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 ČIMBENIKA OŠTEĆENJA IZAZVANIH MINIRANJEM U HOEK-BROWNOVU KRITERIJU SLOMA NA PRAĆENJE OŠTEĆENJA 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 Hoek–Brown 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 Hoek–Brown 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 Hoek–Brown 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 oslobađanja naprezanja u stijenskoj masi, što rezultira određenom razinom loma i oštećenja. Vibracije izazvane miniranjem također mogu utjecati na kvalitetu minirane stijenske mase, kao i na stabilnost i praćenje oštećenja etaža (BDM) površinskoga kopa. Koeficijent poremećenosti stijenske mase (D) uključen je u Hoek-Brownov kriterij sloma za izračunavanje oštećenja stijenske mase pri izradi kosine. Odabir vrijednosti i širine zone miniranja prema Hoek-Brownovu kriteriju ključan je u analizi sigurnosti i BDM-a kopova. Međutim, odabir još uvijek predstavlja ključni tehnički izazov. Koristeći se nelinearnom slojevitošću, ova analiza dijeli stijensku masu iza minske bušotine u nekoliko slojeva sa smanjivanim vrijednostima D za pojedini sloj. Numerička simulacija provedena je korištenjem softvera FLAC za procjenu vibracija na etažama i praćenje oštećenja provjerom vršne brzine čestica (PPV) na etaži s različitim geometrijama. Iza minske bušotine razmatrano je pet različitih nizova D kroz koje su Hoek-Brownova svojstva stijenske mase nelinearno mijenjana tijekom analize modela. Budući da je granična vrijednost PPV-a pretpostavljena na 120 mm/s, vrh i središnji dijelovi malih etaža bili su na graničnoj vrijednosti oštećenja, dok je za srednje i visoke etaže samo vrh etaže bio unutar granične vrijednosti oštećenja

MEHANIZAM KAISEROVA EFEKTA U FILITU PRI VLAČNOME OPTEREĆENJU 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 određivanje naprezanja, među ostalim, služi kao važan korak u projektiranju i izradi građevinskih i rudarskih projekata. Konvencionalne in situ metode mjerenja naprezanja vremenski su i troškovno zahtjevne. Stoga istraživači sve više razmatraju primjenu jeftinih, ali brzih metodologija za procjenu in situ naprezanja. Metoda akustične emisije koja se temelji na Kaiserovu efektu jedan je od takvih novih pristupa u procjeni in situ naprezanja. Ne samo točka u kojoj se Kaiserov efekt javlja, nego i mehanizam Kaiserova efekta od iznimne je važnosti. U ovome su istraživanju provedena ispitivanja akustičke emisije na uzorcima filitnih stijena pri ispitivanju vlačne čvrstoće stijena uporabom brazilskoga testa kako bi se prikupili različiti akustički podatci uključujući amplitudu, vrijeme porasta, broj, trajanje i energiju. Potom je na temelju prikupljenih podataka o akustičkim parametrima određena točka Kaiserova efekta te je ispitan mehanizam njezina nastanka. Osim toga, usvojene su matematičke transformacije za transformaciju akustičkoga signala iz vremenske domene u frekvencijsko područje, gdje je analizirana vršna frekvencija. Rezultati analize omjera RA/AF pokazali su da je akustička emisija nastala iz vlačnih mikropukotina. Štoviše, visoka razina energije upućuje na visok intenzitet stvaranja pukotina u točki Kaiserova efekta. Velik broj primljenih impulsa pokazao je da se broj novonastalih pukotina naglo povećava unutar raspona Kaiserova efekta. Osim toga, dobivena visoka vrijednost vršne frekvencije implicira da je brzina širenja pukotine visoka u točki 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 različite metode za određivanje in situ naprezanja. Većina uobičajenih metoda koje se koriste za određivanje in situ naprezanja vremenski su i financijski zahtjevne te je u mnogim slučajevima potrebna posebna pristupačnost. Stoga se sve više pažnje posvećuje metodama temeljenim na ispitivanjima provedenim na jezgrama. Jedna je od tih metoda i metoda akustičke emisije koja se temelji na Kaiserovu efektu. Ubraja se u metode naprezanja postupcima opterećenja i rasterećenja, a temelji se na promatranju ponašanja stijena bez znatnoga utjecaja na nju. Poznavanje principa akustičke emisije i parametara akustičkoga signala prvi je korak u primjeni metode za određivanje 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 različite metode za određivanje Kaiserova efekta u okviru parametara (metoda tangente i maksimalni nagib itd.) i obrade signala (Fourierova transformacija, valićna transformacija i sl.). Pored navedenog, rezultati dobiveni metodom Kaiserova efekta uspoređeni su s drugim uobičajenim metodama koje se koriste za mjerenje in situ naprezanja, kao što su overcoring metoda i metoda hidrauličkoga frakturiranja te je na temelju rezultata ustanovljena znatna podudarnost između njih. Također su istraženi ključni parametri za određivanje točke naprezanja kod Kaiserova efekta. Ključni parametri bili su postupak ispitivanja, ograničavajući tlak, fizička svojstva stijene, vrijeme kašnjenja i vrijeme zadržavanja, smjer i količina opterećenja, kut anizotropije i brzina opterećenja

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 “properly colored” 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