A phenomenological model of proton FLASH oxygen depletion effects depending on tissue vasculature and oxygen supply

Introduction

Radiation-induced oxygen depletion in tissue is assumed as a contributor to the FLASH sparing effects. In this study, we simulated the heterogeneous oxygen depletion in the tissue surrounding the vessels and calculated the proton FLASH effective-dose-modifying factor (FEDMF), which could be used for biology-based treatment planning.

Methods

The dose and dose-weighted linear energy transfer (LET) of a small animal proton irradiator was simulated with Monte Carlo simulation. We deployed a parabolic partial differential equation to account for the generalized radiation oxygen depletion, tissue oxygen diffusion, and metabolic processes to investigate oxygen distribution in 1D, 2D, and 3D solution space. Dose and dose rates, particle LET, vasculature spacing, and blood oxygen supplies were considered. Using a similar framework for the hypoxic reduction factor (HRF) developed previously, the FEDMF was derived as the ratio of the cumulative normoxic-equivalent dose (CNED) between CONV and UHDR deliveries.

Results

Dynamic equilibrium between oxygen diffusion and tissue metabolism can result in tissue hypoxia. The hypoxic region displayed enhanced radio-resistance and resulted in lower CNED under UHDR deliveries. In 1D solution, comparing 15 Gy proton dose delivered at CONV 0.5 and UHDR 125 Gy/s, 61.5% of the tissue exhibited ≥20% FEDMF at 175 μm vasculature spacing and 18.9 μM boundary condition. This percentage reduced to 34.5% and 0% for 8 and 2 Gy deliveries, respectively. Similar trends were observed in the 3D solution space. The FLASH versus CONV differential effect remained at larger vasculature spacings. A higher FLASH dose rate showed an increased region with ≥20% FEDMF. A higher LET near the proton Bragg peak region did not appear to alter the FLASH effect.

Conclusion

We developed 1D, 2D, and 3D oxygen depletion simulation process to obtain the dynamic HRF and derive the proton FEDMF related to the dose delivery parameters and the local tissue vasculature information. The phenomenological model can be used to simulate or predict FLASH effects based on tissue vasculature and oxygen concentration data obtained from other experiments.

Current delivery limitations of proton PBS for FLASH

PURPOSE

Proton Pencil Beam Scanning (PBS) is an attractive solution to realize the advantageous normal tissue sparing elucidated from FLASH high dose rates. The mechanics of PBS spot delivery will impose limitations on the effective field dose rate for PBS.

METHODS

This study incorporates measurements from clinical and FLASH research beams on uniform single energy and the spread-out Bragg Peak PBS fields to extrapolate the PBS dose rate to high cyclotron beam currents 350, 500, and 800 nA. The impact of the effective field dose rate from cyclotron current, spot spacing, slew time and field size were studied.

RESULTS

When scanning magnet slew time and energy switching time are not considered, single energy effective field FLASH dose rate (≥40 Gy/s) can only be achieved with less than 4 × 4 cm² fields when the cyclotron output current is above 500 nA. Slew time and energy switching time remain the limiting factors for achieving high effective dose rate of the field. The dose rate-time structures were obtained. The amount of the total dose delivered at the FLASH dose rate in single energy layer and volumetric field was also studied.

CONCLUSION

It is demonstrated that while it is difficult to achieve FLASH dose rate for a large field or in a volume, local FLASH delivery to certain percentage of the total dose is possible. With further understanding of the FLASH radiobiological mechanism, this study could provide guidance to adapt current clinical multi-field proton PBS delivery practice for FLASH proton radiotherapy.

Tunneling resonances and coherence in an optical lattice

The center-of-mass quantization of atoms trapped in a gray optical lattice is observed to manifest itself in the steady-state properties of the atoms. Modulations in the lifetime and macroscopic magnetization as a function of an applied B field are attributed to quantum mechanical tunneling resonances and are shown to exist only under conditions which afford spatial coherence of the trapped atoms over several lattice wells and coherence times that exceed the tunneling period.

A comparative study of third-order nonlinear optical properties of silver phenylacetylide and related compounds via ultrafast optical Kerr effect measurements

A comparative study of the third-order nonlinear optical properties, via the newly developed heterodyned optical Kerr effect (OHD-OKE) measurements, of silver phenylacetylide and related compounds is reported. [AgC[triple bond]CC(6)H(5)](n) (1) was found to exhibit efficient third-order nonlinear optical susceptibility chi((3)) of 2.4 x 10(-14) esu, and second hyperpolarizability gamma of 9.07 x 10(-32) esu. These results are compared with those of two related silver phenylacetylide compounds, namely, a double salt, (silver phenylacetylide).(silver tert-butylthiolate) [AgC[triple bond]CC(6)H(5).AgS(t-C(4)H(9))](n) complex (2), and a cluster, triphenylphosphine silver phenylacetylide tetramer, [(C(6)H(5))(3)PAgC[triple bond]CC(6)H(5)](4) (3), as well as that of the related organic polymer polyphenylacetylene (4). These four compounds represent different types of phenylacetylide derivatives: 1 is an organometallic polymer, 2 a polymeric double salt, 3 a discrete metal cluster, and 4 an organic polymer. It was found that the third-order optical nonlinear response was enhanced by the incorporation of silver d electrons into the delocalized conjugated organic pi system, and its magnitude is highly dependent upon the extent of the pi delocalization. Specifically, the relative magnitudes of chi((3)) and gamma follow the order silver phenylacetylide polymer (1) > (silver phenylacetylide).(silver tert-butylthiolate) double salt (2) > polyphenylacetylene polymer (4) > tetrameric (triphenylphosphine silver phenylacetylide)(4) cluster (3). The observed trend may be attributed to the decreasing length of pi conjugation. It is interesting to note that the incorporation of Ag(I) into the polymeric framework of polyphenylacetylene enhances the chi((3)) by 25-fold for the same degree of polymerization (n = 7). The signs of chi((3)) and gamma, which are related to the response mechanisms, were found to be solvent dependent.

Synthesis and Structure of [DB24C8)Na][Cd(SCN)3. Formation of a novel linear Cd...Cd...Cd chain with a mer-CdN3S3 coordination confirmation and new coiled [(DB24C8)Na]+ cation

We report herein a novel coordination solid, [(DB24C8)Na][Cd(SCN)3] (6) (DB24C8 denotes dibenzo-24-crown-8), which exhibits a new type of [Cd(SCN)3-]infinity chain with two unusual stereochemical characteristics: (1) a mer-CdN3S3 coordination and (2) a linear Cd chain with a Cd...Cd...Cd angle of 180 degrees. In addition, the [(DB24C8)Na]+ monocation adopts a new structural type-a coiled structure-for the combination of crown ether DB24C8 and alkali metal Na+. The title compound crystallizes in a monoclinic unit cell of C2/c space group symmetry with lattice parameters a = 16.110(8) A, b = 20.380(5) A, c = 11.01(1) A, beta = 119.87(3) degrees, and Z = 4. The arrangement of the [Cd(SCN)3-](infinity) chains in the crystal lattice in the title compound is approximately hexagonal, creating triangular channels which are filled with [(DB24C8)Na]+ monocations. It was previously reasoned by us that the coiled [(DB24C8)Na]+ monocation, which lacks inversion or mirror symmetries, should enhance the tendency for the formation of the noncentrosymmetric space group of the title crystal, making it a potential second-order nonlinear optical crystal. Interestingly, however, the title compound crystallizes in a centrosymmetric space group (C2/c) and gives rise to no second harmonic generation (SHG). Previously known [Cd(SCN)3-](infinity) chains adopt fac-CdN3S3 coordination and a zigzag Cd chain configuration with a Cd...Cd...Cd angle of 165 degrees. The zigzag chains can align in either parallel or antiparallel fashion, resulting in efficient or no SHG effects, respectively. The linear Cd.Cd.Cd chain configuration observed in the title compound, on the other hand, makes it indistinguishable between parallel and antiparallel alignments. It is concluded that, to ensure the formation of noncentrosymmetric space groups, it is necessary to employ optically pure chiral cations as spacers and/or controllers. Furthermore, to enhance the nonlinear optical responses, [Cd(SCN)3-]infinity chains with fac-CdN3S3 coordination and parallel alignments of the zigzag Cd chains should be used.

Wide spectral range nonlinear optical crystals of one-dimensional coordination solids [Et4N][Cd(SCN)3] and [Et4N][Cd(SeCN)3] and the general design criteria for [R4N][Cd(XCN)3] (Where R = Alkyl and X = S, Se, Te) as NLO crystals

We report herein two new nonlinear optical (NLO) crystals, [Et4N][Cd(XCN)3], where X = S (1) and Se (2), that are transparent from 220 to 3300 nm, covering the entire near-ultraviolet, the visible, and the near-infrared spectral regions and giving rise to a very wide and continuous optical window, which is useful for many frequency conversion applications. Both 1 and 2 exhibit highly efficient second harmonic generation (SHG) as measured via the Kurtz-Perry method. The corresponding [Me4N]+ salts, [Me4N][Cd(XCN)3 where X = S (3) and Se (4), show no SHG effects. All four structures adopt noncentrosymmetric space groups (Cmc2(1) for 1 and 2 and Pna2(1) for 3 and presumably 4) and are based on one-dimensional anionic [Cd(XCN)3-] infinity zigzag chains. However, a detailed analysis of the structures of [R4N][Cd(XCN)3], where R = Et, Me and X = S, Se revealed that the difference in the second-order nonlinear responses of the Et4N+ salts (1 and 2) and the Me4N+ salts (3 and 4) is attributable to the relative alignment of the [Cd(XCN)3-] infinity zigzag chains, being parallel in the crystals of 1 and 2 but antiparallel in the crystals of 3 and 4. Also reported, for the first time, are the synthesis and crystal structure of [Et4N][Cd(SeCN)3] (2). Compound 2 crystallizes in an orthorhombic unit cell of Cmc21 space group symmetry with lattice parameters of 9.938(1) A, 16.868(2) A, 11.054(1) A, and Z = 4. Other issues related to the molecular and crystal engineering of this class of NLO materials are also discussed.

Characterization of organometallic coordinative cluster compounds of silver by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry

Matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOFMS) was successfully applied to characterize the organosilver coordinative cluster compounds, silver phenylacetylide and three silver thiolates, namely, silver tertiary butylthiolate, silver 2,6-dimethylbenzenethiolate, and silver 2, 6-dichlorobenzenethiolate. Samples and dithranol matrix were finely dispersed in 1:1 tetrahydrofuran (THF)/chloroform (CHCl(3)) mixed solvent. In most cases the monomer units remained intact during ionization, and the oligomeric molecular ions were produced through silver cationization, with a general molecular ion formula [nM + Ag](+). This was further verified by the relative abundances of the isotopic peaks within the molecular ion clusters, which were in close agreement with those theoretically calculated for nM cationized with one silver ion. In the case of silver 2, 6-dichlorobenzenethiolate, in addition to the dominant [nM + Ag](+) peaks, weak peaks corresponding to the successive losses of hydrogen chloride molecules were observed. Copyright 2000 John Wiley & Sons, Ltd.

Clusters of clusters: self-organization and self-similarity in the intermediate stages of cluster growth of Au-Ag supraclusters

A systematic structural investigation of a new series of high-nuclearity Au-Ag clusters containing 25, 37, 38, and 46 metal atoms led to the description of these clusters as "clusters of clusters" based on vertex-sharing icosahedra as building blocks. Based on the observed structures, a growth sequence is proposed here for the formation of these secondary clusters (clusters of clusters) from a single 13-atom icosahedron to a 127-atom icosahedron of icosahedra via successive additions of vertex-sharing icosahedral units. This cluster-of-clusters growth mechanism parallels the atom-by-atom growth pathway for the primary clusters from a single atom to a 13-atom icosahedron. It is hypothesized that the formation of these clusters of clusters is a manifestation of the spontaneous self-organization and self-similarity processes often observed in nature. It is conceivable that the concept of cluster of clusters may be important in the intermediate stages of some cluster growth as exemplified by the polyicosahedral growth of Au-Ag supraclusters.

Core dimensions in the 3Fe cluster of Desulfovibrio gigas ferredoxin II by extended X-ray absorption fine structure spectroscopy

We have obtained the iron K-edge extended X-ray adsorption fine structure spectra of the 3Fe ferredoxin II of Desulfovibrio gigas in the oxidized and reduced states. For both states, interpretation of the EXAFS data suggests that the Fe-S first shell coordination distance is near 2.25 A, in agreement with crystallographic studies of model compounds and proteins containing 2Fe-2S and 4Fe-4S centers, as well as with a recent crystallographic study of Azotobacter vinelandii ferredoxin I (Ghosh, D., Furey, W., Jr., O'Donnell, S., and Stout, C. D. (1981) J. Biol. Chem. 256, 4185-4192). The apparent Fe-Fe distance we obtain for the desulfovibrio protein (2.7 A) also agrees with similar distances seen in other Fe-S centers, except with the 3Fe cluster in the Azotobacter vinelandii ferredoxin I structure, for which an Fe-Fe distance of 4.2 A was reported. We conclude that either the two 3Fe ferredoxins have substantially different core dimensions, a possibility apparently unique to 3Fe centers among known Fe-S systems in proteins, or that one (or more) of the structural studies is in substantial error.