Coupling biomechanics to a cellular level model: An approach to patient-specific image driven multi-scale and multi-physics tumor simulation

Modeling of tumor growth has been performed according to various approaches addressing different biocomplexity levels and spatiotemporal scales. Mathematical treatments range from partial differential equation based diffusion models to rule-based cellular level simulators, aiming at both improving our quantitative understanding of the underlying biological processes and, in the mid- and long term, constructing reliable multi-scale predictive platforms to support patient-individualized treatment planning and optimization. The aim of this paper is to establish a multi-scale and multi-physics approach to tumor modeling taking into account both the cellular and the macroscopic mechanical level. Therefore, an already developed biomodel of clinical tumor growth and response to treatment is self-consistently coupled with a biomechanical model. Results are presented for the free growth case of the imageable component of an initially point-like glioblastoma multiforme tumor. The composite model leads to significant tumor shape corrections that are achieved through the utilization of environmental pressure information and the application of biomechanical principles. Using the ratio of smallest to largest moment of inertia of the tumor material to quantify the effect of our coupled approach, we have found a tumor shape correction of 20\% by coupling biomechanics to the cellular simulator as compared to a cellular simulation without preferred growth directions. We conclude that the integration of the two models provides additional morphological insight into realistic tumor growth behavior. Therefore, it might be used for the development of an advanced oncosimulator focusing on tumor types for which morphology plays an important role in surgical and/or radio-therapeutic treatment planning.

Theoretical considerations to the verification of dynamic multileaf collimated fields with a SLIC-type portal image detector

The verification possibilities of dynamically collimated treatment beams with a scanning liquid ionization chamber electronic portal image device (SLIC-EPID) are investigated. The ion concentration in the liquid of a SLIC-EPID and therefore the read-out signal is determined by two parameters of a differential equation describing the creation and recombination of the ions. Due to the form of this equation, the portal image detector describes a nonlinear dynamic system with memory. In this work, the parameters of the differential equation were experimentally determined for the particular chamber in use and for an incident open 6 MV photon beam. The mathematical description of the ion concentration was then used to predict portal images of intensity-modulated photon beams produced by a dynamic delivery technique, the sliding window approach. Due to the nature of the differential equation, a mathematical condition for 'reliable leaf motion verification' in the sliding window technique can be formulated. It is shown that the time constants for both formation and decay of the equilibrium concentration in the chamber is in the order of seconds. In order to guarantee reliable leaf motion verification, these time constants impose a constraint on the rapidity of the image-read out for a given maximum leaf speed. For a leaf speed of 2 cm s(-1), a minimum image acquisition frequency of about 2 Hz is required. Current SLIC-EPID systems are usually too slow since they need about a second to acquire a portal image. However, if the condition is fulfilled, the memory property of the system can be used to reconstruct the leaf motion. It is shown that a simple edge detecting algorithm can be employed to determine the leaf positions. The method is also very robust against image noise.

Comparative theoretical analysis of continuous wave laser cutting of metals at 1 and 10 um wavelength

We present a derivation and, based on it, an extension of a model originally proposed by V.G. Niziev to describe continuous wave laser cutting of metals. Starting from a local energy balance and by incorporating heat removal through heat conduction to the bulk material, we find a differential equation for the cutting profile. This equation is solved numerically and yields, besides the cutting profiles, the maximum cutting speed, the absorptivity profiles, and other relevant quantities. Our main goal is to demonstrate the model’s capability to explain some of the experimentally observed differences between laser cutting at around 1 and 10 μm wavelengths. To compare our numerical results to experimental observations, we perform simulations for exactly the same material and laser beam parameters as those used in a recent comparative experimental study. Generally, we find good agreement between theoretical and experimental results and show that the main differences between laser cutting with 1- and 10-μm beams arise from the different absorptivity profiles and absorbed intensities. Especially the latter suggests that the energy transfer, and thus the laser cutting process, is more efficient in the case of laser cutting with 1-μm beams.

Using the theory of planned behaviour to model antecedents of surgical checklist use: a cross-sectional study.

BACKGROUND Compliance with surgical checklist use remains an obstacle in the context of checklist implementation programs. The theory of planned behaviour was applied to analyse attitudes, perceived behaviour control, and norms as psychological antecedents of individuals' intentions to use the checklist. METHODS A cross-sectional survey study with staff (N = 866) of 10 Swiss hospitals was conducted in German and French. Group mean differences between individuals with and without managerial function were computed. Structural equation modelling and confirmatory factor analysis was applied to investigate the structural relation between attitudes, perceived behaviour control, norms, and intentions. RESULTS Significant mean differences in favour of individuals with managerial function emerged for norms, perceived behavioural control, and intentions, but not for attitudes. Attitudes and perceived behavioural control had a significant direct effect on intentions whereas norms had not. CONCLUSIONS Individuals with managerial function exhibit stronger perceived behavioural control, stronger norms, and stronger intentions. This could be applied in facilitating checklist implementation. The structural model of the theory of planned behaviour remains stable across groups, indicating a valid model to describe antecedents of intentions in the context of surgical checklist implementation.

Optimized CUDA-Based PDE Solver for Reaction Diffusion Systems on Arbitrary Surfaces

Partial differential equation (PDE) solvers are commonly employed to study and characterize the parameter space for reaction-diffusion (RD) systems while investigating biological pattern formation. Increasingly, biologists wish to perform such studies with arbitrary surfaces representing ‘real’ 3D geometries for better insights. In this paper, we present a highly optimized CUDA-based solver for RD equations on triangulated meshes in 3D. We demonstrate our solver using a chemotactic model that can be used to study snakeskin pigmentation, for example. We employ a finite element based approach to perform explicit Euler time integrations. We compare our approach to a naive GPU implementation and provide an in-depth performance analysis, demonstrating the significant speedup afforded by our optimizations. The optimization strategies that we exploit could be generalized to other mesh based processing applications with PDE simulations.

Solution of the relativistic Schrödinger equation for the δ ′ -Function potential in one dimension using cutoff regularization

We study the relativistic version of the Schrödinger equation for a point particle in one dimension with the potential of the first derivative of the delta function. The momentum cutoff regularization is used to study the bound state and scattering states. The initial calculations show that the reciprocal of the bare coupling constant is ultraviolet divergent, and the resultant expression cannot be renormalized in the usual sense, where the divergent terms can just be omitted. Therefore, a general procedure has been developed to derive different physical properties of the system. The procedure is used first in the nonrelativistic case for the purpose of clarification and comparisons. For the relativistic case, the results show that this system behaves exactly like the delta function potential, which means that this system also shares features with quantum filed theories, like being asymptotically free. In addition, in the massless limit, it undergoes dimensional transmutation, and it possesses an infrared conformal fixed point. The comparison of the solution with the relativistic delta function potential solution shows evidence of universality.