The kinetic energy of electrons is mainly deposited in a penetration depth of a few micrometres after entering the target medium of tungsten. Finite elements modelled by voxels adopted in size based on the local geometry allowed to keep the calculation space reasonably small. Virtual FACT model Power and timing for a single anode and the source ring During the cooling phase for a single thermally isolated fixed anode, the other identical anodes in the source ring operate equally in succession. The electron beam cannot be instantaneously switched between anodes. To qualitatively incorporate technically required operations d such as rise and fall phases during the pulsed operation of X-ray sources d we incorporated a beam pause (t0 ), which can be introduced between two projections. The simulation environment for a single anode was also used to study the performance of an entire ring of anodes, as required with FACT. Based on intermediate results, we considered various beam pauses (t0 ) of 0 ms, 1 ms, 3 ms, and 5 ms. Figure 3 (b) presents an example of the operating time for a source ring with 1160 fixed anodes. The indicated projection duration (Dt) for each single fixed anode was 10 ms. With a beam pause of t0 ¼ 1 ms, the temporally possible repetition frequency at a single fixed anode (i.e. gantry rounds per second) was 78.4 Hz. To achieve the expected image quality within a typical scanning time, the question became whether FACT could provide the necessary number of superpositions for a projection direction. Superpositions were necessary because the projection duration (Dt) of FACT was approximately only 1/20 as compared with that of the reference CT. With about the same Pth/A an equal amount of total energy was emitted after 20 projections for the same direction, as with the reference CT. Thus, FACT is theoretically able to acquire the same detected information and obtain the same image quality as in the reference scan. The term “same image quality” refers in this comparison of the systems to the parameter image noise, which is related to the tube current-scan time product (see also section Medical Imaging) for the same tube output configuration. In FACT, the shorter projection durations result in noisier images, however, patient and organ movements under high temporal and spatial resolution can be theoretically extracted. In this theoretical approach, it was assumed that detection is independent of the readout rate. Under identical conditions, the photon spectra and fluence (Jph ) for both fixed and rotating anode technologies were equal in the first approximation and proportional to the deposited thermal energy, Eth:
Jph fEth :
(2)
Assuming a known deposition of energy, it was thus possible to determine image quality, provided that only the nature of energy deposition differs between systems. As a reference, we used a conventional CT with a constant (Pth/A)const (see Table 1) for an unlimited operation time (toperation). The thermal energy in the FACT source ring for a single round was determined by the number of rectangular pulses, N, with a fixed projection duration (Dt). The following definition of nmin gives the theoretical minimum number of rounds from the ratio of the thermal focal spot energies within any operation time toperation ¼ N (Dt þ t0 ) under the assumption of a 300 K initial anode temperature at FACT:
nmin
ðPth =AÞconst $toperation CT ¼ : ðPth =AÞmax $Dt $N FACT
(3)
A possible remaining residual heat from previous pulses in a single anode is not taken into account in formula (3). Thus, mathematically, an infinite cooling phase for FACT is assumed between source activities after each round. For exact consideration of finite cooling phases between the source activities at a possible round frequency, (Pth/A)max is reduced due to the residual heat in the anode. For this, we investigated the potential order of temporal sequences (Dt þ t0 ) for the source ring operating in pulsed mode. Values for the round frequency (fpossible) of successively active sources in the source ring were determined for various possible timings using the following equation:
fpossible ¼
1 0 : N$ ðDt þ t Þ
(4)
In addition to such theoretical investigations, we considered technical feasibility, exploring the maximum operating frequencies achievable for a limited range of realizable specifications. We limited to be restricted to a determined the limited round frequency fpossible maximum operating frequency k:
limited fpossible ¼
k ; for fpossible ; else :
fpossible > k
(5)
Based on our intermediate results, we suggest 60 Hz as a lower limit for the operating frequency d i.e. k1 ¼ 60 Hz d and a further limit of k2 ¼ 100 Hz with respect to the high dataflow from the detector ring to a CPU (cf. Fig. 13). During pulsed operation, the maximum temperature of Cu (cf. Fig. 6) can increase as a function of the duration of the cooling phase. To account for a finite cooling phase during which the temperature of the anode does not reach 300 K, we defined the scaling factor h for (Pth/A)max to prevent the maximum temperature of 2500 K in the tungsten target layer during long-time operation in pulsed mode (cf. II.A.3):
Figure 3. Operating times for a single fixed anode and for a source ring with 1160 fixed anodes. (Pth/A)max was determined by the power factor h (see Eq. (6)). (a) Illustration showing a projection duration (Dt) of 10 ms. The repetition frequency is 78.4 Hz. (b) Each fixed anode in the source ring operates with the same given repetition frequencydi.e. the gantry rounds amount to 78.4 1/s.
Please cite this article in press as: Kellermeier M, et al., A novel concept for CT with fixed anodes (FACT): Medical imaging based on the feasibility of thermal load capacity, Physica Medica (2015), http://dx.doi.org/10.1016/j.ejmp.2015.03.012
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Figure 4. (a) Simulation results for determining the maximum thermal focal spot power density, (Pth/A)max, which caused a temperature increase from 300 K to 2500 K during a certain projection duration (Dt). Comparisons of our 3D simulation results with those from analytical formulas in the literature [28] and the reference CT. The value from the simulations of a rotating anode with a load limit at 10 s and the value of the reference CT, (Pth/A)const, were time-independently projected onto this figure to make direct comparisons with the (Pth/A)max values from fixed anodes. (b) Relative deviations of these comparisons.
h 0 . Pth A
i max FACT
¼ h$ðPth =AÞmax
FACT
:
(6)
Relative performance (RP) of FACT with regard to the reference CT With the ratio between the maximal possible thermal loads of FACT and reference CT an assessment factor, relative performance (RP), was introduced as follows:
h RP ¼
. i 0 Pth A $ Dt$N$ f max FACT ðPth =AÞconst CT
(7)
5
Figure 6. Example temperature profile during pulsed operation of a fixed anode. The maximum temperature in the tungsten (W) target was 2500 K (±0.5%). In the copper (Cu) block, the maximum temperature did not reach 500 K. A time-unlimited operation was assumed based on the plateau for the maximum temperatures in the medium of a fixed anode.
with reference to Eqs. (2)e(6)) and (P'th/A)max (see Eq. (6)) for pulsed operation at a given round frequency f.
Medical imaging Image reconstruction using FACT is based on the same fundamentals used with conventional CT [29]. Using a spiral scan, it is known that spatial resolution and image quality are determined by z-filtering/z-interpolation during pre-processing. Alternatively, this information can be combined during post-processing by interpolating the reconstructed images (cf. Fig. 1 (d)). As previously indicated, the FACT concept uses the principle of superposition, which can be illustrated with a CT image reconstruction (see Fig. 10). For this purpose, permission was given to use the reconstruction library of the Institute of Medical Physics, University Erlangen-Nürnberg, Germany. The parameters for simulation were closely linked to SOMATOM Definitions, Siemens Medical Solutions, Forchheim, Germany from ~2007 which form the basis for the defined reference CT (see Table 1) in this paper.
Figure 5. 3D simulation model of (a) fixed anode and (b) rotating anode along with the temperature distribution after 10 s of operation using the maximum possible electrical X-ray tube power, Pel, that was set for each projection. Both models are also described in Fig. 2. The trajectories of the emitted charged electrons (e) are indicated based on simulation results in conjunction with a static electromagnetic field between the cathode and the anode. For reasons of comparability, an exact tube design was not pursued. However, a study of these trajectories (with COMSOL Multiphysics) showed that the reflected electrons provided their energy away from the thermal focal spot in a first approximation after multiple uniform reflections over the relatively large interior surfaces of the X-ray vacuum tube. The re-entry energy was neglected in our simulations, as this would have resulted in a small increase in background temperature.
Please cite this article in press as: Kellermeier M, et al., A novel concept for CT with fixed anodes (FACT): Medical imaging based on the feasibility of thermal load capacity, Physica Medica (2015), http://dx.doi.org/10.1016/j.ejmp.2015.03.012
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M. Kellermeier et al. / Physica Medica xxx (2015) 1e10
Figure 7. Operating results for (a) power factor h and (b) maximum temperature of a copper block. The gantry rounds correspond to the possible and possible but limited gantry rounds from Fig. 8. Note: The projection duration is an adjustable parameter and no integral term.
The dependence of image quality was discussed in a previous paper, in which a dose-weighted contrast-to-noise ratio ðCNRDÞ was chosen as the criterion for image quality optimization [30]. The standard deviation (SD) in the image plane was used as a surrogate for what the signal noise would be for n number of rounds:
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u M u 1 X 2 1 1 $ SD ¼ t x x f pffiffiffiffi ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi: M 1 i¼1 i Q I $ N$ Dt$ n
(8)
SD was determined from M pixel values, xi, in a region of interest (ROI) in a homogeneous image section with respect to their mean value, x. Equation (8) gives the well-known proportion to the tube current-scan time product, Q. The question of a quantitative improvement in image sharpness due to a sharp focus on a fixed anode is not answered in this article. The same extension of focal spot width in relation to the blurred focus in CT is included in the following boundary value analysis.
Boundary value analysis In contrast to conventional CT using rotating X-ray tubes, no blurring of the optical focal spot (OFS, see Table 1) occurs with FACT, which is an advantage for image sharpness. In practice with
conventional CT with specifications used for the reference CT, due to rotational movement during scanning, the OFS blurs to a factor of 4.6 in each integrated projection direction. If one follows this expansion with FACT, the result is an OFSþ and an Aþ. In this thought experiment, the thermal load capacity is thus increased (in the ratio Aþ/A ¼ 4.6) at a cost of the theoretically equivalent OFSþ, which is known from conventional CT gantry rotation within a measurement integral for a projection. These values are listed in Table 3. This application of boundary value analysis corresponds to a successive distribution of the thermal load on an entire body source ring. Results The Results section follows the structure of the Methods section: Consideration of the individual fixed anode in comparison to the rotating anode and the use of fixed anode as an isolated and independent module in the arrangement for the FACT concept. Simulations of thermal loads of a single anode Applying the 3D simulation model described in Fig. 2, we used Monte Carlo simulations with an incident electron beam within the
Figure 8. Minimum, possible, and possible but limited gantry rounds defined in Eqs. (3)e(5). The different figures show the results for the given beam pauses (t0 ): (a) without beam pause, (b) t0 ¼ 1 ms, (c) t0 ¼ 3 ms and (d) t0 ¼ 5 ms. The minimal values were determined according to Eq. (3) at infinite cooling phases between the pulsesdi.e. without any residual thermal energy from a previous pulse, in a single anode from the source ring. The possible gantry rounds, however, note residual heat with the above-introduced power factor h, which ensured compliance with the thermal load limit at 2500 K.
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Figure 11. Illustrations of boundary value analysis. The operating range for FACT shown with a dark grey time bar is made available to the operating time of the reference CT. The light grey time bar marks the range for the FACTþ with a broadened focal spot area.
Figure 9. Relative Performance (RP) for a given beam pause, t0 , (a) at no frequency limit, (b) at a limit of 100 Hz, and (c) at a limit of 60 Hz.
extent of the thermal focal spot area A defined in Table 1. Simulations used for heat transfer in the X-ray target are described in Sec. Methods. In addition to actual observations of a fixed anode, in order to understand the differences between the types of anodes, we performed simulations for the rotating anode to explain the differences in thermal load capacity. Figure 5 shows our 3D simulation models for the thermal focal spot and typical trajectories of the particles as well as the simulation results for the temperature distribution after an assumed 10 s of operation with an X-ray tube. (Pth/A)max values are plotted in Fig. 4 (a) that caused an increase in temperature from 300 K to 2500 K at the fixed anode within a
Figure 10. Example of FACT application for reconstructed and post-processed images and comparison with the reference CT. Based on 100 kW at 80 kV, the tube current-scan time product, Q, with (a) FACT in one of 18 rounds was 20.8 mAs and with (c) the reference CT in one round was 375 mAs. (b) After interpolating 18 images with FACT (18 20.8 mAs), the measured SD was equal to that of the reference CT. The scan time for the same image quality with FACT was less by a factor of 1.3.
Please cite this article in press as: Kellermeier M, et al., A novel concept for CT with fixed anodes (FACT): Medical imaging based on the feasibility of thermal load capacity, Physica Medica (2015), http://dx.doi.org/10.1016/j.ejmp.2015.03.012
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M. Kellermeier et al. / Physica Medica xxx (2015) 1e10 Table 3 Further specifications used for FACT and the reference CT. (compare with Table 1.). Symbol
Specification
FACT
Reference CT
OFSþ Aþ
OFS including blurring A corresponding to blurring
3.2a x 0.9 mm2 27.6 mm2
3.2b 0.9 mm2 6 mm2
a b
Figure 12. Spot diagram. Pel is used as a scale for X-ray outputs of the respective concepts. The heat content illustrates the resulting heat transfer to an anode, which must be dissipated by cooling. Since the fixed anodes of the source ring reach a temperature plateau, a time-unlimited operation is assumed with FACT.
given projection duration (Dt). In comparison, the results from analytical formulas [28] were mapped using Table 1 and the material data was shown in Table 2. The relative deviations of these comparisons are shown in Fig. 4 (b). There was a relatively good correlation, particularly in the area around Dt ¼ 10 ms. This projection duration is also highlighted in the following chapters, as it represents the optimum operating range for FACT, particularly with regard to RP (cf. Fig. 9). Figure 5 shows for comparison of the anode models their temperature distribution after 10 s of operation using the maximum possible electrical X-ray tube power, Pel, which was set for each projection. The maximum temperature in the copper block of the fixed anode did not reach 500 K, whereas in the rotating anode, a temperature of 1000 K has been exceeded. The value for the heat content shows that the rotating anode is charged 1000 times higher than a fixed anode at the operating point of a FACT, as is presented in the following section. Virtual FACT model Power and timing for a single anode and the source ring The simulations performed above for a 3D model of fixed anodes described one target module of the source ring of FACT without neighbourhood influence. Studies of repeated pulsed loads showed that, at fixed anodes, a pulsed operation could have an unlimited time frame. As representative results of our simulations at projection durations of 10 ms, Fig. 6 shows the FEM simulation results for the maximum temperatures in the anode medium resulting from
Figure 13. Relative dataflow with FACT as compared to that with the reference CT.
Focal spot width corresponding to blurring. Blurring assumed from the rotational movement during the detection.
pulsed long-time operations with a repetition frequency of 78.4 Hz (see Fig. 3). Here, after a pulsed operation time of around 6 s, the maximum temperature in the tungsten target reached a plateau of 2500 K (±0.5%), whereas the maximum temperature in the adjoining copper block did not exceed 500 K (see 7 (b)). The constant power factor, h, had a value of 0.915 (see Fig. 7 (a)). Figure 7 shows the simulation results for (a) the power factor h and (b) the maximum temperature of the copper block using various projection durations (Dt). The power factor h was close to 1 at low gantry rounds because sufficient time passes to the next activity at each single anode. In this case, the copper block could hardly accumulate heat energy due to the relatively small thermal focal spot power (Pth, see Fig. 4) per pulse as well as the long cooling phase between the pulses on a single anode. The shorter the projection durations, the higher was Pth and the initial temperature in the anode increased due to accumulated heat energy from previous pulses. The different cases of various beam pauses (t0 ) and the restriction to a maximum operating frequency (k) became apparent at projection durations of Dt < 0.8 ms. The corresponding gantry rounds per second are plotted in Fig. 8. The feature of time-unlimited operation at one fixed anode was transferred to a circular array of fixed anodes, which are addressed in succession below. This led to the concept of FACT. These results are described below. Using Eqs. (3)e(5) for the given beam pauses (t0 ¼ 0, 1, 3 and 5 ms) the resulting round frequencies (Gantry rounds per second) are plotted in Fig. 8 for three different conditions: no limitation, limitation at 100 Hz and 60 Hz. Our preferred FACT operation point, f possible ðDt ¼ 10 msÞ, is indicated by an arrow: 86.2 1/s for t0 ¼ 0 ms, 78.4 1/s for t0 ¼ 1 ms, 66.3 1/s for t0 ¼ 3 ms and 57.5 1/s for t0 ¼ 5 ms. For comparisons, the referenced CT gantry rounds of 3.33 1/s is projected independent of Dt and the projection duration of 0.26 ms is marked. Relative performance (RP) of FACT with regard to reference CT In Eq. (7), relative performance (RP) was defined to show the relationship between FACT and the reference CT from the perspective of possible source performance. Figure 9 shows the RP curves for the given projection durations (Dt) and the beam pauses (t0 ). As a reminder, the purpose for preparing these figures was to find the operating range for FACT with an RP 1. In this paper, we did not consider t0 > 5 ms, because the source performance for the reference CT may have been difficult to achieve (see Fig. 9 (a)). The FACT operating range for RP 1 is displayed as a time bar. The typical operating range of a CT is shown to the right with a time bar from 0.2 ms to 1 ms for comparison. Limiting the gantry rounds to the round frequency at 100 Hz restricted the lower projection time range for FACT to about 4 ms, as shown in Fig. 9 (b). A maximum round frequency at 60 Hz reduced the operating range to an operating point around 10 ms, which is shown in a short time bar in Fig. 9 (c). Medical imaging Following is a brief example of the relationship of projection duration, beam pause, gantry rounds and X-ray tube power. Using the operating point highlighted above (Dt ¼ 10 ms, t0 ¼ 1 ms), the
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applied superposition with FACT required validation. Figure 1 (c) and (d) illustrates the principle of data acquisition with FACT in comparison to a conventional CT. Figure 10 (a, b) shows the simulation results for post-processed data, i.e. data which are generated by accumulating the raw-data of several rounds. In the circular region of interest (ROI), the SD (in HU) of the image voxels was determined. After interpolating 18 images with FACT (18 , 20.8 mAs), the determined SD was equal to that of the reference CT. The ratio of tube current-scan time product (QCT/QFACT)0.5 is 0.24 and reflects the standard deviation ratio SDCT/SDFACT of 0.24 according relation to Eq. (8). The scan time for the equal image quality using FACT was less by a factor of 1.3. For comparison, simulated imaging after one round with the reference CT is shown in Fig. 10 (c). Under the assumption of the same detector conditions, the criterion for image quality optimization (CNRD) is not further affected because the same operating conditions for X-ray sources are provided. Theoretically, however, the image sharpness for FACT can be better than in the referenced CT because in the simulation of the reference CT we neglected blurring of the optical focal spot caused by the rotational motion. Boundary value analysis Using the focal spot size of Aþ, compensates for the advantage of the higher image sharpness due to a static optical focal spot. The right side of the operating range for FACT shifted towards the operating range for a conventional CT. At the transition to the CT operating range, RP / 1. This can demonstrate the smooth transition between the novel FACT concept and the conventional CT. At the highlighted operating point (Dt ¼ 10 ms, t0 ¼ 1 ms) in Fig. 11 (a), the minimum number of rounds has been reduced from 55 to 12. At the same point, the RP increased from 1.3 (see Fig. 9 (b)) to 6 (see Fig. 11 (b)). This reflected the focal spot broadening by a factor of 4.6. Discussion Our results for a source ring of fixed anodes showed that it should be thermally possible to achieve a novel concept for CT, the performance of which is equal to or even better than that of conventional CT. The necessary energy fluence for a beam projection for a typical image quality is theoretically achievable, as the number of rounds was sufficient for the principle of superposition to be used within a typical scan time. With FACT, at least 60 gantry rounds per second were necessary theoretically to achieve the same imaging performance as the reference CT with an X-ray tube power of 100 kW. In this case, the operating point for a projection was in the range of 10 ms. If 50 kW is sufficient, then FACT could be operated at 30 rounds per second or a projection duration in the range of 60 ms could be used, which is about one fourth of the typical integration time for CT detectors. Thus, a significant advantage of a fixed CT system is that the optical focal spot is not blurred, which would enhance the sharpness of a reconstructed image. The resulting high image frame rate would be possible with a typical X-ray exposure to a patient. This would be beneficial for its applications, such as in cardiac imaging, CT angiography, perfusion studies, and other demanding imaging applications. Figure 12 shows a spot diagram of the respective typical and common operating ranges based on the electrical X-ray tube and source ring power (Pel). When the focal spot size is increased, which occurs with current CT technology due to movement, FACT shows an enhanced performance by a factor of about six. This superior performance could be used to scan faster or to increase image
9
quality. Another advantage should be noted: By ensuring sufficient direct cooling of the fixed anodes, FACT provides for time-unlimited operation. Based on the frequency rounds, our calculations for the volume of data (about 8 GB/s for 64 slices) from the detector ring show that only interfaces currently under development could transfer this accumulating data in real time. Even from this perspective, developing FACT would be in keeping with the current zeitgeist. Figure 13 shows the relative dataflow with FACT as compared to that with the reference CT. In parallel to the investigated source ring, a fixed detector ring is defined. Thus, projections from each anode element on the detector occur obliquely to the reconstructed transverse plane. In conjunction with the detector elements, we will not discuss further the lack of collimation of the scattered X-rays. In this context, the development of fast detectors is desirable for capturing the incidence direction. Before the FACT can replace the third-generation CT, we see that a number of technical developments have to be made. On the source side the production, switching, and distribution of a focused electron beam will result into additional challenges such as dedicated power electronics. These have to result in rectangular pulses at the anode positions which will itself suffer from the thermal load such that thermomechanical long-term studies will be essential. Also regarding the detector improvements, e.g., regarding the readout speed, the efficiency for small quantum numbers, and the distinction between primary X-ray beam and X-ray scatter during the detection have to be accomplished. All of these issues present additional challenges that need even more detailed investigations. A distinct advantage over conventional CT could be considered by setting a second source ring on the other side of the detector. Figure e2 (see supplementary data) shows a schematic for this advanced concept. This provides a rectangular beam field in the zdirection and doing away with over-scanning, which could result in reducing unnecessary doses to a patient without any additional complex technology. Such a dual-source FACT would theoretically provide for a doubling of the relative performance of the FACT concept introduced above.
Conclusions FACT, a new CT concept relying on fixed anodes was proposed. The design was compared with a known conventional CT to evaluate the thermal load capacity and medical imaging capabilities. Although concerned primarily with physical assessment, we have also considered it necessary to dwell on the technical limits of FACT. The simulations showed that FACT is thermally feasible. Image data are acquired in multiple gantry rounds using the principle of superposition, yielding high image frame rates at very thin slices, which can be beneficial for numerous medical applications. As an example, at the same radiation exposure for the patient, the much thinner layers (at high axial spatial resolution) of FACT are indeed noisy. However, at high contrast, via the use of contrast agents for CT angiography or at calcification in the breast, the branching of blood vessels or the size assessment could be improved. The thermal load capacity allows a time-unlimited operation that could have an application in industrial use, as well as in safety and security. As a fixed system, FACT has no blurring of the optical focal spot during projection. In comparison to the third-generation CT, the relative performance (RP) of 1.3 was determined at a given thermal focal spot area. With an RP > 1 can be achieved a shorter scan time while maintaining radiation exposure and image quality as defined above.
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Acknowledgement The present work was performed in fulfilment of the requirements for obtaining the degree of Dr. rer. biol. hum.
Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.ejmp.2015.03.012.
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Original paper
A novel concept for CT with fixed anodes (FACT): Medical imaging based on the feasibility of thermal load capacity Markus Kellermeier a, b, *, Christoph Bert a, b, c, Reinhold G. Müller a, b a
Department of Radiation Oncology, University Clinic Erlangen, Germany Friedrich-Alexander-University Erlangen-Nürnberg, Germany c GSI Helmholtz Centre for Heavy Ion Research, Darmstadt, Germany b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 15 July 2014 Received in revised form 19 March 2015 Accepted 20 March 2015 Available online xxx
Focussing primarily on thermal load capacity, we describe the performance of a novel fixed anode CT (FACT) compared with a 100 kW reference CT. Being a fixed system, FACT has no focal spot blurring of the X-ray source during projection. Monte Carlo and finite element methods were used to determine the fluence proportional to thermal capacity. Studies of repeated short-time exposures showed that FACT could operate in pulsed mode for an unlimited period. A virtual model for FACT was constructed to analyse various temporal sequences for the X-ray source ring, representing a circular array of 1160 fixed anodes in the gantry. Assuming similar detector properties at a very small integration time, image quality was investigated using an image reconstruction library. Our model showed that approximately 60 gantry rounds per second, i.e. 60 sequential targetings of the 1160 anodes per second, were required to achieve a performance level equivalent to that of the reference CT (relative performance, RP ¼ 1) at equivalent image quality. The optimal projection duration in each direction was about 10 ms. With a beam pause of 1 ms between projections, 78.4 gantry rounds per second with consecutive source activity were thermally possible at a given thermal focal spot. The settings allowed for a 1.3-fold (RP ¼ 1.3) shorter scan time than conventional CT while maintaining radiation exposure and image quality. Based on the high number of rounds, FACT supports a high image frame rate at low doses, which would be beneficial in a wide range of diagnostic and technical applications. © 2015 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
Keywords: CT physics Fixed anode CT FACT Thermal load capacity X-ray anode
Introduction Third-generation computed tomography (CT) scanners incorporate an X-ray tube and a detector arrangement that mechanically rotate around the patient. Current clinical CT scanners and most industrial CT scanners operate on this principle. During recent decades, volumetric CT imaging has advanced with the advent of spiral acquisition [1,2] and the progression to multidetector row CT (MDCT) scanners [3]. During continuous movement of the couch, these systems acquire sufficient information in a helical path for reconstructing images from raw projection data. An increased number of detector rows provides the advantages of thinner slices, shorter scan times, and reduced motion artefacts.
* Corresponding author. Department of Radiation Oncology, University Clinic Erlangen, Germany. E-mail address: [email protected] (M. Kellermeier).
Particularly due to the rapid increase in the number of installed detector rows, there is a desire to obtain sufficient volume coverage in the axial direction during a single rotation, in which the X-ray tube rotates around in the gantry. However, a wide X-ray beam has a number of drawbacks, such as increased scattering, overscanning, and cone-beam artefacts at large cone angles. Various approaches and novel concepts have been proposed to address different issues [4e10]. Besides, the approaches of the fourthgeneration CT and the electron beam CT (EBCT) [11] are currently not in widespread use. Recently, an inverse-geometry CT (IGCT) system was proposed to achieve a scanned volume during a single gantry rotation that was essentially free of cone-beam artefacts [12e15]. Scanning a volume during a single rotation is limited by the gantry rotation time because centrifugal force can become destructive. Taking this mechanical restriction out of a system, the maximum temperature at the focal spot of an X-ray anode poses a serious limitation for the scanning time.
http://dx.doi.org/10.1016/j.ejmp.2015.03.012 1120-1797/© 2015 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
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In this paper, we described a concept for CT based on a ring of stationary X-ray sources, as proposed by Foster and Müller [16e18] from our group. The investigations of possible achievable image frame rates were closely related to potential performance. In general, a number of medical applications can benefit from a high image frame rate for a volume, including cardiac imaging, CT angiography, perfusion studies, and other demanding imaging applications. The potential performance of a conventional CT is primarily limited by the thermal load capacity of the X-ray anode. Thus, we began with studies on the thermal load capacities of anode focal spots. For these studies, a CT concept was outlined that had no mechanical restrictions due to gantry movements and that allowed for a high image frame rate, which was coupled with operated rounds in the stationary X-ray source ring at doses normally used for patients. The aim of the paper is to provide a conceptual theoretical framework for CT with fixed anodes based on the feasibility of thermal load capacity. However, this paper does not cover technical feasibility of the source ring and does not consider detector performance or efficiency. Since detectors need to be developed as per their specific requirements, we used as a benchmark today's acquisition of X-ray attenuation without an adaptation to the novel concept. Furthermore, the detection properties of the currently used integration times are extrapolated linearly to small time ranges. This means that the same total energy and photon fluence per projection yields identical image quality.
Throughout these studies, we chose parameters of our design in accordance with the reference CT, which was also used as a benchmark to determine the performance of our novel concept. The operating data for this reference CT (see Table 1) were based on SOMATOM Definition, Siemens Medical Solutions, Forchheim, Germany. Using an impact angle close to the right angle to the target surface, as considered by us at 84 (anode angle of 6 ), the following approximate relation [19] applies to electrical X-ray tube power (Pel) and thermal focal spot power (Pth):
Basic concept
Simulations of the thermal loads for a single anode
The basic concept for CT with fixed anodes (FACT) is illustrated in Fig. 1. The generation of a primary X-ray beam from an X-ray tube follows the same principle that has been known for over a century. A rotating anode X-ray tube, which conventionally revolves in a gantry around an object, is replaced in FACT by a stationary source ring of fixed anodes. In the current study, 1160 fixed X-ray anodes were used, analogous to the reference CT specified in Table 1. For theoretical analysis, the beam at a single fixed anode allows being switched on and off at any frequency. The fixed anodes in the source ring were used in sequential operation. Due to the restricted exposure time for each direction, the required number of projections for typical image information was acquired using multiple gantry rounds (~20). Projection data were combined during pre- or post-processing to acquire equivalent information analogous to the principle used in the reference CT.
3D simulation models In a simulation model, each fixed anode in the source ring of FACT was usually modelled as a sandwich of a high-Z material, a body with high thermal conductivity, and a heat bath for cooling: The square body was made of copper (Cu) with a base area of 25 mm by 3.2 mm and a height of 20 mm. Towards the focal spot, the tungsten (W) target layer of 0.5 mm thickness was adjoined without contact resistance. On the opposite side of the copper body, a heat bath at 300 K for cooling was defined. Away from the heat bath for all other surface boundary conditions and for the worst case scenario, a thermal insulation was chosen (see also Fig. 2). This fixed anode model was extended to a rotating anode model analogous to the principle used for the reference CT (see Table 1). Our model of a rotating anode with a radius of 60 mm had the same sandwich configuration as the fixed anode defined above. The nonconventional use of copper as a base for a rotating disk was
1 Pth z $Pel 2
(1)
This approximation applies to both fixed anodes, used in the FACT concept, as well as the rotating anode, used in the reference CT. Preliminary simulations of energy deposition in the focal spot confirmed this approximation within a deviation of 1% for the considered acceleration voltages of 80 kV, and even of 120 kV. We thus only present the simulation results at 80 kV. Methods In the following, the thermal load capability of a single fixed anode is first studied and compared with a rotating anode. Subsequently, the fixed anode is used as an isolated and independent module in the arrangement for the FACT concept.
Figure 1. Basic concept for FACT. (a) Geometric relationships of a FACT with a single source ring and a detector ring. (b) At helical source path for FACT, compared to that of a multislice spiral CT, the reconstructed images are normally determined by pre-processing. Alternatively, the information for the reconstructed images could be combined during postprocessing, as employed in Section Medical Imaging. (Additional figures can be found in supplementary data, Fig. 1e).
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Table 1 Specifications used for FACT and reference CT. Symbol
Specification
FACT
Reference CT
Pel U tround N SID OFS A (Pth/A)
Electrical X-ray tube power X-ray tube voltage Gantry round time of the source Source positions per round Source-to-isocenter distance Optical focal spot Thermal focal spot area Thermal focal spot power density
Depending on (Pth/A)max 80 kV Up to 300 ms 1160 60 cm 0.7 0.9 mm2 6 mm2 (Pth/A)max is shown in Fig. 4 (a)
100 kW 80 kV 300 ms 1160 60 cm (rounded) 0.7 0.9 mm2 6 mm2 (Pth/A)const ¼ 8.6 kW/mm2
considered a useable approximation for theoretical investigations during a short-time operation. Using copper for a rotating anode model with its outstanding material property of thermal conductivity also leads to the worst case scenario for FACT, when compared with conventional clinical CTs. The material properties used in the two 3D simulation models described above are listed in Table 2. Energy deposition The energy deposition of accelerated electrons in the so-called thermal focal spot was determined based on the latest research on particle interactions included in the Monte Carlo simulation GEANT4 [20]. Within the GAMOS framework, rapid access to verified programming routines is provided [21]. All simulations were performed using GAMOS 3.0 by accessing GEANT 4.9.4.p01. The physics of low-energy interactions was described by the Livermore models [22] (also known as EEDL [23]-EPDL [24] models) and tracks were followed down to the production cut length of 10 nm or an energy of 1 eV, including rest energy deposition, below which the particles were placed under split in terms of probability. Energy was collected in 1 nm voxels. These voxels were averaged in the lateral extension to have a representative 1D distribution of energy along a penetration depth of 8 mm, in which the voxel value was four orders of magnitude less than the maximum at
Figure 2. 3D simulation model with representation of incident electron beam (e): (a) at the fixed anode model in short intervals with a given projection duration and (b) at the rotating anode model with continuous long-lasting beam. The fixed anode designed as a square body was made of copper (Cu) with a base area of 25 mm by 3.2 mm and a height of 20 mm. The tungsten (W) target layer had a material thickness of 0.5 mm. The rotating model used the same construction, but as a cylindrical body with a rotational frequency of 150 Hz and a radius of 60 mm. The thermal focal spot area, A, on the anode surface is formed by the entering electrons of equally distributed intensity. For cooling, a heat bath of 300 K has been defined. The surfaces, except for the heat bath, were considered thermally insulated.
0.4 mm. Thus, a small effect of scattering on field boundaries was eliminated when used only in the central area with half the focal spot width. Preliminary investigations showed that a deeper penetration depth did not give significantly different results in the subsequent FEM applications. The trajectories and energy of the emitted particles were registered on the target surface. Based on the differences between the primary energy of the incident electron beam and the energy of the emitted electrons and photons, we calculated the relative proportions of deposited energy in the thermal focal spot. Overall, the deposition of energy in the thermal focal spot on the tungsten target results in an increase in temperature, which could be determined from the solutions of partial differential equations.
Heat transfer Applying partial differential equations to describe the temperature profile in the X-ray anode from the deposited energy, the finite element method (FEM) was used. For this purpose, commercial software COMSOL Multiphysics (version 4.3) was applied using its standard heat transfer module for solid interfaces. For FEM simulations, the corresponding temperature-dependent data of material properties (cf. Table 2) were used from the Material Library of COMSOL Multiphysics, which was based on the Material Property Database (MPDB) from JAHM Software, Inc. The acquired depth energy distribution was evenly applied over the thermal focal spot area A (see Table 1) and scaled using the relative proportion of deposited energy. Based on a number of simulations, values for the maximum thermal power density, (Pth/A)max, were obtained. This caused an increase in temperature from 300 K to 2500 K within a certain period, which we called the projection duration (Dt). Krieger [25] indicated that, due to the vapour pressure of anode material, the favourable operating temperature of an anode is around 70% of its melting temperature (cf. Table 2) to obtain a service life at an usual expectation. This led us to the absolute upper temperature limit of 2500 K for the tungsten target layer. Bouwers [26] and Oosterkamp [27] did fundamental work on the load capacities of X-ray tubes while in operation. We used formulas based on simple modelling assumptions [28] for comparisons with our simulation results. In addition to the initial temperature, which could be estimated from values in the literature, we were interested in heat transport under various conditions in terms of both, temporal and spatial resolution. Thus, we did consider a 3D simulation model with an atomic interaction region
Table 2 Material properties used for Monte Carlo simulations and literature formulas. Symbol
Specification
Tungsten (W)
Copper (Cu)
l
Thermal conductivity Specific heat capacity Density
170 W m1 K1 138 J kg1 K1 19.25 g cm3
400 W m1 K1 385 J kg1 K1 8.92 g cm3
c
r
Melting point for W: 3695 K and Cu: 1358 K.
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in the thermal focal spot and with macroscopic dimensions with respect to the basic copper block. The kinetic energy of electrons is mainly deposited in a penetration depth of a few micrometres after entering the target medium of tungsten. Finite elements modelled by voxels adopted in size based on the local geometry allowed to keep the calculation space reasonably small. Virtual FACT model Power and timing for a single anode and the source ring During the cooling phase for a single thermally isolated fixed anode, the other identical anodes in the source ring operate equally in succession. The electron beam cannot be instantaneously switched between anodes. To qualitatively incorporate technically required operations d such as rise and fall phases during the pulsed operation of X-ray sources d we incorporated a beam pause (t0 ), which can be introduced between two projections. The simulation environment for a single anode was also used to study the performance of an entire ring of anodes, as required with FACT. Based on intermediate results, we considered various beam pauses (t0 ) of 0 ms, 1 ms, 3 ms, and 5 ms. Figure 3 (b) presents an example of the operating time for a source ring with 1160 fixed anodes. The indicated projection duration (Dt) for each single fixed anode was 10 ms. With a beam pause of t0 ¼ 1 ms, the temporally possible repetition frequency at a single fixed anode (i.e. gantry rounds per second) was 78.4 Hz. To achieve the expected image quality within a typical scanning time, the question became whether FACT could provide the necessary number of superpositions for a projection direction. Superpositions were necessary because the projection duration (Dt) of FACT was approximately only 1/20 as compared with that of the reference CT. With about the same Pth/A an equal amount of total energy was emitted after 20 projections for the same direction, as with the reference CT. Thus, FACT is theoretically able to acquire the same detected information and obtain the same image quality as in the reference scan. The term “same image quality” refers in this comparison of the systems to the parameter image noise, which is related to the tube current-scan time product (see also section Medical Imaging) for the same tube output configuration. In FACT, the shorter projection durations result in noisier images, however, patient and organ movements under high temporal and spatial resolution can be theoretically extracted. In this theoretical approach, it was assumed that detection is independent of the readout rate. Under identical conditions, the photon spectra and fluence (Jph ) for both fixed and rotating anode technologies were equal in the first approximation and proportional to the deposited thermal energy, Eth:
Jph fEth :
(2)
Assuming a known deposition of energy, it was thus possible to determine image quality, provided that only the nature of energy deposition differs between systems. As a reference, we used a conventional CT with a constant (Pth/A)const (see Table 1) for an unlimited operation time (toperation). The thermal energy in the FACT source ring for a single round was determined by the number of rectangular pulses, N, with a fixed projection duration (Dt). The following definition of nmin gives the theoretical minimum number of rounds from the ratio of the thermal focal spot energies within any operation time toperation ¼ N (Dt þ t0 ) under the assumption of a 300 K initial anode temperature at FACT:
nmin
ðPth =AÞconst $toperation CT ¼ : ðPth =AÞmax $Dt $N FACT
(3)
A possible remaining residual heat from previous pulses in a single anode is not taken into account in formula (3). Thus, mathematically, an infinite cooling phase for FACT is assumed between source activities after each round. For exact consideration of finite cooling phases between the source activities at a possible round frequency, (Pth/A)max is reduced due to the residual heat in the anode. For this, we investigated the potential order of temporal sequences (Dt þ t0 ) for the source ring operating in pulsed mode. Values for the round frequency (fpossible) of successively active sources in the source ring were determined for various possible timings using the following equation:
fpossible ¼
1 0 : N$ ðDt þ t Þ
(4)
In addition to such theoretical investigations, we considered technical feasibility, exploring the maximum operating frequencies achievable for a limited range of realizable specifications. We limited to be restricted to a determined the limited round frequency fpossible maximum operating frequency k:
limited fpossible ¼
k ; for fpossible ; else :
fpossible > k
(5)
Based on our intermediate results, we suggest 60 Hz as a lower limit for the operating frequency d i.e. k1 ¼ 60 Hz d and a further limit of k2 ¼ 100 Hz with respect to the high dataflow from the detector ring to a CPU (cf. Fig. 13). During pulsed operation, the maximum temperature of Cu (cf. Fig. 6) can increase as a function of the duration of the cooling phase. To account for a finite cooling phase during which the temperature of the anode does not reach 300 K, we defined the scaling factor h for (Pth/A)max to prevent the maximum temperature of 2500 K in the tungsten target layer during long-time operation in pulsed mode (cf. II.A.3):
Figure 3. Operating times for a single fixed anode and for a source ring with 1160 fixed anodes. (Pth/A)max was determined by the power factor h (see Eq. (6)). (a) Illustration showing a projection duration (Dt) of 10 ms. The repetition frequency is 78.4 Hz. (b) Each fixed anode in the source ring operates with the same given repetition frequencydi.e. the gantry rounds amount to 78.4 1/s.
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M. Kellermeier et al. / Physica Medica xxx (2015) 1e10
Figure 4. (a) Simulation results for determining the maximum thermal focal spot power density, (Pth/A)max, which caused a temperature increase from 300 K to 2500 K during a certain projection duration (Dt). Comparisons of our 3D simulation results with those from analytical formulas in the literature [28] and the reference CT. The value from the simulations of a rotating anode with a load limit at 10 s and the value of the reference CT, (Pth/A)const, were time-independently projected onto this figure to make direct comparisons with the (Pth/A)max values from fixed anodes. (b) Relative deviations of these comparisons.
h 0 . Pth A
i max FACT
¼ h$ðPth =AÞmax
FACT
:
(6)
Relative performance (RP) of FACT with regard to the reference CT With the ratio between the maximal possible thermal loads of FACT and reference CT an assessment factor, relative performance (RP), was introduced as follows:
h RP ¼
. i 0 Pth A $ Dt$N$ f max FACT ðPth =AÞconst CT
(7)
5
Figure 6. Example temperature profile during pulsed operation of a fixed anode. The maximum temperature in the tungsten (W) target was 2500 K (±0.5%). In the copper (Cu) block, the maximum temperature did not reach 500 K. A time-unlimited operation was assumed based on the plateau for the maximum temperatures in the medium of a fixed anode.
with reference to Eqs. (2)e(6)) and (P'th/A)max (see Eq. (6)) for pulsed operation at a given round frequency f.
Medical imaging Image reconstruction using FACT is based on the same fundamentals used with conventional CT [29]. Using a spiral scan, it is known that spatial resolution and image quality are determined by z-filtering/z-interpolation during pre-processing. Alternatively, this information can be combined during post-processing by interpolating the reconstructed images (cf. Fig. 1 (d)). As previously indicated, the FACT concept uses the principle of superposition, which can be illustrated with a CT image reconstruction (see Fig. 10). For this purpose, permission was given to use the reconstruction library of the Institute of Medical Physics, University Erlangen-Nürnberg, Germany. The parameters for simulation were closely linked to SOMATOM Definitions, Siemens Medical Solutions, Forchheim, Germany from ~2007 which form the basis for the defined reference CT (see Table 1) in this paper.
Figure 5. 3D simulation model of (a) fixed anode and (b) rotating anode along with the temperature distribution after 10 s of operation using the maximum possible electrical X-ray tube power, Pel, that was set for each projection. Both models are also described in Fig. 2. The trajectories of the emitted charged electrons (e) are indicated based on simulation results in conjunction with a static electromagnetic field between the cathode and the anode. For reasons of comparability, an exact tube design was not pursued. However, a study of these trajectories (with COMSOL Multiphysics) showed that the reflected electrons provided their energy away from the thermal focal spot in a first approximation after multiple uniform reflections over the relatively large interior surfaces of the X-ray vacuum tube. The re-entry energy was neglected in our simulations, as this would have resulted in a small increase in background temperature.
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M. Kellermeier et al. / Physica Medica xxx (2015) 1e10
Figure 7. Operating results for (a) power factor h and (b) maximum temperature of a copper block. The gantry rounds correspond to the possible and possible but limited gantry rounds from Fig. 8. Note: The projection duration is an adjustable parameter and no integral term.
The dependence of image quality was discussed in a previous paper, in which a dose-weighted contrast-to-noise ratio ðCNRDÞ was chosen as the criterion for image quality optimization [30]. The standard deviation (SD) in the image plane was used as a surrogate for what the signal noise would be for n number of rounds:
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u M u 1 X 2 1 1 $ SD ¼ t x x f pffiffiffiffi ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi: M 1 i¼1 i Q I $ N$ Dt$ n
(8)
SD was determined from M pixel values, xi, in a region of interest (ROI) in a homogeneous image section with respect to their mean value, x. Equation (8) gives the well-known proportion to the tube current-scan time product, Q. The question of a quantitative improvement in image sharpness due to a sharp focus on a fixed anode is not answered in this article. The same extension of focal spot width in relation to the blurred focus in CT is included in the following boundary value analysis.
Boundary value analysis In contrast to conventional CT using rotating X-ray tubes, no blurring of the optical focal spot (OFS, see Table 1) occurs with FACT, which is an advantage for image sharpness. In practice with
conventional CT with specifications used for the reference CT, due to rotational movement during scanning, the OFS blurs to a factor of 4.6 in each integrated projection direction. If one follows this expansion with FACT, the result is an OFSþ and an Aþ. In this thought experiment, the thermal load capacity is thus increased (in the ratio Aþ/A ¼ 4.6) at a cost of the theoretically equivalent OFSþ, which is known from conventional CT gantry rotation within a measurement integral for a projection. These values are listed in Table 3. This application of boundary value analysis corresponds to a successive distribution of the thermal load on an entire body source ring. Results The Results section follows the structure of the Methods section: Consideration of the individual fixed anode in comparison to the rotating anode and the use of fixed anode as an isolated and independent module in the arrangement for the FACT concept. Simulations of thermal loads of a single anode Applying the 3D simulation model described in Fig. 2, we used Monte Carlo simulations with an incident electron beam within the
Figure 8. Minimum, possible, and possible but limited gantry rounds defined in Eqs. (3)e(5). The different figures show the results for the given beam pauses (t0 ): (a) without beam pause, (b) t0 ¼ 1 ms, (c) t0 ¼ 3 ms and (d) t0 ¼ 5 ms. The minimal values were determined according to Eq. (3) at infinite cooling phases between the pulsesdi.e. without any residual thermal energy from a previous pulse, in a single anode from the source ring. The possible gantry rounds, however, note residual heat with the above-introduced power factor h, which ensured compliance with the thermal load limit at 2500 K.
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M. Kellermeier et al. / Physica Medica xxx (2015) 1e10
7
Figure 11. Illustrations of boundary value analysis. The operating range for FACT shown with a dark grey time bar is made available to the operating time of the reference CT. The light grey time bar marks the range for the FACTþ with a broadened focal spot area.
Figure 9. Relative Performance (RP) for a given beam pause, t0 , (a) at no frequency limit, (b) at a limit of 100 Hz, and (c) at a limit of 60 Hz.
extent of the thermal focal spot area A defined in Table 1. Simulations used for heat transfer in the X-ray target are described in Sec. Methods. In addition to actual observations of a fixed anode, in order to understand the differences between the types of anodes, we performed simulations for the rotating anode to explain the differences in thermal load capacity. Figure 5 shows our 3D simulation models for the thermal focal spot and typical trajectories of the particles as well as the simulation results for the temperature distribution after an assumed 10 s of operation with an X-ray tube. (Pth/A)max values are plotted in Fig. 4 (a) that caused an increase in temperature from 300 K to 2500 K at the fixed anode within a
Figure 10. Example of FACT application for reconstructed and post-processed images and comparison with the reference CT. Based on 100 kW at 80 kV, the tube current-scan time product, Q, with (a) FACT in one of 18 rounds was 20.8 mAs and with (c) the reference CT in one round was 375 mAs. (b) After interpolating 18 images with FACT (18 20.8 mAs), the measured SD was equal to that of the reference CT. The scan time for the same image quality with FACT was less by a factor of 1.3.
Please cite this article in press as: Kellermeier M, et al., A novel concept for CT with fixed anodes (FACT): Medical imaging based on the feasibility of thermal load capacity, Physica Medica (2015), http://dx.doi.org/10.1016/j.ejmp.2015.03.012
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M. Kellermeier et al. / Physica Medica xxx (2015) 1e10 Table 3 Further specifications used for FACT and the reference CT. (compare with Table 1.). Symbol
Specification
FACT
Reference CT
OFSþ Aþ
OFS including blurring A corresponding to blurring
3.2a x 0.9 mm2 27.6 mm2
3.2b 0.9 mm2 6 mm2
a b
Figure 12. Spot diagram. Pel is used as a scale for X-ray outputs of the respective concepts. The heat content illustrates the resulting heat transfer to an anode, which must be dissipated by cooling. Since the fixed anodes of the source ring reach a temperature plateau, a time-unlimited operation is assumed with FACT.
given projection duration (Dt). In comparison, the results from analytical formulas [28] were mapped using Table 1 and the material data was shown in Table 2. The relative deviations of these comparisons are shown in Fig. 4 (b). There was a relatively good correlation, particularly in the area around Dt ¼ 10 ms. This projection duration is also highlighted in the following chapters, as it represents the optimum operating range for FACT, particularly with regard to RP (cf. Fig. 9). Figure 5 shows for comparison of the anode models their temperature distribution after 10 s of operation using the maximum possible electrical X-ray tube power, Pel, which was set for each projection. The maximum temperature in the copper block of the fixed anode did not reach 500 K, whereas in the rotating anode, a temperature of 1000 K has been exceeded. The value for the heat content shows that the rotating anode is charged 1000 times higher than a fixed anode at the operating point of a FACT, as is presented in the following section. Virtual FACT model Power and timing for a single anode and the source ring The simulations performed above for a 3D model of fixed anodes described one target module of the source ring of FACT without neighbourhood influence. Studies of repeated pulsed loads showed that, at fixed anodes, a pulsed operation could have an unlimited time frame. As representative results of our simulations at projection durations of 10 ms, Fig. 6 shows the FEM simulation results for the maximum temperatures in the anode medium resulting from
Figure 13. Relative dataflow with FACT as compared to that with the reference CT.
Focal spot width corresponding to blurring. Blurring assumed from the rotational movement during the detection.
pulsed long-time operations with a repetition frequency of 78.4 Hz (see Fig. 3). Here, after a pulsed operation time of around 6 s, the maximum temperature in the tungsten target reached a plateau of 2500 K (±0.5%), whereas the maximum temperature in the adjoining copper block did not exceed 500 K (see 7 (b)). The constant power factor, h, had a value of 0.915 (see Fig. 7 (a)). Figure 7 shows the simulation results for (a) the power factor h and (b) the maximum temperature of the copper block using various projection durations (Dt). The power factor h was close to 1 at low gantry rounds because sufficient time passes to the next activity at each single anode. In this case, the copper block could hardly accumulate heat energy due to the relatively small thermal focal spot power (Pth, see Fig. 4) per pulse as well as the long cooling phase between the pulses on a single anode. The shorter the projection durations, the higher was Pth and the initial temperature in the anode increased due to accumulated heat energy from previous pulses. The different cases of various beam pauses (t0 ) and the restriction to a maximum operating frequency (k) became apparent at projection durations of Dt < 0.8 ms. The corresponding gantry rounds per second are plotted in Fig. 8. The feature of time-unlimited operation at one fixed anode was transferred to a circular array of fixed anodes, which are addressed in succession below. This led to the concept of FACT. These results are described below. Using Eqs. (3)e(5) for the given beam pauses (t0 ¼ 0, 1, 3 and 5 ms) the resulting round frequencies (Gantry rounds per second) are plotted in Fig. 8 for three different conditions: no limitation, limitation at 100 Hz and 60 Hz. Our preferred FACT operation point, f possible ðDt ¼ 10 msÞ, is indicated by an arrow: 86.2 1/s for t0 ¼ 0 ms, 78.4 1/s for t0 ¼ 1 ms, 66.3 1/s for t0 ¼ 3 ms and 57.5 1/s for t0 ¼ 5 ms. For comparisons, the referenced CT gantry rounds of 3.33 1/s is projected independent of Dt and the projection duration of 0.26 ms is marked. Relative performance (RP) of FACT with regard to reference CT In Eq. (7), relative performance (RP) was defined to show the relationship between FACT and the reference CT from the perspective of possible source performance. Figure 9 shows the RP curves for the given projection durations (Dt) and the beam pauses (t0 ). As a reminder, the purpose for preparing these figures was to find the operating range for FACT with an RP 1. In this paper, we did not consider t0 > 5 ms, because the source performance for the reference CT may have been difficult to achieve (see Fig. 9 (a)). The FACT operating range for RP 1 is displayed as a time bar. The typical operating range of a CT is shown to the right with a time bar from 0.2 ms to 1 ms for comparison. Limiting the gantry rounds to the round frequency at 100 Hz restricted the lower projection time range for FACT to about 4 ms, as shown in Fig. 9 (b). A maximum round frequency at 60 Hz reduced the operating range to an operating point around 10 ms, which is shown in a short time bar in Fig. 9 (c). Medical imaging Following is a brief example of the relationship of projection duration, beam pause, gantry rounds and X-ray tube power. Using the operating point highlighted above (Dt ¼ 10 ms, t0 ¼ 1 ms), the
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applied superposition with FACT required validation. Figure 1 (c) and (d) illustrates the principle of data acquisition with FACT in comparison to a conventional CT. Figure 10 (a, b) shows the simulation results for post-processed data, i.e. data which are generated by accumulating the raw-data of several rounds. In the circular region of interest (ROI), the SD (in HU) of the image voxels was determined. After interpolating 18 images with FACT (18 , 20.8 mAs), the determined SD was equal to that of the reference CT. The ratio of tube current-scan time product (QCT/QFACT)0.5 is 0.24 and reflects the standard deviation ratio SDCT/SDFACT of 0.24 according relation to Eq. (8). The scan time for the equal image quality using FACT was less by a factor of 1.3. For comparison, simulated imaging after one round with the reference CT is shown in Fig. 10 (c). Under the assumption of the same detector conditions, the criterion for image quality optimization (CNRD) is not further affected because the same operating conditions for X-ray sources are provided. Theoretically, however, the image sharpness for FACT can be better than in the referenced CT because in the simulation of the reference CT we neglected blurring of the optical focal spot caused by the rotational motion. Boundary value analysis Using the focal spot size of Aþ, compensates for the advantage of the higher image sharpness due to a static optical focal spot. The right side of the operating range for FACT shifted towards the operating range for a conventional CT. At the transition to the CT operating range, RP / 1. This can demonstrate the smooth transition between the novel FACT concept and the conventional CT. At the highlighted operating point (Dt ¼ 10 ms, t0 ¼ 1 ms) in Fig. 11 (a), the minimum number of rounds has been reduced from 55 to 12. At the same point, the RP increased from 1.3 (see Fig. 9 (b)) to 6 (see Fig. 11 (b)). This reflected the focal spot broadening by a factor of 4.6. Discussion Our results for a source ring of fixed anodes showed that it should be thermally possible to achieve a novel concept for CT, the performance of which is equal to or even better than that of conventional CT. The necessary energy fluence for a beam projection for a typical image quality is theoretically achievable, as the number of rounds was sufficient for the principle of superposition to be used within a typical scan time. With FACT, at least 60 gantry rounds per second were necessary theoretically to achieve the same imaging performance as the reference CT with an X-ray tube power of 100 kW. In this case, the operating point for a projection was in the range of 10 ms. If 50 kW is sufficient, then FACT could be operated at 30 rounds per second or a projection duration in the range of 60 ms could be used, which is about one fourth of the typical integration time for CT detectors. Thus, a significant advantage of a fixed CT system is that the optical focal spot is not blurred, which would enhance the sharpness of a reconstructed image. The resulting high image frame rate would be possible with a typical X-ray exposure to a patient. This would be beneficial for its applications, such as in cardiac imaging, CT angiography, perfusion studies, and other demanding imaging applications. Figure 12 shows a spot diagram of the respective typical and common operating ranges based on the electrical X-ray tube and source ring power (Pel). When the focal spot size is increased, which occurs with current CT technology due to movement, FACT shows an enhanced performance by a factor of about six. This superior performance could be used to scan faster or to increase image
9
quality. Another advantage should be noted: By ensuring sufficient direct cooling of the fixed anodes, FACT provides for time-unlimited operation. Based on the frequency rounds, our calculations for the volume of data (about 8 GB/s for 64 slices) from the detector ring show that only interfaces currently under development could transfer this accumulating data in real time. Even from this perspective, developing FACT would be in keeping with the current zeitgeist. Figure 13 shows the relative dataflow with FACT as compared to that with the reference CT. In parallel to the investigated source ring, a fixed detector ring is defined. Thus, projections from each anode element on the detector occur obliquely to the reconstructed transverse plane. In conjunction with the detector elements, we will not discuss further the lack of collimation of the scattered X-rays. In this context, the development of fast detectors is desirable for capturing the incidence direction. Before the FACT can replace the third-generation CT, we see that a number of technical developments have to be made. On the source side the production, switching, and distribution of a focused electron beam will result into additional challenges such as dedicated power electronics. These have to result in rectangular pulses at the anode positions which will itself suffer from the thermal load such that thermomechanical long-term studies will be essential. Also regarding the detector improvements, e.g., regarding the readout speed, the efficiency for small quantum numbers, and the distinction between primary X-ray beam and X-ray scatter during the detection have to be accomplished. All of these issues present additional challenges that need even more detailed investigations. A distinct advantage over conventional CT could be considered by setting a second source ring on the other side of the detector. Figure e2 (see supplementary data) shows a schematic for this advanced concept. This provides a rectangular beam field in the zdirection and doing away with over-scanning, which could result in reducing unnecessary doses to a patient without any additional complex technology. Such a dual-source FACT would theoretically provide for a doubling of the relative performance of the FACT concept introduced above.
Conclusions FACT, a new CT concept relying on fixed anodes was proposed. The design was compared with a known conventional CT to evaluate the thermal load capacity and medical imaging capabilities. Although concerned primarily with physical assessment, we have also considered it necessary to dwell on the technical limits of FACT. The simulations showed that FACT is thermally feasible. Image data are acquired in multiple gantry rounds using the principle of superposition, yielding high image frame rates at very thin slices, which can be beneficial for numerous medical applications. As an example, at the same radiation exposure for the patient, the much thinner layers (at high axial spatial resolution) of FACT are indeed noisy. However, at high contrast, via the use of contrast agents for CT angiography or at calcification in the breast, the branching of blood vessels or the size assessment could be improved. The thermal load capacity allows a time-unlimited operation that could have an application in industrial use, as well as in safety and security. As a fixed system, FACT has no blurring of the optical focal spot during projection. In comparison to the third-generation CT, the relative performance (RP) of 1.3 was determined at a given thermal focal spot area. With an RP > 1 can be achieved a shorter scan time while maintaining radiation exposure and image quality as defined above.
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Acknowledgement The present work was performed in fulfilment of the requirements for obtaining the degree of Dr. rer. biol. hum.
Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.ejmp.2015.03.012.
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Please cite this article in press as: Kellermeier M, et al., A novel concept for CT with fixed anodes (FACT): Medical imaging based on the feasibility of thermal load capacity, Physica Medica (2015), http://dx.doi.org/10.1016/j.ejmp.2015.03.012