The interior spacetimes of stars in Palatini f(R) gravity

We study the interior spacetimes of stars in the Palatini formalism of f(R) gravity and derive a generalized Tolman-Oppenheimer-Volkoff and mass equation for a static, spherically symmetric star. We show that matching the interior solution with the exterior Schwarzschild-De Sitter solution in general gives a relation between the gravitational mass and the density profile of a star, which is different from the one in General Relativity. These modifications become neglible in models for which $\delta F(R) \equiv \partial f/\partial R - 1$ is a decreasing function of R however. As a result, both Solar System constraints and stellar dynamics are perfectly consistent with $f(R) = R - \mu^4/R$.Comment: Published version, 6 pages, 1 figur

Spherically symmetric spacetimes in f(R) gravity theories

We study both analytically and numerically the gravitational fields of stars in f(R) gravity theories. We derive the generalized Tolman-Oppenheimer-Volkov equations for these theories and show that in metric f(R) models the Parameterized Post-Newtonian parameter $\gamma_{\rm PPN} = 1/2$ is a robust outcome for a large class of boundary conditions set at the center of the star. This result is also unchanged by introduction of dark matter in the Solar System. We find also a class of solutions with $\gamma_{\rm PPN} \approx 1$ in the metric $f(R)=R-\mu^4/R$ model, but these solutions turn out to be unstable and decay in time. On the other hand, the Palatini version of the theory is found to satisfy the Solar System constraints. We also consider compact stars in the Palatini formalism, and show that these models are not inconsistent with polytropic equations of state. Finally, we comment on the equivalence between f(R) gravity and scalar-tensor theories and show that many interesting Palatini f(R) gravity models can not be understood as a limiting case of a Jordan-Brans-Dicke theory with $\omega \to -3/2$.Comment: Published version, 12 pages, 7 figure

Multicellular dosimetric chain for molecular radiotherapy exemplified with dose simulations on 3D cell spheroids

Purpose: Absorbed radiation dose-response relationships are not clear in molecular radiotherapy (MRT). Here, we propose a voxel-based dose calculation system for multicellular dosimetry in MRT. We applied confocal microscope images of a spherical cell aggregate i.e. a spheroid, to examine the computation of dose distribution within a tissue from the distribution of radiopharmaceuticals. Methods: A confocal microscope Z-stack of a human hepatocellular carcinoma HepG2 spheroid was segmented using a support-vector machine algorithm and a watershed function. Heterogeneity in activity uptake was simulated by selecting a varying amount of the cell nuclei to contain In-111, I-125, or Lu-177. Absorbed dose simulations were carried out using vxlPen, a software application based on the Monte Carlo code PENELOPE. Results: We developed a schema for radiopharmaceutical dosimetry. The schema utilizes a partially supervised segmentation method for cell-level image data together with a novel main program for voxel-based radiation dose simulations. We observed that for 177Lu, radiation cross-fire enabled full dose coverage even if the radiopharmaceutical had accumulated to only 60% of the spheroid cells. This effect was not found with 111In and 125I. Using these Auger/internal conversion electron emitters seemed to guarantee that only the cells with a high enough activity uptake will accumulate a lethal amount of dose, while neighboring cells are spared. Conclusions: We computed absorbed radiation dose distributions in a 3D-cultured cell spheroid with a novel multicellular dosimetric chain. Combined with pharmacological studies in different tissue models, our cell-level dosimetric calculation method can clarify dose-response relationships for radiopharmaceuticals used in MRT. (C) 2017 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.Peer reviewe

Brachytherapy of Choroidal Melanomas Less Than 10 mm in Largest Basal Diameter Comparison of 10-mm and 15-mm Ruthenium Plaques

Purpose: To compare tumor control, vision, and complications between patients with a choroidal melanoma of Design: Retrospective, comparative case series. Participants: One hundred sixty-four consecutive patients with a choroidal melanoma of Methods: Diagnosis was based on growth or high-risk characteristics. The apical dose was 100 to 120 Gy aiming to deliver >= 250 Gy to the sclera. Plaque positioning was modeled retrospectively. An increase of >= 0.3 mm in thickness and >= 0.5 mm in LBD indicated local recurrence. Outcomes were compared with cumulative incidence analysis and Cox regression. Median follow-up time for patients still alive was 8.4 years. Main Outcome Measures: Recurrence rate, low vision, blindness, radiation maculopathy, and optic neuropathy. Results: Melanomas treated with the 10-mm plaque were smaller (median thickness, 1.9 mm vs. 2.6 mm; LBD, 7.1 mm vs. 8.6 mm) and located closer to foveola (median, 2.0 mm vs. 2.8 mm) than those treated with the 15-mm plaque (P <0.001). The 2 plaques provided a safety margin in 43% versus 40% eyes, provided no safety margin to guard foveola in 17% versus 33%, and did not entirely cover tumor mainly close to the disc in 32% versus 18% of eyes, respectively (P = 0.052). The incidence of a local recurrence was comparable (13% vs. 15% at 10 years; P = 0.31) and associated with plaque positioning (hazard ratio [HR], 2.81 for no safety margin; P = 0.041). At 5 years, the incidence of low vision was 14% versus 24%, and that of blindness was 3% versus 6%. Distance to the foveola was associated with loss of both levels of vision (HR, 0.65 per 1 mm vs. 0.68 per 1 mm; P Conclusions: The 10-mm ruthenium plaque contributes to better visual preservation, particularly with tumors close to fovea, without increase in local recurrence rate, and may therefore be preferable to the 15-mm plaque. (C) 2020 by the American Academy of OphthalmologyPeer reviewe

On gravitational fields of stars in f(R) gravity theories

Einstein's general relativity is a classical theory of gravitation: it is a postulate on the coupling between the four-dimensional, continuos spacetime and the matter fields in the universe, and it yields their dynamical evolution. It is believed that general relativity must be replaced by a quantum theory of gravity at least at extremely high energies of the early universe and at regions of strong curvature of spacetime, cf. black holes. Various attempts to quantize gravity, including conceptually new models such as string theory, have suggested that modification to general relativity might show up even at lower energy scales. On the other hand, also the late time acceleration of the expansion of the universe, known as the dark energy problem, might originate from new gravitational physics. Thus, although there has been no direct experimental evidence contradicting general relativity so far - on the contrary, it has passed a variety of observational tests - it is a question worth asking, why should the effective theory of gravity be of the exact form of general relativity? If general relativity is modified, how do the predictions of the theory change? Furthermore, how far can we go with the changes before we are face with contradictions with the experiments? Along with the changes, could there be new phenomena, which we could measure to find hints of the form of the quantum theory of gravity? This thesis is on a class of modified gravity theories called f(R) models, and in particular on the effects of changing the theory of gravity on stellar solutions. It is discussed how experimental constraints from the measurements in the Solar System restrict the form of f(R) theories. Moreover, it is shown that models, which do not differ from general relativity at the weak field scale of the Solar System, can produce very different predictions for dense stars like neutron stars. Due to the nature of f(R) models, the role of independent connection of the spacetime is emphasized throughout the thesis.Einsteinin yleinen suhteellisuusteoria on klassinen teoria painovoimasta jatkuvan aika-avaruuden ja maailmankaikkeuden ainekenttien välisenä vuorovaikutuksena: kuinka niiden kehitys on kytkeytynyt toisiinsa. Pohjimmiltaan yleinen suhteellisuusteoria on postulaatti, eikä sen muoto sinänsä ole yksikäsitteinen teoreettiselta kannalta. Yleisesti uskotaankin, että yleinen suhteellisuusteoria on korvattava kvanttiteorialla gravitaatiosta, joka välttämättä näyttäytyy ainakin varhaisessa maailmankaikkeudessa ja aika-avaruuden alueilla, joissa kaarevuus on suurta - vrt. mustat aukot. Yritykset kvantisoida gravitaatiota - mukaanlukien käsitteellisesti uudet mallit aika-avaruuden ja materian luonteesta kuten säieteoria - ovat vihjanneet, että poikkeamia yleisestä suhteellisuusteoriasta saattaa esiintyä suhteellisen alhaisillakin energiaskaaloilla. Toisaalta on myös ehdotettu, että maailmankaikkeuden laajenemisen nykyinen kiihtyminen, joka tunnetaan pimeän energian ongelmana, saattaa olla peräisin gravitaation alueelta. Vaikkakin yleinen suhteellisuusteoria on läpäissyt käytännössä kaikki sille tehdyt tarkkuusmittaukset Maan päällä ja Aurinkokunnassa, sekä antanut muutoinkin johdonmukaisia ennusteita muutoinkin avaruusfysiikan ja tähtitieteen alueella, on aiheellista kysyä miksi efektiivisen painovoimateorian tulisi ottaa juuri yleisen suhteellisuusteorian muoto. Kuinka teorian ennusteet muuttuvat, jos yleistä suhteellisuusteoriaa muokataan? Entä kuinka pitkälle muutoksia ylipäätään voidaan tehdä ennenkuin rajoitukset kokeista tulevat vastaan? Voisiko teorian muokkaaminen tuottaa mukanaan uusia ilmiöitä, joita mittaamalla voitaisiin saada vihjeitä kvanttigravitaation luonteesta? Tämä väitöskirja käsittelee tiettyä painovoimamalliluokkaa, joka tunnetaan f(R)-teorioina. Erityisesti työssä keskitytään aiheeseen, kuinka painovoiman muuttaminen f(R)-teorian puitteissa saattaa vaikuttaa tähtien rakenteeseen ja kuinka teorioiden muotoa voidaan rajoittaa vertaamalla niiden ennusteita kokeellisiin havaintoihin Aurinkokunnasta sekä myös muista astrofysikaalisista kohteista. Näytämme myös, kuinka mallit, jotka eivät poikkea yleisestä suhteellisuusteoriasta Aurinkokunnan skaalalla, saattavat tuottaa hyvinkin poikkeavia ennusteita tiiviiden tähtien kuten neutronitähtien tapauksessa. f(R)-teorioiden luonteeseen liittyy, että on aiheellista keskustella avaruusaikaan liittyvän konnektion roolista vapaana muuttujana, ja siksi aihetta onkin painotettu johdannossa