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.

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.

Social cognition as a mediator variable between neurocognition and functional outcome in schizophrenia: empirical review and new results by structural equation modeling

Cognitive impairments are currently regarded as important determinants of functional domains and are promising treatment goals in schizophrenia. Nevertheless, the exact nature of the interdependent relationship between neurocognition and social cognition as well as the relative contribution of each of these factors to adequate functioning remains unclear. The purpose of this article is to systematically review the findings and methodology of studies that have investigated social cognition as a mediator variable between neurocognitive performance and functional outcome in schizophrenia. Moreover, we carried out a study to evaluate this mediation hypothesis by the means of structural equation modeling in a large sample of 148 schizophrenia patients. The review comprised 15 studies. All but one study provided evidence for the mediating role of social cognition both in cross-sectional and in longitudinal designs. Other variables like motivation and social competence additionally mediated the relationship between social cognition and functional outcome. The mean effect size of the indirect effect was 0.20. However, social cognitive domains were differentially effective mediators. On average, 25% of the variance in functional outcome could be explained in the mediation model. The results of our own statistical analysis are in line with these conclusions: Social cognition mediated a significant indirect relationship between neurocognition and functional outcome. These results suggest that research should focus on differential mediation pathways. Future studies should also consider the interaction with other prognostic factors, additional mediators, and moderators in order to increase the predictive power and to target those factors relevant for optimizing therapy effects.

Differential healing response attributed to culprit lesions of patients with acute coronary syndromes and stable coronary artery after implantation of drug-eluting stents: An optical coherence tomography study

BACKGROUND Pathology studies have shown delayed arterial healing in culprit lesions of patients with acute coronary syndrome (ACS) compared with stable coronary artery disease (CAD) after placement of drug-eluting stents (DES). It is unknown whether similar differences exist in-vivo during long-term follow-up. Using optical coherence tomography (OCT), we assessed differences in arterial healing between patients with ACS and stable CAD five years after DES implantation. METHODS AND RESULTS A total of 88 patients comprised of 53 ACS lesions with 7864 struts and 35 stable lesions with 5298 struts were suitable for final OCT analysis five years after DES implantation. The analytical approach was based on a hierarchical Bayesian random-effects model. OCT endpoints were strut coverage, malapposition, protrusion, evaginations and cluster formation. Uncovered (1.7% vs. 0.7%, adjusted p=0.041) or protruding struts (0.50% vs. 0.13%, adjusted p=0.038) were more frequent among ACS compared with stable CAD lesions. A similar trend was observed for malapposed struts (1.33% vs. 0.45%, adj. p=0.072). Clusters of uncovered or malapposed/protruding struts were present in 34.0% of ACS and 14.1% of stable patients (adj. p=0.041). Coronary evaginations were more frequent in patients with ST-elevation myocardial infarction compared with stable CAD patients (0.16 vs. 0.13 per cross section, p=0.027). CONCLUSION Uncovered, malapposed, and protruding stent struts as well as clusters of delayed healing may be more frequent in culprit lesions of ACS compared with stable CAD patients late after DES implantation. Our observational findings suggest a differential healing response attributable to lesion characteristics of patients with ACS compared with stable CAD in-vivo.

Numerical solution of optimal control problems with constant control delays

We investigate a class of optimal control problems that exhibit constant exogenously given delays in the control in the equation of motion of the differential states. Therefore, we formulate an exemplary optimal control problem with one stock and one control variable and review some analytic properties of an optimal solution. However, analytical considerations are quite limited in case of delayed optimal control problems. In order to overcome these limits, we reformulate the problem and apply direct numerical methods to calculate approximate solutions that give a better understanding of this class of optimization problems. In particular, we present two possibilities to reformulate the delayed optimal control problem into an instantaneous optimal control problem and show how these can be solved numerically with a stateof- the-art direct method by applying Bock’s direct multiple shooting algorithm. We further demonstrate the strength of our approach by two economic examples.

[Meningitis (I)--differential diagnosis; aseptic and chronic meningitis].

Meningitis is the most common serious manifestation of infection of the central nervous system. Inflammatory involvement of the subarachnoid space with meningeal irritation leads to the classical triad of headache, fever, and meningism, and to a pleocytosis of the cerebrospinal fluid (CSF). Meningitis is clinically categorized into an acute and chronic disease based on the acuity of symptoms. Acute meningitis develops over hours to days, while in chronic meningitis symptoms evolve over days or even weeks. Aseptic meningitis, in which no bacterial pathogen can be isolated by routine cultures, can mimic bacterial meningitis, but the disease has a much more favorable prognosis. Many cases of aseptic meningitis are caused by viruses, primarily enteroviruses, but bacteria and noninfectious etiologies also cause meningitis with negative cultures. Symptoms of meningeal inflammation with CSF pleocytosis that persist for more than 4 weeks define the chronic meningitis syndrome. The diagnosis is based on the patient history, clinical evidence of meningitis, CSF examination, and often imaging studies. The differential diagnosis is broad, and the predominant CSF cell type can provide clues as to the underlying disease. Empiric therapy is primarily based on the age of the patient, with modifications if there are positive findings on CSF gram stain or if the patient presents with special risk factors. In patients with chronic meningitis, a definite diagnosis is often not available or delayed for days, in which case empiric therapy may have to be initiated. It is important to cover the treatable causes of meningitis, for which the outcome is poor if treatment is delayed.