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

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data

Towards Neural Charged Particle Tracking in Digital Tracking Calorimeters with Reinforcement Learning

We propose a novel reconstruction scheme for reconstructing charged particles in digital tracking calorimeters using model-free reinforcement learning aiming to benefit from the rapid progress and success of neural network architectures for tracking without the dependency on simulated or manually labeled data. Here we optimize by trial-and-error a behavior policy acting as a heuristic approximation to the full combinatorial optimization problem, maximizing the physical plausibility of sampled trajectories. In modern data processing pipelines used in high energy physics experiments and related high energy physics driven applications tracking plays an essential role allowing to identify and follow charged particle trajectories traversing particle detectors. Due to the usual high multiplicity of charged particles as well as the occurring physical interactions, randomly deflecting the particles from their initial path, the reconstruction is a challenging undertaking, requiring fast, accurate and robust algorithms. Our approach works on graph-structured data, capturing possible track hypotheses through edge connections between particles in the sensitive detector layers. We demonstrate in a comprehensive study on simulated data generated for a particle detector used for proton computed tomography, the overall high potential as well as the competitiveness of our approach compared to a heuristic search algorithm and a model trained on ground truth information. Finally, we point out limitations of our approach, guiding towards a robust foundation for further development of reinforcement learning based tracking algorithms in high energy physics.</p

An interplay between the spin density distribution and magnetic superexchange interactions: a case study of mononuclear [nBu4N]2[Cu(opooMe)] and novel asymmetric trinuclear [Cu3(opooMe)(pmdta)2](NO3)2·3MeCN

Treatment of the diethyl ester of o-phenylenebis(oxamic acid) (opbaH2Et2, 1) with 5/6 equivalent of MeNH2 in abs. EtOH results in the exclusive formation of the ethyl ester of o-phenylene(N′-methyl oxamide)(oxamic acid) (opooH3EtMe, 2) in ca. 50% yield. Treatment of 2 with four equivalents of [Me4N]OH followed by the addition of Cu(ClO4)2·6H2O gave [Me4N]2[Cu(opooMe)]·H2O (3A) in ca. 80% yield. As 3A appears to be a hygroscopic solid, the related [nBu4N]+ salts [nBu4N]2[M(opooMe)]·H2O (M = Cu (3B), Ni (4)) have been synthesized. By addition of two equivalents of [Cu(pmdta)(NO3)2] to a MeCN solution of 3B the novel asymmetric trinuclear complex [Cu3(opooMe)(pmdta)2](NO3)2 (5) could be obtained in ca. 90% yield. Compounds 2, 3A, 3B, 4 and 5 have been characterized by elemental analysis and NMR/IR spectroscopy. Furthermore, the solid state structures of 3A in the form of [Me4N]2[Cu(opooMe)]·MeOH (3A′), 3B in the form of [nBu4N]2[Cu(opooMe)] (3B′), 4 in the form of [nBu4N]2[Ni(opooMe)]·1.25H2O (4′) and 5 in the form of [Cu3(opooMe)(pmdta)2] (NO3)2·3MeCN (5′), respectively, have been determined by single-crystal X-ray diffraction studies. By controlled cocrystallization, diamagnetically diluted 3B (1%) in the host lattice of 4 (99%) in the form of single crystals have been made available, allowing single crystal EPR studies to extract all components of the g-factor and the tensors of onsite CuA and transferred NA hyperfine interaction. Out of these studies the spin density distribution of the [Cu(opooMe)]2− complex fragment could be determined. The magnetic properties of 5 were studied by susceptibility measurements versus temperature. An intramolecular J parameter of −65 cm−1 has been obtained, unexpectedly, as 5 should possess two different J values due to its two different spacers between the adjacent CuII ions, namely an oxamate (C2NO3) and an oxamidate (C2N2O2) fragment. This unexpected result is explained by a summarizing discussion of the experimentally obtained EPR results (spin density distribution) of 3B, the geometries of the terminal [Cu(pmdta)]2+ fragments of 5 determined by X-ray crystallographic studies and accompanying quantum chemical calculations of the spin density distribution of the mononuclear [Cu(opooMe)]2− and of the magnetic exchange interactions of trinuclear [Cu3(opooMe)(pmdta)2]2+ complex fragments.Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich

Magnetic superexchange interactions: Trinuclear bis(oxamidato) versus bis(oxamato) type complexes

The diethyl ester of o-phenylenebis(oxamic acid) (opbaH2Et2) was treated with an excess of RNH2 in MeOH to cause the exclusive formation of the respective o-phenylenebis(N(R)-oxamides) (opboH4R2, R = Me 1, Et 2, nPr 3) in good yields. Treatment of 1–3 with half an equivalent of [Cu2(AcO)4(H2O)2] or one equivalent of [Ni(AcO)2(H2O)4] followed by the addition of four equivalents of [nBu4N]OH resulted in the formation of mononuclear bis(oxamidato) type complexes [nBu4N]2[M(opboR2)] (M = Ni, R = Me 4, Et 5, nPr 6; M = Cu, R = Me 7, Et 8, nPr 9). By addition of two equivalents of [Cu(pmdta)(NO3)2] to MeCN solutions of 7–9, novel trinuclear complexes [Cu3(opboR2)(L)2](NO3)2 (L = pmdta, R = Me 10, Et 11, nPr 12) could be obtained. Compounds 4–12 have been characterized by elemental analysis and NMR/IR spectroscopy. Furthermore, the solid state structures of 4–10 and 12 have been determined by single-crystal X-ray diffraction studies. By controlled cocrystallization, diamagnetically diluted 8 and 9 (1%) in the host lattice of 5 and 6 (99%) (8@5 and 9@6), respectively, in the form of single crystals have been made available, allowing single crystal ESR studies to extract all components of the g-factor and the tensors of onsite CuA and transferred NA hyperfine (HF) interaction. From these studies, the spin density distribution of the [Cu(opboEt2)]2− and [Cu(opbonPr2)]2− complex fragments of 8 and 9, respectively, could be determined. Additionally, as a single crystal ENDOR measurement of 8@5 revealed the individual HF tensors of the N donor atoms to be unequal, individual estimates of the spin densities on each N donor atom were made. The magnetic properties of 10–12 were studied by susceptibility measurements versus temperature to give J values varying from −96 cm−1 (10) over −104 cm−1 (11) to −132 cm−1 (12). These three trinuclear CuII-containing bis(oxamidato) type complexes exhibit J values which are comparable to and slightly larger in magnitude than those of related bis(oxamato) type complexes. In a summarizing discussion involving experimentally obtained ESR results (spin density distribution) of 8 and 9, the geometries of the terminal [Cu(pmdta)]2+ fragments of 12 determined by crystallographic studies, together with accompanying quantum chemical calculations, an approach is derived to explain these phenomena and to conclude if the spin density distribution of mononuclear bis(oxamato)/bis(oxamidato) type complexes could be a measure of the J couplings of corresponding trinuclear complexes

Magnetic superexchange interactions: trinuclear bis(oxamidato) versus bis(oxamato) type complexes

The diethyl ester of o-phenylenebis(oxamic acid) (opbaH2Et2) was treated with an excess of RNH2 in MeOH to cause the exclusive formation of the respective o-phenylenebis(N(R)-oxamides) (opboH4R2, R = Me 1, Et 2, nPr 3) in good yields. Treatment of 1–3 with half an equivalent of [Cu2(AcO)4(H2O)2] or one equivalent of [Ni(AcO)2(H2O)4] followed by the addition of four equivalents of [nBu4N]OH resulted in the formation of mononuclear bis(oxamidato) type complexes [nBu4N]2[M(opboR2)] (M = Ni, R = Me 4, Et 5, nPr 6; M = Cu, R = Me 7, Et 8, nPr 9). By addition of two equivalents of [Cu(pmdta)(NO3)2] to MeCN solutions of 7–9, novel trinuclear complexes [Cu3(opboR2)(L)2](NO3)2 (L = pmdta, R = Me 10, Et 11, nPr 12) could be obtained. Compounds 4–12 have been characterized by elemental analysis and NMR/IR spectroscopy. Furthermore, the solid state structures of 4–10 and 12 have been determined by single-crystal X-ray diffraction studies. By controlled cocrystallization, diamagnetically diluted 8 and 9 (1%) in the host lattice of 5 and 6 (99%) (8@5 and 9@6), respectively, in the form of single crystals have been made available, allowing single crystal ESR studies to extract all components of the g-factor and the tensors of onsite CuA and transferred NA hyperfine (HF) interaction. From these studies, the spin density distribution of the [Cu(opboEt2)]2− and [Cu(opbonPr2)]2− complex fragments of 8 and 9, respectively, could be determined. Additionally, as a single crystal ENDOR measurement of 8@5 revealed the individual HF tensors of the N donor atoms to be unequal, individual estimates of the spin densities on each N donor atom were made. The magnetic properties of 10–12 were studied by susceptibility measurements versus temperature to give J values varying from −96 cm−1 (10) over −104 cm−1 (11) to −132 cm−1 (12). These three trinuclear CuII-containing bis(oxamidato) type complexes exhibit J values which are comparable to and slightly larger in magnitude than those of related bis(oxamato) type complexes. In a summarizing discussion involving experimentally obtained ESR results (spin density distribution) of 8 and 9, the geometries of the terminal [Cu(pmdta)]2+ fragments of 12 determined by crystallographic studies, together with accompanying quantum chemical calculations, an approach is derived to explain these phenomena and to conclude if the spin density distribution of mononuclear bis(oxamato)/bis(oxamidato) type complexes could be a measure of the J couplings of corresponding trinuclear complexes.Dieser Beitrag ist aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich

Redox-Active Ferrocene as a Tuning Functionality for Magnetic Superexchange Interactions of Bis(oxamato) Type Complexes

The reaction of 1,1′-diaminoferrocene with two equivalents of ethyloxalyl chloride in THF afforded the diethyl ester of <i>N,N</i>′-ferrocenylenebis­(oxamic acid) (1,1′-fcbaH₂Et₂, <b>1</b>). <b>1</b> was converted readily to its saponificated form only, namely [^<i>n</i>Bu₄N]₂[(1,1′-fcbaH₂)] (<b>2</b>), when treated with 4 equiv of [^<i>n</i>Bu₄N]­OH followed by the subsequent addition of [Ni­(H₂O)₆]­Cl₂, whereas [^<i>n</i>Bu₄N]₂[Cu­(1,1′-fcba)] (<b>3</b>) was obtained in ca. 70% yield by using CuCl₂·2H₂O. Oxidation of <b>3</b> with I₂ led to the formation of [^<i>n</i>Bu₄N]­[Cu­(1,1′-fcba)] (<b>4</b>). A combined study of <b>4</b> by ESR and ⁵⁷Fe Mössbauer spectroscopy, supported by DFT calculations, revealed the iron atom of <b>4</b> to possess the oxidation state +3. Treatment of <b>1</b> with MeNH₂ resulted in the exclusive formation of the methyl ester of ferrocenylene-1-(<i>N</i>-methyloxamide)-1′-(oxamic acid) (1,1′-fcooH₃Me₂, <b>5</b>). Successive treatment of <b>5</b> with [Cu₂(OAc)₄(H₂O)₂] and [^<i>n</i>Bu₄N]­OH gave rise to the formation of [^<i>n</i>Bu₄N]₂[Cu­(fcooMe)]·2H₂O (<b>6A</b>·2H₂O and <b>6B</b>·2H₂O), for which single crystals of the compositions [^<i>n</i>Bu₄N]₂[Cu­(1,1′-fcooMe)]·¹/₂MeOH·¹/₂H₂O (<b>6A</b>·¹/₂MeOH·¹/₂H₂O) and [^<i>n</i>Bu₄N]₂[Cu­(1,1′-fcooMe)]·2.25H₂O (<b>6B</b>·2.25H₂O) were grown. Single-crystal X-ray diffraction studies revealed <b>6A</b>·¹/₂MeOH·¹/₂H₂O and <b>6B</b>·2.25H₂O to contain [Cu­(fcooMe)]^2– fragments in the form of two different conformers, having a significant difference in their total energy, as found by DFT calculations. Treatment of <b>3</b> and <b>4</b>, respectively, with [Cu­(pmdta)­(NO₃)₂] afforded the tetranuclear complexes [Cu₃(1,1′-fcba)­(pmdta)₂]­(NO₃)_<i>n</i> (<i>n</i> = 2 (<b>7</b>), 3 (<b>8</b>)). The solid-state structures of <b>1</b>–<b>3</b>, <b>7</b>, and <b>8</b> were determined by single-crystal X-ray diffraction studies. The magnetic properties of <b>3</b>, <b>4</b>, <b>7</b>, and <b>8</b> were studied by susceptibility measurements versus temperature. For <b>4</b> a weak antiferromagnetic coupling between the Cu^II and Fe^III ions has been obtained with <i>J</i> = −2 cm^–1, whereas <b>3</b> can be understood as a purely paramagnetic, Cu^II/Fe^II-containing complex only. For <b>7</b> a <i>J</i> parameter of −58 cm^–1 has been obtained due to an antiferromagnetic interaction between its Cu^II ions. This magnetic exchange interaction modifies in <b>8</b> to −64 cm^–1, and an additional ferromagnetic coupling of 4 cm^–1 between the Fe^III ion and the central Cu^II ion is obtained

Redox-Active Ferrocene as a Tuning Functionality for Magnetic Superexchange Interactions of Bis(oxamato) Type Complexes

The reaction of 1,1′-diaminoferrocene with two equivalents of ethyloxalyl chloride in THF afforded the diethyl ester of <i>N,N</i>′-ferrocenylenebis­(oxamic acid) (1,1′-fcbaH₂Et₂, <b>1</b>). <b>1</b> was converted readily to its saponificated form only, namely [^<i>n</i>Bu₄N]₂[(1,1′-fcbaH₂)] (<b>2</b>), when treated with 4 equiv of [^<i>n</i>Bu₄N]­OH followed by the subsequent addition of [Ni­(H₂O)₆]­Cl₂, whereas [^<i>n</i>Bu₄N]₂[Cu­(1,1′-fcba)] (<b>3</b>) was obtained in ca. 70% yield by using CuCl₂·2H₂O. Oxidation of <b>3</b> with I₂ led to the formation of [^<i>n</i>Bu₄N]­[Cu­(1,1′-fcba)] (<b>4</b>). A combined study of <b>4</b> by ESR and ⁵⁷Fe Mössbauer spectroscopy, supported by DFT calculations, revealed the iron atom of <b>4</b> to possess the oxidation state +3. Treatment of <b>1</b> with MeNH₂ resulted in the exclusive formation of the methyl ester of ferrocenylene-1-(<i>N</i>-methyloxamide)-1′-(oxamic acid) (1,1′-fcooH₃Me₂, <b>5</b>). Successive treatment of <b>5</b> with [Cu₂(OAc)₄(H₂O)₂] and [^<i>n</i>Bu₄N]­OH gave rise to the formation of [^<i>n</i>Bu₄N]₂[Cu­(fcooMe)]·2H₂O (<b>6A</b>·2H₂O and <b>6B</b>·2H₂O), for which single crystals of the compositions [^<i>n</i>Bu₄N]₂[Cu­(1,1′-fcooMe)]·¹/₂MeOH·¹/₂H₂O (<b>6A</b>·¹/₂MeOH·¹/₂H₂O) and [^<i>n</i>Bu₄N]₂[Cu­(1,1′-fcooMe)]·2.25H₂O (<b>6B</b>·2.25H₂O) were grown. Single-crystal X-ray diffraction studies revealed <b>6A</b>·¹/₂MeOH·¹/₂H₂O and <b>6B</b>·2.25H₂O to contain [Cu­(fcooMe)]^2– fragments in the form of two different conformers, having a significant difference in their total energy, as found by DFT calculations. Treatment of <b>3</b> and <b>4</b>, respectively, with [Cu­(pmdta)­(NO₃)₂] afforded the tetranuclear complexes [Cu₃(1,1′-fcba)­(pmdta)₂]­(NO₃)_<i>n</i> (<i>n</i> = 2 (<b>7</b>), 3 (<b>8</b>)). The solid-state structures of <b>1</b>–<b>3</b>, <b>7</b>, and <b>8</b> were determined by single-crystal X-ray diffraction studies. The magnetic properties of <b>3</b>, <b>4</b>, <b>7</b>, and <b>8</b> were studied by susceptibility measurements versus temperature. For <b>4</b> a weak antiferromagnetic coupling between the Cu^II and Fe^III ions has been obtained with <i>J</i> = −2 cm^–1, whereas <b>3</b> can be understood as a purely paramagnetic, Cu^II/Fe^II-containing complex only. For <b>7</b> a <i>J</i> parameter of −58 cm^–1 has been obtained due to an antiferromagnetic interaction between its Cu^II ions. This magnetic exchange interaction modifies in <b>8</b> to −64 cm^–1, and an additional ferromagnetic coupling of 4 cm^–1 between the Fe^III ion and the central Cu^II ion is obtained