Continuum modeling perspectives of non-Fourier heat conduction in biological systems

The thermal modeling of biological systems has increasing importance in developing more advanced, more precise techniques such as ultrasound surgery. One of the primary barriers is the complexity of biological materials: the geometrical, structural, and material properties vary in a wide range, and they depend on many factors. Despite these difficulties, there is a tremendous effort to develop a reliable and implementable thermal model. In the present paper, we focus on the continuum modeling of heterogeneous materials with biological origin. There are numerous examples in the literature for non-Fourier thermal models. However, as we realized, they are associated with a few common misconceptions. Therefore, we first aim to clarify the basic concepts of non-Fourier thermal models. These concepts are demonstrated by revisiting two experiments from the literature in which the Cattaneo-Vernotte and the dual phase lag models are utilized. Our investigation revealed that using these non-Fourier models is based on misinterpretations of the measured data, and the seeming deviation from Fourier's law originates in the source terms and boundary conditions

Challenges in the thermal modeling of highly porous carbon foams

The heat pulse experiment is a well-known method for determining thermal diffusivity. However, neither the measurement nor the evaluation methodologies are straightforward for heterogeneous, highly porous materials. In the present paper, we focus on two open-cell carbon foam types, differing in their porosity but having the same size. Recent experiments showed that a non-Fourier behaviour, called 'over-diffusive' propagation, is probably present for such a complex structure. The (continuum) Guyer-Krumhansl equation stands as a promising candidate to model such transient thermal behaviour. In order to obtain a reliable evaluation and thus reliable thermal parameters, we utilize a novel, state-of-the-art evaluation procedure developed recently using an analytical solution of the Guyer-Krumhansl equation. Based on our observations, it turned out that the presence of high porosity alone is necessary but not satisfactory for non-Fourier behaviour. Additionally, the mentioned non-Fourier effects are porosity-dependent. However, porous samples can also follow the Fourier law. These data serve as a basis to correctly identify the characteristic heat transfer mechanisms and their corresponding time scales, which altogether result in the present non-Fourier behaviour. Keywords: flash experiments, non-Fourier heat conduction, highly porous carbon foams

Uncertainty-aware spot rejection rate as quality metric for proton therapy using a digital tracking calorimeter

Objective. Proton therapy is highly sensitive to range uncertainties due to the nature of the dose deposition of charged particles. To ensure treatment quality, range verification methods can be used to verify that the individual spots in a pencil beam scanning treatment fraction match the treatment plan. This study introduces a novel metric for proton therapy quality control based on uncertainties in range verification of individual spots. Approach. We employ uncertainty-aware deep neural networks to predict the Bragg peak depth in an anthropomorphic phantom based on secondary charged particle detection in a silicon pixel telescope designed for proton computed tomography. The subsequently predicted Bragg peak positions, along with their uncertainties, are compared to the treatment plan, rejecting spots which are predicted to be outside the 95% confidence interval. The such-produced spot rejection rate presents a metric for the quality of the treatment fraction. Main results. The introduced spot rejection rate metric is shown to be well-defined for range predictors with well-calibrated uncertainties. Using this method, treatment errors in the form of lateral shifts can be detected down to 1 mm after around 1400 treated spots with spot intensities of 1 × 107 protons. The range verification model used in this metric predicts the Bragg peak depth to a mean absolute error of 1.107 ± 0.015 mm. Significance. Uncertainty-aware machine learning has potential applications in proton therapy quality control. This work presents the foundation for future developments in this area.publishedVersio

Uncertainty-aware spot rejection rate as quality metric for proton therapy using a digital tracking calorimeter

Objective. Proton therapy is highly sensitive to range uncertainties due to the nature of the dose deposition of charged particles. To ensure treatment quality, range verification methods can be used to verify that the individual spots in a pencil beam scanning treatment fraction match the treatment plan. This study introduces a novel metric for proton therapy quality control based on uncertainties in range verification of individual spots. Approach. We employ uncertainty-aware deep neural networks to predict the Bragg peak depth in an anthropomorphic phantom based on secondary charged particle detection in a silicon pixel telescope designed for proton computed tomography. The subsequently predicted Bragg peak positions, along with their uncertainties, are compared to the treatment plan, rejecting spots which are predicted to be outside the 95% confidence interval. The such-produced spot rejection rate presents a metric for the quality of the treatment fraction. Main results. The introduced spot rejection rate metric is shown to be well-defined for range predictors with well-calibrated uncertainties. Using this method, treatment errors in the form of lateral shifts can be detected down to 1 mm after around 1400 treated spots with spot intensities of 1 × 107 protons. The range verification model used in this metric predicts the Bragg peak depth to a mean absolute error of 1.107 ± 0.015 mm. Significance. Uncertainty-aware machine learning has potential applications in proton therapy quality control. This work presents the foundation for future developments in this area

Exploration of differentiability in a proton computed tomography simulation framework

Objective. Gradient-based optimization using algorithmic derivatives can be a useful technique to improve engineering designs with respect to a computer-implemented objective function. Likewise, uncertainty quantification through computer simulations can be carried out by means of derivatives of the computer simulation. However, the effectiveness of these techniques depends on how ‘well-linearizable’ the software is. In this study, we assess how promising derivative information of a typical proton computed tomography (pCT) scan computer simulation is for the aforementioned applications. Approach. This study is mainly based on numerical experiments, in which we repeatedly evaluate three representative computational steps with perturbed input values. We support our observations with a review of the algorithmic steps and arithmetic operations performed by the software, using debugging techniques. Main results. The model-based iterative reconstruction (MBIR) subprocedure (at the end of the software pipeline) and the Monte Carlo (MC) simulation (at the beginning) were piecewise differentiable. However, the observed high density and magnitude of jumps was likely to preclude most meaningful uses of the derivatives. Jumps in the MBIR function arose from the discrete computation of the set of voxels intersected by a proton path, and could be reduced in magnitude by a ‘fuzzy voxels’ approach. The investigated jumps in the MC function arose from local changes in the control flow that affected the amount of consumed random numbers. The tracking algorithm solves an inherently non-differentiable problem. Significance. Besides the technical challenges of merely applying AD to existing software projects, the MC and MBIR codes must be adapted to compute smoother functions. For the MBIR code, we presented one possible approach for this while for the MC code, this will be subject to further research. For the tracking subprocedure, further research on surrogate models is necessary

Exploration of Differentiability in a Proton Computed Tomography Simulation Framework

Objective. Algorithmic differentiation (AD) can be a useful technique to numerically optimize design and algorithmic parameters by, and quantify uncertainties in, computer simulations. However, the effectiveness of AD depends on how 'well-linearizable' the software is. In this study, we assess how promising derivative information of a typical proton computed tomography (pCT) scan computer simulation is for the aforementioned applications. Approach. This study is mainly based on numerical experiments, in which we repeatedly evaluate three representative computational steps with perturbed input values. We support our observations with a review of the algorithmic steps and arithmetic operations performed by the software, using debugging techniques. Main results. The model-based iterative reconstruction (MBIR) subprocedure (at the end of the software pipeline) and the Monte Carlo (MC) simulation (at the beginning) were piecewise differentiable. Jumps in the MBIR function arose from the discrete computation of the set of voxels intersected by a proton path. Jumps in the MC function likely arose from changes in the control flow that affect the amount of consumed random numbers. The tracking algorithm solves an inherently non-differentiable problem. Significance. The MC and MBIR codes are ready for the integration of AD, and further research on surrogate models for the tracking subprocedure is necessary

A High-Granularity Digital Tracking Calorimeter Optimized for Proton CT

A typical proton CT (pCT) detector comprises a tracking system, used to measure the proton position before and after the imaged object, and an energy/range detector to measure the residual proton range after crossing the object. The Bergen pCT collaboration was established to design and build a prototype pCT scanner with a high granularity digital tracking calorimeter used as both tracking and energy/range detector. In this work the conceptual design and the layout of the mechanical and electronics implementation, along with Monte Carlo simulations of the new pCT system are reported. The digital tracking calorimeter is a multilayer structure with a lateral aperture of 27 cm × 16.6 cm, made of 41 detector/absorber sandwich layers (calorimeter), with aluminum (3.5 mm) used both as absorber and carrier, and two additional layers used as tracking system (rear trackers) positioned downstream of the imaged object; no tracking upstream the object is included. The rear tracker’s structure only differs from the calorimeter layers for the carrier made of ∼200 μm carbon fleece and carbon paper (carbon-epoxy sandwich), to minimize scattering. Each sensitive layer consists of 108 ALICE pixel detector (ALPIDE) chip sensors (developed for ALICE, CERN) bonded on a polyimide flex and subsequently bonded to a larger flexible printed circuit board. Beam tests tailored to the pCT operation have been performed using high-energetic (50–220 MeV/u) proton and ion beams at the Heidelberg Ion-Beam Therapy Center (HIT) in Germany. These tests proved the ALPIDE response independent of occupancy and proportional to the particle energy deposition, making the distinction of different ion tracks possible. The read-out electronics is able to handle enough data to acquire a single 2D image in few seconds making the system fast enough to be used in a clinical environment. For the reconstructed images in the modeled Monte Carlo simulation, the water equivalent path length error is lower than 2 mm, and the relative stopping power accuracy is better than 0.4%. Thanks to its ability to detect different types of radiation and its specific design, the pCT scanner can be employed for additional online applications during the treatment, such as in-situ proton range verification

A high-granularity digital tracking calorimeter optimized for proton CT

A typical proton CT (pCT) detector comprises a tracking system, used to measure the proton position before and after the imaged object, and an energy/range detector to measure the residual proton range after crossing the object. The Bergen pCT collaboration was established to design and build a prototype pCT scanner with a high granularity digital tracking calorimeter used as both tracking and energy/range detector. In this work the conceptual design and the layout of the mechanical and electronics implementation, along with Monte Carlo simulations of the new pCT system are reported. The digital tracking calorimeter is a multilayer structure with a lateral aperture of 27 cm × 16.6 cm, made of 41 detector/absorber sandwich layers (calorimeter), with aluminum (3.5 mm) used both as absorber and carrier, and two additional layers used as tracking system (rear trackers) positioned downstream of the imaged object; no tracking upstream the object is included. The rear tracker’s structure only differs from the calorimeter layers for the carrier made of ∼200 μm carbon fleece and carbon paper (carbon-epoxy sandwich), to minimize scattering. Each sensitive layer consists of 108 ALICE pixel detector (ALPIDE) chip sensors (developed for ALICE, CERN) bonded on a polyimide flex and subsequently bonded to a larger flexible printed circuit board. Beam tests tailored to the pCT operation have been performed using high-energetic (50–220 MeV/u) proton and ion beams at the Heidelberg Ion-Beam Therapy Center (HIT) in Germany. These tests proved the ALPIDE response independent of occupancy and proportional to the particle energy deposition, making the distinction of different ion tracks possible. The read-out electronics is able to handle enough data to acquire a single 2D image in few seconds making the system fast enough to be used in a clinical environment. For the reconstructed images in the modeled Monte Carlo simulation, the water equivalent path length error is lower than 2 mm, and the relative stopping power accuracy is better than 0.4%. Thanks to its ability to detect different types of radiation and its specific design, the pCT scanner can be employed for additional online applications during the treatment, such as in-situ proton range verification

A high-granularity digital tracking calorimeter optimized for proton CT

A typical proton CT (pCT) detector comprises a tracking system, used to measure the proton position before and after the imaged object, and an energy/range detector to measure the residual proton range after crossing the object. The Bergen pCT collaboration was established to design and build a prototype pCT scanner with a high granularity digital tracking calorimeter used as both tracking and energy/range detector. In this work the conceptual design and the layout of the mechanical and electronics implementation, along with Monte Carlo simulations of the new pCT system are reported. The digital tracking calorimeter is a multilayer structure with a lateral aperture of 27 cm × 16.6 cm, made of 41 detector/absorber sandwich layers (calorimeter), with aluminum (3.5 mm) used both as absorber and carrier, and two additional layers used as tracking system (rear trackers) positioned downstream of the imaged object; no tracking upstream the object is included. The rear tracker’s structure only differs from the calorimeter layers for the carrier made of ∼200 μm carbon fleece and carbon paper (carbon-epoxy sandwich), to minimize scattering. Each sensitive layer consists of 108 ALICE pixel detector (ALPIDE) chip sensors (developed for ALICE, CERN) bonded on a polyimide flex and subsequently bonded to a larger flexible printed circuit board. Beam tests tailored to the pCT operation have been performed using high-energetic (50–220 MeV/u) proton and ion beams at the Heidelberg Ion-Beam Therapy Center (HIT) in Germany. These tests proved the ALPIDE response independent of occupancy and proportional to the particle energy deposition, making the distinction of different ion tracks possible. The read-out electronics is able to handle enough data to acquire a single 2D image in few seconds making the system fast enough to be used in a clinical environment. For the reconstructed images in the modeled Monte Carlo simulation, the water equivalent path length error is lower than 2 mm, and the relative stopping power accuracy is better than 0.4%. Thanks to its ability to detect different types of radiation and its specific design, the pCT scanner can be employed for additional online applications during the treatment, such as in-situ proton range verification