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.

Ventricular-arterial coupling in a rat model of reduced arterial compliance provoked by hypervitaminosis D and nicotine

The vitamin D(3) and nicotine (VDN) model is one of isolated systolic hypertension (ISH) in which arterial calcification raises arterial stiffness and vascular impedance. The effects of VDN treatment on arterial and cardiac hemodynamics have been investigated; however, a complete analysis of ventricular-arterial interaction is lacking. Wistar rats were treated with VDN (VDN group, n = 9), and a control group (n = 10) was included without the VDN. At week 8, invasive indexes of cardiac function were obtained using a conductance catheter. Simultaneously, aortic pressure and flow were measured to derive vascular impedance and characterize ventricular-vascular interaction. VDN caused significant increases in systolic (138 +/- 6 vs. 116 +/- 13 mmHg, P < 0.01) and pulse (42 +/- 10 vs. 26 +/- 4 mmHg, P < 0.01) pressures with respect to control. Total arterial compliance decreased (0.12 +/- 0.08 vs. 0.21 +/- 0.04 ml/mmHg in control, P < 0.05), and pulse wave velocity increased significantly (8.8 +/- 2.5 vs. 5.1 +/- 2.0 m/s in control, P < 0.05). The arterial elastance and end-systolic elastance rose significantly in the VDN group (P < 0.05). Wave reflection was augmented in the VDN group, as reflected by the increase in the wave reflection coefficient (0.63 +/- 0.06 vs. 0.52 +/- 0.05 in control, P < 0.05) and the amplitude of the reflected pressure wave (13.3 +/- 3.1 vs. 8.4 +/- 1.0 mmHg in control, P < 0.05). We studied ventricular-arterial coupling in a VDN-induced rat model of reduced arterial compliance. The VDN treatment led to development of ISH and provoked alterations in cardiac function, arterial impedance, arterial function, and ventricular-arterial interaction, which in many aspects are similar to effects of an aged and stiffened arterial tree.

Intermittent spike-wave dynamics in a heterogeneous, spatially extended neural mass model

Generalised epileptic seizures are frequently accompanied by sudden, reversible transitions from low amplitude, irregular background activity to high amplitude, regular spike-wave discharges (SWD) in the EEG. The underlying mechanisms responsible for SWD generation and for the apparently spontaneous transitions to SWD and back again are still not fully understood. Specifically, the role of spatial cortico-cortical interactions in ictogenesis is not well studied. We present a macroscopic, neural mass model of a cortical column which includes two distinct time scales of inhibition. This model can produce both an oscillatory background and a pathological SWD rhythm. We demonstrate that coupling two of these cortical columns can lead to a bistability between out-of-phase, low amplitude background dynamics and in-phase, high amplitude SWD activity. Stimuli can cause state-dependent transitions from background into SWD. In an extended local area of cortex, spatial heterogeneities in a model parameter can lead to spontaneous reversible transitions from a desynchronised background to synchronous SWD due to intermittency. The deterministic model is therefore capable of producing absence seizure-like events without any time dependent adjustment of model parameters. The emergence of such mechanisms due to spatial coupling demonstrates the importance of spatial interactions in modelling ictal dynamics, and in the study of ictogenesis.

Interhemispheric coupling, the West Antarctic Ice Sheet and warm Antarctic interglacials

Ice core evidence indicates that even though atmospheric CO2 concentrations did not exceed ~300 ppm at any point during the last 800 000 years, East Antarctica was at least ~3–4 °C warmer than preindustrial (CO2~280 ppm) in each of the last four interglacials. During the previous three interglacials, this anomalous warming was short lived (~3000 years) and apparently occurred before the completion of Northern Hemisphere deglaciation. Hereafter, we refer to these periods as "Warmer than Present Transients" (WPTs). We present a series of experiments to investigate the impact of deglacial meltwater on the Atlantic Meridional Overturning Circulation (AMOC) and Antarctic temperature. It is well known that a slowed AMOC would increase southern sea surface temperature (SST) through the bipolar seesaw and observational data suggests that the AMOC remained weak throughout the terminations preceding WPTs, strengthening rapidly at a time which coincides closely with peak Antarctic temperature. We present two 800 kyr transient simulations using the Intermediate Complexity model GENIE-1 which demonstrate that meltwater forcing generates transient southern warming that is consistent with the timing of WPTs, but is not sufficient (in this single parameterisation) to reproduce the magnitude of observed warmth. In order to investigate model and boundary condition uncertainty, we present three ensembles of transient GENIE-1 simulations across Termination II (135 000 to 124 000 BP) and three snapshot HadCM3 simulations at 130 000 BP. Only with consideration of the possible feedback of West Antarctic Ice Sheet (WAIS) retreat does it become possible to simulate the magnitude of observed warming.

A protective antiarrhythmic role of ursodeoxycholic acid in an in vitro rat model of the cholestatic fetal heart

Intrahepatic cholestasis of pregnancy may be complicated by fetal arrhythmia, fetal hypoxia, preterm labor, and, in severe cases, intrauterine death. The precise etiology of fetal death is not known. However, taurocholate has been demonstrated to cause arrhythmia and abnormal calcium dynamics in cardiomyocytes. To identify the underlying reason for increased susceptibility of fetal cardiomyocytes to arrhythmia, we studied myofibroblasts (MFBs), which appear during structural remodeling of the adult diseased heart. In vitro, they depolarize rat cardiomyocytes via heterocellular gap junctional coupling. Recently, it has been hypothesized that ventricular MFBs might appear in the developing human heart, triggered by physiological fetal hypoxia. However, their presence in the fetal heart (FH) and their proarrhythmogenic effects have not been systematically characterized. Immunohistochemistry demonstrated that ventricular MFBs transiently appear in the human FH during gestation. We established two in vitro models of the maternal heart (MH) and FH, both exposed to increasing doses of taurocholate. The MH model consisted of confluent strands of rat cardiomyocytes, whereas for the FH model, we added cardiac MFBs on top of cardiomyocytes. Taurocholate in the FH model, but not in the MH model, slowed conduction velocity from 19 to 9 cm/s, induced early after depolarizations, and resulted in sustained re-entrant arrhythmias. These arrhythmic events were prevented by ursodeoxycholic acid, which hyperpolarized MFB membrane potential by modulating potassium conductance. CONCLUSION: These results illustrate that the appearance of MFBs in the FH may contribute to arrhythmias. The above-described mechanism represents a new therapeutic approach for cardiac arrhythmias at the level of MFB.

The S-1/S-2 exciton interaction in 2-pyridone center dot 6-methyl-2-pyridone: Davydov splitting, vibronic coupling, and vibronic quenching

The excitonic splitting between the S-1 and S-2 electronic states of the doubly hydrogen-bonded dimer 2-pyridone center dot 6-methyl-2-pyridone (2PY center dot 6M2PY) is studied in a supersonic jet, applying two-color resonant two-photon ionization (2C-R2PI), UV-UV depletion, and dispersed fluorescence spectroscopies. In contrast to the C-2h symmetric (2-pyridone) 2 homodimer, in which the S-1 <- S-0 transition is symmetry-forbidden but the S-2 <- S-0 transition is allowed, the symmetry-breaking by the additional methyl group in 2PY center dot 6M2PY leads to the appearance of both the S-1 and S-2 origins, which are separated by Delta(exp) = 154 cm(-1). When combined with the separation of the S-1 <- S-0 excitations of 6M2PY and 2PY, which is delta = 102 cm(-1), one obtains an S-1/S-2 exciton coupling matrix element of V-AB, el = 57 cm(-1) in a Frenkel-Davydov exciton model. The vibronic couplings in the S-1/S-2 <- S-0 spectrum of 2PY center dot 6M2PY are treated by the Fulton-Gouterman single-mode model. We consider independent couplings to the intramolecular 6a' vibration and to the intermolecular sigma' stretch, and obtain a semi-quantitative fit to the observed spectrum. The dimensionless excitonic couplings are C(6a') = 0.15 and C(sigma') = 0.05, which places this dimer in the weak-coupling limit. However, the S-1/S-2 state exciton splittings Delta(calc) calculated by the configuration interaction singles method (CIS), time-dependent Hartree-Fock (TD-HF), and approximate second-order coupled-cluster method (CC2) are between 1100 and 1450 cm(-1), or seven to nine times larger than observed. These huge errors result from the neglect of the coupling to the optically active intra-and intermolecular vibrations of the dimer, which lead to vibronic quenching of the purely electronic excitonic splitting. For 2PY center dot 6M2PY the electronic splitting is quenched by a factor of similar to 30 (i.e., the vibronic quenching factor is Gamma(exp) = 0.035), which brings the calculated splittings into close agreement with the experimentally observed value. The 2C-R2PI and fluorescence spectra of the tautomeric species 2-hydroxypyridine center dot 6-methyl-2-pyridone (2HP center dot 6M2PY) are also observed and assigned. (C) 2011 American Institute of Physics.

Transport model of the human Na+-coupled L-ascorbic acid (vitamin C) transporter SVCT1

Vitamin C (L-ascorbic acid) is an essential micronutrient that serves as an antioxidant and as a cofactor in many enzymatic reactions. Intestinal absorption and renal reabsorption of the vitamin is mediated by the epithelial apical L-ascorbic acid cotransporter SVCT1 (SLC23A1). We explored the molecular mechanisms of SVCT1-mediated L-ascorbic acid transport using radiotracer and voltage-clamp techniques in RNA-injected Xenopus oocytes. L-ascorbic acid transport was saturable (K(0.5) approximately 70 microM), temperature dependent (Q(10) approximately 5), and energized by the Na(+) electrochemical potential gradient. We obtained a Na(+)-L-ascorbic acid coupling ratio of 2:1 from simultaneous measurement of currents and fluxes. L-ascorbic acid and Na(+) saturation kinetics as a function of cosubstrate concentrations revealed a simultaneous transport mechanism in which binding is ordered Na(+), L-ascorbic acid, Na(+). In the absence of L-ascorbic acid, SVCT1 mediated pre-steady-state currents that decayed with time constants 3-15 ms. Transients were described by single Boltzmann distributions. At 100 mM Na(+), maximal charge translocation (Q(max)) was approximately 25 nC, around a midpoint (V(0.5)) at -9 mV, and with apparent valence approximately -1. Q(max) was conserved upon progressive removal of Na(+), whereas V(0.5) shifted to more hyperpolarized potentials. Model simulation predicted that the pre-steady-state current predominantly results from an ion-well effect on binding of the first Na(+) partway within the membrane electric field. We present a transport model for SVCT1 that will provide a framework for investigating the impact of specific mutations and polymorphisms in SLC23A1 and help us better understand the contribution of SVCT1 to vitamin C metabolism in health and disease.

Steady-state function of the ubiquitous mammalian Na/H exchanger (NHE1) in relation to dimer coupling models with 2Na/2H stoichiometry

We describe the steady-state function of the ubiquitous mammalian Na/H exchanger (NHE)1 isoform in voltage-clamped Chinese hamster ovary cells, as well as other cells, using oscillating pH-sensitive microelectrodes to quantify proton fluxes via extracellular pH gradients. Giant excised patches could not be used as gigaseal formation disrupts NHE activity within the patch. We first analyzed forward transport at an extracellular pH of 8.2 with no cytoplasmic Na (i.e., nearly zero-trans). The extracellular Na concentration dependence is sigmoidal at a cytoplasmic pH of 6.8 with a Hill coefficient of 1.8. In contrast, at a cytoplasmic pH of 6.0, the Hill coefficient is <1, and Na dependence often appears biphasic. Results are similar for mouse skin fibroblasts and for an opossum kidney cell line that expresses the NHE3 isoform, whereas NHE1(-/-) skin fibroblasts generate no proton fluxes in equivalent experiments. As proton flux is decreased by increasing cytoplasmic pH, the half-maximal concentration (K(1/2)) of extracellular Na decreases less than expected for simple consecutive ion exchange models. The K(1/2) for cytoplasmic protons decreases with increasing extracellular Na, opposite to predictions of consecutive exchange models. For reverse transport, which is robust at a cytoplasmic pH of 7.6, the K(1/2) for extracellular protons decreases only a factor of 0.4 when maximal activity is decreased fivefold by reducing cytoplasmic Na. With 140 mM of extracellular Na and no cytoplasmic Na, the K(1/2) for cytoplasmic protons is 50 nM (pH 7.3; Hill coefficient, 1.5), and activity decreases only 25% with extracellular acidification from 8.5 to 7.2. Most data can be reconstructed with two very different coupled dimer models. In one model, monomers operate independently at low cytoplasmic pH but couple to translocate two ions in "parallel" at alkaline pH. In the second "serial" model, each monomer transports two ions, and translocation by one monomer allosterically promotes translocation by the paired monomer in opposite direction. We conclude that a large fraction of mammalian Na/H activity may occur with a 2Na/2H stoichiometry.

Statistical inference for the optimal approximating model

In the setting of high-dimensional linear models with Gaussian noise, we investigate the possibility of confidence statements connected to model selection. Although there exist numerous procedures for adaptive (point) estimation, the construction of adaptive confidence regions is severely limited (cf. Li in Ann Stat 17:1001–1008, 1989). The present paper sheds new light on this gap. We develop exact and adaptive confidence regions for the best approximating model in terms of risk. One of our constructions is based on a multiscale procedure and a particular coupling argument. Utilizing exponential inequalities for noncentral χ2-distributions, we show that the risk and quadratic loss of all models within our confidence region are uniformly bounded by the minimal risk times a factor close to one.

Coupling of eastern and western subpolar North Atlantic: salt transport in the Irminger Current

Salt transport in the Irminger Current and thus the coupling between eastern and western subpolar North Atlantic plays an important role for climate variability across a wide range of time scales. High-resolution ocean modeling and observations indicate that 5 salinities in the eastern subpolar North Atlantic decrease with enhanced circulation of the North Atlantic subpolar gyre (SPG). This has led to the perception that a stronger SPG also transports less salt westward. In this study, we analyze a regional ocean model and a comprehensive global coupled climate model, and show that a stronger SPG transports more salt in the Irminger Current irrespective of lower salinities in its 10 source region. The additional salt converges in the Labrador Sea and the Irminger Basin by eddy transports, increases surface salinity in the western SPG, and favors more intense deep convection. This is part of a positive feedback mechanism with potentially large implications for climate variability and predictability.

Land-atmosphere coupling over North America in CRCM5

Land-atmosphere coupling and its impact on extreme precipitation and temperature events over North America are studied using the fifth generation of the Canadian Regional Climate Model (CRCM5). To this effect, two 30 year long simulations, spanning the 1981–2010 period, with and without land-atmosphere coupling, have been performed with CRCM5, driven by the European Centre for Medium-Range Weather Forecasts reanalysis at the boundaries. In the coupled simulation, the soil moisture interacts freely with the atmosphere at each time step, while in the uncoupled simulation, soil moisture is replaced with its climatological value computed from the coupled simulation, thus suppressing the soil moisture-atmosphere interactions. Analyses of the coupled and uncoupled simulations, for the summer period, show strong soil moisture-temperature coupling over the Great Plains, consistent with previous studies. The maxima of soil moisture-precipitation coupling is more spread out and covers the semiarid regions of the western U.S. and parts of the Great Plains. However, the strength of soil moisture-precipitation coupling is found to be generally weaker than that of soil moisture-temperature coupling. The study clearly indicates that land-atmosphere coupling increases the interannual variability of the seasonal mean daily maximum temperature in the Great Plains. Land-atmosphere coupling is found to significantly modulate selected temperature extremes such as the number of hot days, frequency, and maximum duration of hot spells over the Great Plains. Results also suggest additional hot spots, where soil moisture modulates extreme events. These hot spots are located in the southeast U.S. for the hot days/hot spells and in the semiarid regions of the western U.S. for extreme wet spells. This study thus demonstrates that climatologically wet/dry regions can become hot spots of land-atmosphere coupling when the soil moisture decreases/increases to an intermediate transitional level where evapotranspiration becomes moisture sensitive and large enough to affect the climate.

A numerical model for inert gas transport in the lung based on fractal airway morphology

Patients suffering from cystic fibrosis (CF) show thick secretions, mucus plugging and bronchiectasis in bronchial and alveolar ducts. This results in substantial structural changes of the airway morphology and heterogeneous ventilation. Disease progression and treatment effects are monitored by so-called gas washout tests, where the change in concentration of an inert gas is measured over a single or multiple breaths. The result of the tests based on the profile of the measured concentration is a marker for the severity of the ventilation inhomogeneity strongly affected by the airway morphology. However, it is hard to localize underlying obstructions to specific parts of the airways, especially if occurring in the lung periphery. In order to support the analysis of lung function tests (e.g. multi-breath washout), we developed a numerical model of the entire airway tree, coupling a lumped parameter model for the lung ventilation with a 4th-order accurate finite difference model of a 1D advection-diffusion equation for the transport of an inert gas. The boundary conditions for the flow problem comprise the pressure and flow profile at the mouth, which is typically known from clinical washout tests. The natural asymmetry of the lung morphology is approximated by a generic, fractal, asymmetric branching scheme which we applied for the conducting airways. A conducting airway ends when its dimension falls below a predefined limit. A model acinus is then connected to each terminal airway. The morphology of an acinus unit comprises a network of expandable cells. A regional, linear constitutive law describes the pressure-volume relation between the pleural gap and the acinus. The cyclic expansion (breathing) of each acinus unit depends on the resistance of the feeding airway and on the flow resistance and stiffness of the cells themselves. Special care was taken in the development of a conservative numerical scheme for the gas transport across bifurcations, handling spatially and temporally varying advective and diffusive fluxes over a wide range of scales. Implicit time integration was applied to account for the numerical stiffness resulting from the discretized transport equation. Local or regional modification of the airway dimension, resistance or tissue stiffness are introduced to mimic pathological airway restrictions typical for CF. This leads to a more heterogeneous ventilation of the model lung. As a result the concentration in some distal parts of the lung model remains increased for a longer duration. The inert gas concentration at the mouth towards the end of the expirations is composed of gas from regions with very different washout efficiency. This results in a steeper slope of the corresponding part of the washout profile.

Achieving a more realistic assessment of rockfall hazards by coupling three-dimensional process models and field-based tree-ring data

Sound knowledge of the spatial and temporal patterns of rockfalls is fundamental for the management of this very common hazard in mountain environments. Process-based, three-dimensional simulation models are nowadays capable of reproducing the spatial distribution of rockfall occurrences with reasonable accuracy through the simulation of numerous individual trajectories on highly-resolved digital terrain models. At the same time, however, simulation models typically fail to quantify the ‘real’ frequency of rockfalls (in terms of return intervals). The analysis of impact scars on trees, in contrast, yields real rockfall frequencies, but trees may not be present at the location of interest and rare trajectories may not necessarily be captured due to the limited age of forest stands. In this article, we demonstrate that the coupling of modeling with tree-ring techniques may overcome the limitations inherent to both approaches. Based on the analysis of 64 cells (40 m × 40 m) of a rockfall slope located above a 1631-m long road section in the Swiss Alps, we illustrate results from 488 rockfalls detected in 1260 trees. We illustrate that tree impact data cannot only be used (i) to reconstruct the real frequency of rockfalls for individual cells, but that they also serve (ii) the calibration of the rockfall model Rockyfor3D, as well as (iii) the transformation of simulated trajectories into real frequencies. Calibrated simulation results are in good agreement with real rockfall frequencies and exhibit significant differences in rockfall activity between the cells (zones) along the road section. Real frequencies, expressed as rock passages per meter road section, also enable quantification and direct comparison of the hazard potential between the zones. The contribution provides an approach for hazard zoning procedures that complements traditional methods with a quantification of rockfall frequencies in terms of return intervals through a systematic inclusion of impact records in trees.

M-AARE - Coupling atmospheric, hydrological, hydrodynamic and damage models in the Aare river basin, Switzerland

The triggering mechanism and the temporal evolution of large flood events, especially of worst-case scenarios, are not yet fully understood. Consequently, the cumulative losses of extreme floods are unknown. To study the link between weather conditions, discharges and flood losses it is necessary to couple atmospheric, hydrological, hydrodynamic and damage models. The objective of the M-AARE project is to test the potentials and opportunities of a model chain that relates atmospheric conditions to flood losses or risks. The M-AARE model chain is a set of coupled models consisting of four main components: the precipitation module, the hydrology module, the hydrodynamic module, and the damage module. The models are coupled in a cascading framework with harmonized time-steps. First exploratory applications show that the one way coupling of the WRF-PREVAH-BASEMENT models has been achieved and provides promising new insights for a better understanding of key aspects in flood risk analysis.