75 research outputs found
Stochastic Model for Tumor Control Probability: Effects of Cell Cycle and (A)symmetric Proliferation
Estimating the required dose in radiotherapy is of crucial importance since
the administrated dose should be sufficient to eradicate the tumor and at the
same time should inflict minimal damage on normal cells. The probability that a
given dose and schedule of ionizing radiation eradicates all the tumor cells in
a given tissue is called the tumor control probability (TCP), and is often used
to compare various treatment strategies used in radiation therapy. In this
paper, we aim to investigate the effects of including cell-cycle phase on the
TCP by analyzing a stochastic model of a tumor comprised of actively dividing
cells and quiescent cells with different radiation sensitivities. We derive an
exact phase-diagram for the steady-state TCP of the model and show that at
high, clinically-relevant doses of radiation, the distinction between active
and quiescent tumor cells (i.e. accounting for cell-cycle effects) becomes of
negligible importance in terms of its effect on the TCP curve. However, for
very low doses of radiation, these proportions become significant determinants
of the TCP. Moreover, we use a novel numerical approach based on the method of
characteristics for partial differential equations, validated by the Gillespie
algorithm, to compute the TCP as a function of time. We observe that our
results differ from the results in the literature using similar existing
models, even though similar parameters values are used, and the reasons for
this are discussed.Comment: 12 pages, 5 figure
Phenotypic heterogeneity in modeling cancer evolution
The unwelcome evolution of malignancy during cancer progression emerges
through a selection process in a complex heterogeneous population structure. In
the present work, we investigate evolutionary dynamics in a phenotypically
heterogeneous population of stem cells (SCs) and their associated progenitors.
The fate of a malignant mutation is determined not only by overall stem cell
and differentiated cell growth rates but also differentiation and
dedifferentiation rates. We investigate the effect of such a complex population
structure on the evolution of malignant mutations. We derive exact analytic
results for the fixation probability of a mutant arising in each of the
subpopulations. The analytic results are in almost perfect agreement with the
numerical simulations. Moreover, a condition for evolutionary advantage of a
mutant cell versus the wild type population is given in the present study. We
also show that microenvironment-induced plasticity in invading mutants leads to
more aggressive mutants with higher fixation probability. Our model predicts
that decreasing polarity between stem and differentiated cells turnover would
raise the survivability of non-plastic mutants; while it would suppress the
development of malignancy for plastic mutants. We discuss our model in the
context of colorectal/intestinal cancer (at the epithelium). This novel
mathematical framework can be applied more generally to a variety of problems
concerning selection in heterogeneous populations, in other contexts such as
population genetics, and ecology.Comment: 28 pages, 7 figures, 2 table
UTJECAJ RASLOJAVANJA ÄIMBENIKA OÅ TEÄENJA IZAZVANIH MINIRANJEM U HOEK-BROWNOVU KRITERIJU SLOMA NA PRAÄENJE OÅ TEÄENJA ETAŽA U KOPOVIMA
The process of creating a slope in a rock mass using the excavation and blasting methods consistently leads to stress release in the rock mass, resulting in a certain level of fracture and disturbance. Blast-induced vibrations can also influence the quality of the rock mass remaining after the blasting, as well as the stability and bench damage monitoring (BDM) of mines. A damage factor (D) is included in the HoekāBrown failure criterion to compute the disturbance of a rock mass in creating a slope. Choosing the value and thickness of the blast zone for the HoekāBrown criterion is crucial in the safety analysis and BDM of mines. However, the selection is still a crucial technical challenge in this criterion. Employing nonlinear layering, the present study divides the rock mass behind a blast hole into several layers with decreasing D values applied to each layer. The numerical simulation was conducted using the FLAC finite difference software for bench vibration assessment and damage monitoring by checking the peak particle velocity (PPV) in the bench face with different geometries. Behind the blast hole, five different layers of D were considered through which the HoekāBrown properties of the rock mass declined nonlinearly during the execution of the model. Since the disturbance threshold of PPV was assumed to be 120 mm/s, the toe and middle parts of the small benches were in the disturbance threshold, while for the medium and high benches, only the bench toe was within the disturbance threshold.Proces stvaranja kosina u stijenskoj masi metodama iskopa i miniranja dovodi do oslobaÄanja naprezanja u stijenskoj masi, Å”to rezultira odreÄenom razinom loma i oÅ”teÄenja. Vibracije izazvane miniranjem takoÄer mogu utjecati na kvalitetu minirane stijenske mase, kao i na stabilnost i praÄenje oÅ”teÄenja etaža (BDM) povrÅ”inskoga kopa. Koeficijent poremeÄenosti stijenske mase (D) ukljuÄen je u Hoek-Brownov kriterij sloma za izraÄunavanje oÅ”teÄenja stijenske mase pri izradi kosine. Odabir vrijednosti i Å”irine zone miniranja prema Hoek-Brownovu kriteriju kljuÄan je u analizi sigurnosti i BDM-a kopova. MeÄutim, odabir joÅ” uvijek predstavlja kljuÄni tehniÄki izazov. KoristeÄi se nelinearnom slojevitoÅ”Äu, ova analiza dijeli stijensku masu iza minske buÅ”otine u nekoliko slojeva sa smanjivanim vrijednostima D za pojedini sloj. NumeriÄka simulacija provedena je koriÅ”tenjem softvera FLAC za procjenu vibracija na etažama i praÄenje oÅ”teÄenja provjerom vrÅ”ne brzine Äestica (PPV) na etaži s razliÄitim geometrijama. Iza minske buÅ”otine razmatrano je pet razliÄitih nizova D kroz koje su Hoek-Brownova svojstva stijenske mase nelinearno mijenjana tijekom analize modela. BuduÄi da je graniÄna vrijednost PPV-a pretpostavljena na 120 mm/s, vrh i srediÅ”nji dijelovi malih etaža bili su na graniÄnoj vrijednosti oÅ”teÄenja, dok je za srednje i visoke etaže samo vrh etaže bio unutar graniÄne vrijednosti oÅ”teÄenja
MEHANIZAM KAISEROVA EFEKTA U FILITU PRI VLAÄNOME OPTEREÄENJU NEIZRAVNIM MJERENJEM
Determination of in-situ stress serves as an important step in the design and construction of civil and mining projects, among others. Conventional methods of the in-situ stress measurement are time- and cost-intensive. Therefore, the application of low-cost yet rapid methodologies for in-situ stress evaluation has been increasingly regarded by researchers. The Kaiser effect-based acoustic emission method is one of such novel approaches to the in-situ stress evaluation. Not only the point at which the Kaiser effect occurs, but also the mechanism of the Kaiser effect is of paramount importance. In this research, acoustic emission tests were conducted on phyllite rock samples under Brazilian tensile loading to collect a variety of acoustic data, including the amplitude, rise time, count, duration, and energy. Then, the Kaiser effect point was determined using the collected data on acoustic parameters, with its occurrence mechanism investigated. In addition, mathematical transformations were adopted to transform the acoustic signal from the time domain to the frequency domain, where the peak frequency was analyzed. The results of the RA/AF ratio analysis showed that the acoustic emission was sourced from tensile micro-cracks. Moreover, the high level of energy indicated a high intensity of crack formation at the Kaiser effect point. The large number of received hits showed that the count of generated cracks increases abruptly within the range of the Kaiser effect. In addition, the obtained high value of the peak frequency implied that the crack growth rate is high at the Kaiser effect point.In situ odreÄivanje naprezanja, meÄu ostalim, služi kao važan korak u projektiranju i izradi graÄevinskih i rudarskih projekata. Konvencionalne in situ metode mjerenja naprezanja vremenski su i troÅ”kovno zahtjevne. Stoga istraživaÄi sve viÅ”e razmatraju primjenu jeftinih, ali brzih metodologija za procjenu in situ naprezanja. Metoda akustiÄne emisije koja se temelji na Kaiserovu efektu jedan je od takvih novih pristupa u procjeni in situ naprezanja. Ne samo toÄka u kojoj se Kaiserov efekt javlja, nego i mehanizam Kaiserova efekta od iznimne je važnosti. U ovome su istraživanju provedena ispitivanja akustiÄke emisije na uzorcima filitnih stijena pri ispitivanju vlaÄne ÄvrstoÄe stijena uporabom brazilskoga testa kako bi se prikupili razliÄiti akustiÄki podatci ukljuÄujuÄi amplitudu, vrijeme porasta, broj, trajanje i energiju. Potom je na temelju prikupljenih podataka o akustiÄkim parametrima odreÄena toÄka Kaiserova efekta te je ispitan mehanizam njezina nastanka. Osim toga, usvojene su matematiÄke transformacije za transformaciju akustiÄkoga signala iz vremenske domene u frekvencijsko podruÄje, gdje je analizirana vrÅ”na frekvencija. Rezultati analize omjera RA/AF pokazali su da je akustiÄka emisija nastala iz vlaÄnih mikropukotina. Å toviÅ”e, visoka razina energije upuÄuje na visok intenzitet stvaranja pukotina u toÄki Kaiserova efekta. Velik broj primljenih impulsa pokazao je da se broj novonastalih pukotina naglo poveÄava unutar raspona Kaiserova efekta. Osim toga, dobivena visoka vrijednost vrÅ”ne frekvencije implicira da je brzina Å”irenja pukotine visoka u toÄki Kaiserova efekta
PREGLED PRIMJENE KAISEROVA EFEKTA U MJERENJU IN SITU NAPREZANJA U STIJENAMA
Knowledge of in-situ rock stress is one of the significant issues in many engineering problems. There are various methods for determining in-situ stress. Most of the common methods used for the determination of in-situ stress are time and cost consuming, and in many cases need specific accessibility. Therefore, attention to core-based methods is increasing. One of these methods is the acoustic emission technique based on the Kaiser effect. This method is among the stress stressing-destressing methods and is based on observing rock behaviour without having any important impact on it. Knowledge of the acoustic emission principles and acoustic signal parameters is the first step to use the Kaiser effect method for in-situ stress determination. Also, using the Kaiser effect method requires knowledge on the mechanism and theory associated with the Kaiser effect. In this research, different methods for determining the Kaiser effect in parametric (tangent method and maximum slope, etc.) and signal processing (Fourier transform, wavelet transform, etc.) terms were reviewed. The results obtained from the Kaiser effect method were compared to other common methods used for in-situ stress measurement, like over-coring and hydraulic fracturing methods, and based on the results, there was a good agreement between them. Also, the effective parameters on determining the Kaiser effect stress point were investigated. The important parameters were the testing procedure, confining pressure, physical properties of rock, delay time and retention time, direction and amount of loading, anisotropy angle and loading rate.Poznavanje in situ naprezanja u stijenskoj masi jedan je od važnijih aspekata u mnogim inženjerskim problemima. Postoje razliÄite metode za odreÄivanje in situ naprezanja. VeÄina uobiÄajenih metoda koje se koriste za odreÄivanje in situ naprezanja vremenski su i financijski zahtjevne te je u mnogim sluÄajevima potrebna posebna pristupaÄnost. Stoga se sve viÅ”e pažnje posveÄuje metodama temeljenim na ispitivanjima provedenim na jezgrama. Jedna je od tih metoda i metoda akustiÄke emisije koja se temelji na Kaiserovu efektu. Ubraja se u metode naprezanja postupcima optereÄenja i rastereÄenja, a temelji se na promatranju ponaÅ”anja stijena bez znatnoga utjecaja na nju. Poznavanje principa akustiÄke emisije i parametara akustiÄkoga signala prvi je korak u primjeni metode za odreÄivanje in situ naprezanja na temelju Kaiserova efekta. Nadalje, primjena metode Kaiserova efekta zahtijeva razumijevanje mehanizma i teorije povezane s Kaiserovim efektom. U ovome istraživanju razmatrane su razliÄite metode za odreÄivanje Kaiserova efekta u okviru parametara (metoda tangente i maksimalni nagib itd.) i obrade signala (Fourierova transformacija, valiÄna transformacija i sl.). Pored navedenog, rezultati dobiveni metodom Kaiserova efekta usporeÄeni su s drugim uobiÄajenim metodama koje se koriste za mjerenje in situ naprezanja, kao Å”to su overcoring metoda i metoda hidrauliÄkoga frakturiranja te je na temelju rezultata ustanovljena znatna podudarnost izmeÄu njih. TakoÄer su istraženi kljuÄni parametri za odreÄivanje toÄke naprezanja kod Kaiserova efekta. KljuÄni parametri bili su postupak ispitivanja, ograniÄavajuÄi tlak, fiziÄka svojstva stijene, vrijeme kaÅ”njenja i vrijeme zadržavanja, smjer i koliÄina optereÄenja, kut anizotropije i brzina optereÄenja
The Moran process on 2-chromatic graphs
Resources are rarely distributed uniformly within a population. Heterogeneity in the concentration of a drug, the quality of breeding sites, or wealth can all affect evolutionary dynamics. In this study, we represent a collection of properties affecting the fitness at a given location using a color. A green node is rich in resources while a red node is poorer. More colors can represent a broader spectrum of resource qualities. For a population evolving according to the birth-death Moran model, the first question we address is which structures, identified by graph connectivity and graph coloring, are evolutionarily equivalent. We prove that all properly two-colored, undirected, regular graphs are evolutionarily equivalent (where āproperly coloredā means that no two neighbors have the same color). We then compare the effects of background heterogeneity on properly two-colored graphs to those with alternative schemes in which the colors are permuted. Finally, we discuss dynamic coloring as a model for spatiotemporal resource fluctuations, and we illustrate that random dynamic colorings often diminish the effects of background heterogeneity relative to a proper two-coloring
- ā¦