Empirical modeling of the percent depth dose for megavoltage photon beams

Introduction This study presents an empirical method to model the high-energy photon beam percent depth dose (PDD) curve by using the home-generated buildup function and tail function (buildup-tail function) in radiation therapy. The modeling parameters n and μ of buildup-tail function can be used to characterize the Collimator Scatter Factor (Sc) either in a square field or in the different individual upper jaw and lower jaw setting separately for individual monitor unit check. Methods and materials The PDD curves for four high-energy photon beams were modeled by the buildup and tail function in this study. The buildup function was a quadratic function in the form of dd2+n with the main parameter of d (depth in water) and n, while the tail function was in the form of e−μd and was composed by an exponential function with the main parameter of d and μ. The PDD was the product of buildup and tail function, PDD = dd2+n·e−μd. The PDD of four-photon energies was characterized by the buildup-tail function by adjusting the parameters n and μ. The Sc of 6 MV and 10 MV can then be expressed simply by the modeling parameters n and μ. Results The main parameters n increases in buildup-tail function when photon energy increased. The physical meaning of the parameter n expresses the beam hardening of photon energy in PDD. The fitting results of parameters n in the buildup function are 0.17, 0.208, 0.495, 1.2 of four-photon energies, 4 MV, 6 MV, 10 MV, 18 MV, respectively. The parameter μ can be treated as attenuation coefficient in tail function and decreases when photon energy increased. The fitting results of parameters μ in the tail function are 0.065, 0.0515, 0.0458, 0.0422 of four-photon energies, 4 MV, 6 MV, 10 MV, 18 MV, respectively. The values of n and μ obtained from the fitted buildup-tail function were applied into an analytical formula of Sc = nE(S)0.63μE to get the collimator to scatter factor Sc for 6 and 10 MV photon beam, while nE, μE, S denotes n, μ at photon energy E of field size S, respectively. The calculated Sc were compared with the measured data and showed agreement at different field sizes to within ±1.5%. Conclusions We proposed a model incorporating a two-parameter formula which can improve the fitting accuracy to be better than 1.5% maximum error for describing the PDD in different photon energies used in clinical setting. This model can be used to parameterize the Sc factors for some clinical requirements. The modeling parameters n and μ can be used to predict the Sc in either square field or individual jaws opening asymmetrically for treatment monitor unit double-check in dose calculation. The technique developed in this study can also be used for systematic or random errors in the QA program, thus improves the clinical dose computation accuracy for patient treatment.

Empirical method for modeling the percent depth dose curves of electron beam in radiation therapy

Introduction: This study presents an empirical method to model the electron beam percent depth dose curve (PDD) using the primary and tail functions in radiation therapy. The modeling parameters N and n can be used to derive the depth relative stopping power of the electron energy in radiation therapy. Methods and Materials: The electrons PDD curves were modeled with the primary-tail function in this study. The primary function included exponential function and main parameters of N, µ while the tail function was composed by a sigmoid function with the main parameter of n. The PDD for five electron energies were modeled by the primary and tail function by adjusting the parameters of N, µ and n. The R50 and Rp can be derived from the modeled straight line of 80% to 20% region of PDD. The same electron energy with different cone sizes was also modeled with the primary-tail function. The stopping power for different electron energies at different depths can also be derived from the parameters of N, µ and n. Percent ionization depth curve can then be derived from the percent depth dose by dividing its depth relevant stopping power for comparing with the original water phantom measurement. Results: The main parameters N, n increase, but µ decreases in primary-tail function when electron energy increased. The relationship of parameters n, N and LN(-µ) with electron energy are n = 31.667 E0 - 88, N = 0.9975 E0 - 2.8535, LN(-µ) = -0.1355 E0 - 6.0986, respectively. Stopping power of different electron energy can be derived from n and N with the equation: stopping power = (−0.042 ln N E 0 + 1.072)e(−n−E0·5·10−5+0.0381·d), where d is the depth in water. Percent depth dose was derived from the percent reading curve by multiplying the stopping power relevant to the depth in water at certain electron energy. Conclusion: The PDD of electrons at different energies and field sizes can be modeled with an empirical model to deal with the stopping power calculation. The primary-tail equation provides a uncomplicated solution than a pencil beam or other numerical algorism for investigators to research the behavior of electron beam in radiation therapy.

Comparative and functional morphology of chevron bones among mammals

Tail morphology and function vary considerably across mammals. While studies of the mammalian tail have paid increasing attention to the caudal vertebrae, the chevron bones, ventrally positioned elements that articulate with the caudal vertebrae of most species and that serve to protect blood vessels and provide attachment sites for tail flexor musculature, have largely been ignored. Here, morphological variation in chevron bones is documented systematically among mammals possessing different tail locomotor functions, including prehensility, terrestrial propulsion (use for pentapedal locomotion), and postural prop, during which chevron bones are presumably under different mechanical stresses or serve different mechanical roles. Several chevron bone morphotypes were identified along the tail, varying both within and between tail regions. While some morphotypes were present across many or all clades surveyed, other morphotypes were clade-specific. Chevron bone dorsoventral height was examined at key vertebral levels among closely related species with different tail locomotor functions to assess whether variation followed any functional patterns. Dorsoventral height of chevron bones differed between prehensile- and nonprehensile-tailed, prop-tailed and nonprop-tailed, and pentapedal and nonpentapedal mammals. However, small sample sizes precluded rigorous statistical analyses. Distinctions were also qualified among species (not grouped by tail locomotor function), and the utility of metrics for quantifying specific aspects of chevron bone anatomy is discussed. This study offers information about the functional morphology of mammalian tails and has implications for reconstructing tail function in the fossil record.

3D Simulation Investigating ZnO NWFET Characteristics

3D Simulation was carried out and compared with fabricated ZnO NWFET. The device had the following electrical output characteristics: mobility value of 10.0 cm2/Vs at a drain voltage of 1.0 V, threshold voltage of 24 V, and subthreshold slope (SS) of 1500 mV/decade. The simulation showed that the device output results are influenced by two main issues: (i) contact resistance (Rcon ≈ 11.3 MΩ) and (ii) interface state trapped charge number density (QIT = 3.79 x 1015 cm-2). The QIT was derived from the Gaussian distribution that depends on two parameters added together. These parameters are: an acceptor-like exponential band tail function gGA(E) and an acceptor-like Gaussian deep state function gTA(E). By de-embedding the contact resistance, the simulation is able to improve the device by producing excellent field effect mobility of 126.9 cm2/Vs.

Flexibility of Heterocercal Tails: What Can the Functional Morphology of Shark Tails Tell Us about Ichthyosaur Swimming?

Synopsis The similarities between ichthyosaurs and sharks are a text-book example of convergence, and similarities in tail morphology have led many to theorize that they had similar swimming styles. The variation of ichthyosaur tail shapes is encompassed within the diversity of shark families. In particular early ichthyosaurs have asymmetrical tails like the heterocercal tails of carcharhinid sharks, while later occurring ichthyosaurs have lunate tails similar to those of lamnid sharks. Because it is not possible to measure ichthyosaur tail function, the goal of this study is to measure and compare the flexibility and stiffness of lunate and heterocercal shark tails, and to measure skeletal and connective tissue features that may affect tail flexibility. We measured flexibility in 10 species and focused on five species in particular, for dissection: one pelagic and one bottom-associated individual from each order, plus the common thresher shark (Alopias vulpinus), a tail-slapping specialist. As expected, lunate tails were overall less flexible than heterocercal tails and had greater flexural stiffness. Our results suggest that the cross-sectional profile of the skeletally supported dorsal lobe dictates flexural stiffness, but that changing tissue composition dictates flexural stiffness in the ventral lobe. We also found structural differences that may enable the tail slapping behavior of the common thresher shark. Finally, we discuss how our morphological measurements compare to ichthyosaur measurements from the literature; noting that similarities in functional morphology suggest sharks may be a good analog for understanding ichthyosaur swimming biomechanics.