This study uses a mathematical model to optimize radiation fractionation schedules by allowing fraction sizes to vary over time. The model accounts for how tumor geometry, sensitivity, and repopulation change as the tumor shrinks during treatment. Optimizing fraction sizes increased the tumor control probability from 0.7 to 0.966. The optimal schedule used larger fractions on Friday afternoons to compensate for weekend breaks, with afternoon fractions being larger than morning fractions. Fraction sizes also escalated over the course of treatment as the tumor became more sensitive and grew faster.
Physical Models For Time Dose & FractionationIsha Jaiswal
Physical Models For Time Dose & Fractionation
Strandqvist Plot
Cohen’s Formula
Fowler Concepts
NSD Model
TDF model
Target Theory
L Q model
BED calculation of different fractionation regimen
describes relationship between radiation dose and the fraction of cells that “survive” that dose
model of cell killing
target model
linear quadratic model
The combined use of radiation therapy and chemotherapy in cancer treatment is a logical and reasonable approach that has already proven beneficial for several malignancies.
Introduction
Time dose & fractionation
Therapeutic index
Four R’s Of Radiobiology
Radiation response
Survival Curves Of Early & Late Responding Cells
Various fractionation schedules
Clinical trials of altered fractionation
Physical Models For Time Dose & FractionationIsha Jaiswal
Physical Models For Time Dose & Fractionation
Strandqvist Plot
Cohen’s Formula
Fowler Concepts
NSD Model
TDF model
Target Theory
L Q model
BED calculation of different fractionation regimen
describes relationship between radiation dose and the fraction of cells that “survive” that dose
model of cell killing
target model
linear quadratic model
The combined use of radiation therapy and chemotherapy in cancer treatment is a logical and reasonable approach that has already proven beneficial for several malignancies.
Introduction
Time dose & fractionation
Therapeutic index
Four R’s Of Radiobiology
Radiation response
Survival Curves Of Early & Late Responding Cells
Various fractionation schedules
Clinical trials of altered fractionation
A presentation and talk at the engagelocal conference (engagelocal.org): ournalists work more intimately with their communities to educate and empower residents? Two Oakland-based journalists will share insights from their local experiments, Hack the Hood and Eyes on Oakland, that blur the lines between journalism, art, education and community organizing. They'll offer out-of-the-box tips on how to jumpstart inclusive, on-the-ground initiatives that invite community members to learn, create and share. Susan Mernit | Hack the Hood; Cole Goins, Reveal and CIR
Preso describing how nonprofits can plan and execute a social media campaign, based on analysis of 2008-09 Knight News Challenge. Presented at Seizing the Moment, SF State Renaissance Center conference for ethnic & community media.
How does search engine oprimisation (SEO) work? What are some of the common SEO factors? This beginner level presentation is a quick guide to get you up to speed to how search engines operate.
For more SEO tips and tricks for your business, visit our site: http://www.ewebmarketing.com.au/
06 - Proposition d’Adoption de la Stratégie de Spécialisation Intelligente en...Mohamed Larbi BEN YOUNES
Proposition d’Adoption de la Stratégie de Spécialisation Intelligente en Tunisie / Adoption of a Strategy for Smart Specialisation in Tunisia
Ms. Sana MRIZAK, Télécom École de management, Évry, France
Séminaire sur la Stratégie de Spécialisation Intelligente / S3 organisé par l'ANPR avec le support de l'UE les 17 et 18 mai 2016 à Hammamet.
Dose Evaluation in the Movement Couch of the Total Body Irradiation Technique...iosrjce
IOSR Journal of Applied Physics (IOSR-JAP) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of physics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in applied physics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Co-Chairs Kurt A. Schalper, MD, PhD, and Vamsidhar Velcheti, MD, prepared useful Practice Aids pertaining to solid tumor for this CME/MOC activity titled “PATHway to Decoding the Impact of Cancer Immunotherapy: Latest Advances in Biomarker Testing and Pathologic Response Assessment.” For the full presentation, downloadable Practice Aids, and complete CME/MOC information, and to apply for credit, please visit us at https://bit.ly/3SsmiMV. CME/MOC credit will be available until February 14, 2025.
Chair & Moderator, Prof. Solange Peters, MD, PhD, Mark M. Awad, MD, PhD, and Jonathan D. Spicer, MD, PhD, FRCSC, prepared useful Practice Aids pertaining to Cancer Immunotherapy for this CME/MOC/CC activity titled “Parsing the Practicalities of Pathologic Response Assessment After Neoadjuvant Immunotherapy to Facilitate Progress in Early-Stage Cancers.” For the full presentation, downloadable Practice Aids, and complete CME/MOC/CC information, and to apply for credit, please visit us at https://bit.ly/3uRHyjk. CME/MOC/CC credit will be available until May 9, 2023.
Co-Chairs, Nasser Altorki, MD, and Jonathan D. Spicer, MD, PhD, FRCSC, prepared useful Practice Aids pertaining to NSCLC for this CME/MOC activity titled “How to Integrate Perioperative Immunotherapy Into Multimodal Treatment Plans to Improve Outcomes in Resectable NSCLC.” For the full presentation, downloadable Practice Aids, and complete CME/MOC information, and to apply for credit, please visit us at https://bit.ly/3xb6WS1. CME/MOC credit will be available until June 14, 2023.
Co-Chairs, Nasser Altorki, MD, and Jonathan D. Spicer, MD, PhD, FRCSC, prepared useful Practice Aids pertaining to NSCLC for this CME/MOC activity titled “Realizing the Promise of Perioperative Immunotherapy in Resectable NSCLC: How to Modernize Best Practices Based on New Evidence and Better Multidisciplinary Alliances.” For the full presentation, downloadable Practice Aids, and complete CME/MOC information, and to apply for credit, please visit us at http://bit.ly/3Gqancr. CME/MOC credit will be available until February 20, 2024.
We tested the hypothesis that macromolecular agents will have a greater sensitivity in identifying areas of high regional mammary tumor permeability-surface area products than low molecular weight agents. New modalities such as ultrasound, MRI, and nuclear medicine may improve breast cancer diagnosis(1). MRI can detect small tumors, 1 mm, with nearly 100% sensitivity(2) and can differentiate benign from malignant tumors with an accuracy of only 30 to 40%(3). A need exists for more accurately characterizing tumor specificity with MR mammography. Dynamic contrast enhanced MR mammography shows promise, and is based on differences in capillary density. Only a subset of tumor cells acquire angiogenic activity and this results in heterogeneous capillary density and surface area(4). High regional capillary density indicates poor prognosis(5). Tumor secreted factors induce angiogenesis, including vascular endothelial growth factor (VEGF), which is necessary for metastasis and regions high in VEGF exhibit hyperpermeability(6). Some of the physiological byproducts of angiogenesis regulate the extraction of an agent by a tumor from the blood. This extraction depends on (a) capillary surface area, S, (b) capillary permeability, P, (c) capillary blood flow, F, (d) transit time of the agent through the tumor interstitium, and (e) the plasma half-life, T1/2 DIST(7, 8). By imaging the time evolution of a contrast agent in the lesion, one can model agent extraction. Knowing the plasma half-life of an agent and regional blood flow provides a measure of the capillary surface area and permeability. Such knowledge may provide a means of differentiating benign from malignant tumors.
how to sell pi coins on Bitmart crypto exchangeDOT TECH
Yes. Pi network coins can be exchanged but not on bitmart exchange. Because pi network is still in the enclosed mainnet. The only way pioneers are able to trade pi coins is by reselling the pi coins to pi verified merchants.
A verified merchant is someone who buys pi network coins and resell it to exchanges looking forward to hold till mainnet launch.
I will leave the telegram contact of my personal pi merchant to trade with.
@Pi_vendor_247
What price will pi network be listed on exchangesDOT TECH
The rate at which pi will be listed is practically unknown. But due to speculations surrounding it the predicted rate is tends to be from 30$ — 50$.
So if you are interested in selling your pi network coins at a high rate tho. Or you can't wait till the mainnet launch in 2026. You can easily trade your pi coins with a merchant.
A merchant is someone who buys pi coins from miners and resell them to Investors looking forward to hold massive quantities till mainnet launch.
I will leave the telegram contact of my personal pi vendor to trade with.
@Pi_vendor_247
how to sell pi coins in South Korea profitably.DOT TECH
Yes. You can sell your pi network coins in South Korea or any other country, by finding a verified pi merchant
What is a verified pi merchant?
Since pi network is not launched yet on any exchange, the only way you can sell pi coins is by selling to a verified pi merchant, and this is because pi network is not launched yet on any exchange and no pre-sale or ico offerings Is done on pi.
Since there is no pre-sale, the only way exchanges can get pi is by buying from miners. So a pi merchant facilitates these transactions by acting as a bridge for both transactions.
How can i find a pi vendor/merchant?
Well for those who haven't traded with a pi merchant or who don't already have one. I will leave the telegram id of my personal pi merchant who i trade pi with.
Tele gram: @Pi_vendor_247
#pi #sell #nigeria #pinetwork #picoins #sellpi #Nigerian #tradepi #pinetworkcoins #sellmypi
what is the best method to sell pi coins in 2024DOT TECH
The best way to sell your pi coins safely is trading with an exchange..but since pi is not launched in any exchange, and second option is through a VERIFIED pi merchant.
Who is a pi merchant?
A pi merchant is someone who buys pi coins from miners and pioneers and resell them to Investors looking forward to hold massive amounts before mainnet launch in 2026.
I will leave the telegram contact of my personal pi merchant to trade pi coins with.
@Pi_vendor_247
Empowering the Unbanked: The Vital Role of NBFCs in Promoting Financial Inclu...Vighnesh Shashtri
In India, financial inclusion remains a critical challenge, with a significant portion of the population still unbanked. Non-Banking Financial Companies (NBFCs) have emerged as key players in bridging this gap by providing financial services to those often overlooked by traditional banking institutions. This article delves into how NBFCs are fostering financial inclusion and empowering the unbanked.
where can I find a legit pi merchant onlineDOT TECH
Yes. This is very easy what you need is a recommendation from someone who has successfully traded pi coins before with a merchant.
Who is a pi merchant?
A pi merchant is someone who buys pi network coins and resell them to Investors looking forward to hold thousands of pi coins before the open mainnet.
I will leave the telegram contact of my personal pi merchant to trade with
@Pi_vendor_247
Poonawalla Fincorp and IndusInd Bank Introduce New Co-Branded Credit Cardnickysharmasucks
The unveiling of the IndusInd Bank Poonawalla Fincorp eLITE RuPay Platinum Credit Card marks a notable milestone in the Indian financial landscape, showcasing a successful partnership between two leading institutions, Poonawalla Fincorp and IndusInd Bank. This co-branded credit card not only offers users a plethora of benefits but also reflects a commitment to innovation and adaptation. With a focus on providing value-driven and customer-centric solutions, this launch represents more than just a new product—it signifies a step towards redefining the banking experience for millions. Promising convenience, rewards, and a touch of luxury in everyday financial transactions, this collaboration aims to cater to the evolving needs of customers and set new standards in the industry.
what is the future of Pi Network currency.DOT TECH
The future of the Pi cryptocurrency is uncertain, and its success will depend on several factors. Pi is a relatively new cryptocurrency that aims to be user-friendly and accessible to a wide audience. Here are a few key considerations for its future:
Message: @Pi_vendor_247 on telegram if u want to sell PI COINS.
1. Mainnet Launch: As of my last knowledge update in January 2022, Pi was still in the testnet phase. Its success will depend on a successful transition to a mainnet, where actual transactions can take place.
2. User Adoption: Pi's success will be closely tied to user adoption. The more users who join the network and actively participate, the stronger the ecosystem can become.
3. Utility and Use Cases: For a cryptocurrency to thrive, it must offer utility and practical use cases. The Pi team has talked about various applications, including peer-to-peer transactions, smart contracts, and more. The development and implementation of these features will be essential.
4. Regulatory Environment: The regulatory environment for cryptocurrencies is evolving globally. How Pi navigates and complies with regulations in various jurisdictions will significantly impact its future.
5. Technology Development: The Pi network must continue to develop and improve its technology, security, and scalability to compete with established cryptocurrencies.
6. Community Engagement: The Pi community plays a critical role in its future. Engaged users can help build trust and grow the network.
7. Monetization and Sustainability: The Pi team's monetization strategy, such as fees, partnerships, or other revenue sources, will affect its long-term sustainability.
It's essential to approach Pi or any new cryptocurrency with caution and conduct due diligence. Cryptocurrency investments involve risks, and potential rewards can be uncertain. The success and future of Pi will depend on the collective efforts of its team, community, and the broader cryptocurrency market dynamics. It's advisable to stay updated on Pi's development and follow any updates from the official Pi Network website or announcements from the team.
Introduction to Indian Financial System ()Avanish Goel
The financial system of a country is an important tool for economic development of the country, as it helps in creation of wealth by linking savings with investments.
It facilitates the flow of funds form the households (savers) to business firms (investors) to aid in wealth creation and development of both the parties
Exploring Abhay Bhutada’s Views After Poonawalla Fincorp’s Collaboration With...beulahfernandes8
The financial landscape in India has witnessed a significant development with the recent collaboration between Poonawalla Fincorp and IndusInd Bank.
The launch of the co-branded credit card, the IndusInd Bank Poonawalla Fincorp eLITE RuPay Platinum Credit Card, marks a major milestone for both entities.
This strategic move aims to redefine and elevate the banking experience for customers.
Even tho Pi network is not listed on any exchange yet.
Buying/Selling or investing in pi network coins is highly possible through the help of vendors. You can buy from vendors[ buy directly from the pi network miners and resell it]. I will leave the telegram contact of my personal vendor.
@Pi_vendor_247
how to sell pi coins at high rate quickly.DOT TECH
Where can I sell my pi coins at a high rate.
Pi is not launched yet on any exchange. But one can easily sell his or her pi coins to investors who want to hold pi till mainnet launch.
This means crypto whales want to hold pi. And you can get a good rate for selling pi to them. I will leave the telegram contact of my personal pi vendor below.
A vendor is someone who buys from a miner and resell it to a holder or crypto whale.
Here is the telegram contact of my vendor:
@Pi_vendor_247
1. Dynamic Optimization of a Linear-Quadratic Model with Incomplete Repair and Volume-Dependent Sensitivity and Repopulation Lawrence M. Wein Jonathan E. Cohen
2. Abstract Purpose : The linear-quadratic model typically assumes that tumor sensitivity and repopulation are constant over the time course of radiotherapy. However, evidence suggests that the growth fraction increases and the cell loss factor decreases as the tumor shrinks. We investigate whether this evolution in tumor geometry , as well as the irregular time intervals between fractions in hyperfractionation schemes, can be exploited by fractionation schedules that employ time-varying fraction sizes .
3. Methods: We construct a mathematical model of a spherical tumor with a hypoxic core and a viable rim , and embed this model into the traditional linear-quadratic model by assuming instantaneous reoxygenation. Dynamic programming is used to numerically compute the fractionation regimen that maximizes the tumor control probability (TCP) subject to constraints on the biologically effective dose of the early and late tissues.
4. Results: In a numerical example that employs 10 fractions per week, optimally varying the fraction sizes increases the TCP from 0.7 to 0.966 , and the optimal regimen incorporates large Friday afternoon doses that are escalated throughout the course of treatment, and larger afternoon doses than morning doses. Conclusions: Numerical results suggest that a significant increase in tumor cure can be achieved by allowing the fraction sizes to vary throughout the course of treatment. Several strategies deserve further investigation: using larger fractions before overnight and weekend breaks , and escalating the dose (particularly on Friday afternoons) throughout the course of treatment.
5. Linear Quadratic Model: Survival Curves plot the fraction of cells surviving radiation against the dose. This survival curve is best described by a linear quadratic model with the following formula: S = e -( α D + β D2) The α and β terms in this equation and the α / β ratio are used to describe survival curve characteristics and to classify cellular response to radiation.
6. Tumor Control Probability Success or failure in controlling a tumor depends on killing the last surviving clonogen . Therefore, in terms of attempting permanent tumor control, if even one clonogen survives, the whole dose is wasted . A plot of control versus dose for a single tumor is therefore one of 0% response up to a certain dose and then an immediate increase to 100% response at the death of the last clonogen. However, the shape of the tumor control probability (TCP) curve for a series of patients , is different because cell killing is a random process. For example, if on an average 4 cars will cross a particular speed breaker in a road in one minute , what is the probability that no car will cross the point in a particular minute, or the probability that 1 car will cross the point. The answer to this question is given by the Poisson Distribution .
7. Similarly, if a certain dose were to reduce the cell survival to an average of one clonogen per tumor , there would be, on average, among the series 37% with no survivors , 37% with one surviving clonogen, 18.4% with two surviving clonogens, 6.1% with three surviving clonogens, and 1.5% with four or more surviving clonogens. This 37% of tumors with no surviving clonogen will be declared cured, and the tumor control probability (TCP) is 37%. Poisson statistics correlate probability of tumor control with cell survival rate by the following formula: P=e -x where x is the average number of surviving clonogens per tumor, which in turn is the product of S.F. (fraction of cells surviving) and M (initial cell number).
8. This study was stimulated by two perceived gaps in the LQ literature. The first gap is that the use of temporal optimization to exploit the irregular time intervals present in traditional non-accelerated protocols has yet to be studied. The second gap is the failure of the LQ model to capture the dynamics of reoxygenation and repopulation throughout the course of treatment. Evidence suggests that the evolution of tumor geometry during radiation treatment and its impact on radiosensitivity and repopulation can be exploited by time-varying fractionation regimens to further improve the therapeutic ratio. As a tumor shrinks during the course of therapy, diffusion-limited hypoxia decreases and necrotic regions become smaller and may eventually vanish.
9.
10. Tumor geometry . We consider a spherical tumor that consists of a hypoxic core and a viable rim . The tumor's size is defined by its radius R , which changes over time as a result of radiation killing, necrotic loss and repopulation. R If the current radius R is less than ro , (Oxygen Diffusion Distance) then the tumor contains no hypoxic core. R < ro R > ro If R > ro then the viable rim consists of the outer shell of thickness ro and the hypoxic core is the inner sphere of radius R - ro.
11. Location-dependent sensitivity and repopulation. In our model, a cell's sensitivity ( α and β ) and its net repopulation rate ( γ ) depends upon its radial distance, r , from the center of the tumor, and on the current tumor radius, R. All three quantities, which will be defined by α (r, R), β (r, R) and γ (r, R), take on a fixed well-oxygenated level (denoted by α 0, β 0, γ 0 ) at the tumor surface (i.e., r = R) and decrease linearly as r decreases. α 0, β 0, γ 0 (r=R) 0,0,0 (r=R-ro)
12. A tumor's overall sensitivity and repopulation rate. If f( α , β , γ ) is the joint probability density function of the three parameters for the various cells in a tumor of fixed size ,then the expected surviving fraction of cells after a dose of size d given over the infinitesimal interval of time The effective values of α , β , and γ are given by, respectively.
13. The equivalent ODE . Suppose an arbitrary dose rate dt is applied over the time interval [0, T]. The surviving fraction of cells under the traditional (i.e., constant α and β and γ = 0 ) LQ model with incomplete repair (with repair rate μ ) is α D β D 2 To obtain an analogous result for volume-dependent sensitivity ( α t , β t ) and repopulation ( γ t ), we use the ODE model. Because the sensitivity and repopulation functions are expressed in terms of the radius, we need to express the differential equation in terms of the radius, not the number of cells.
14. Problem formulation: The optimization problem is to choose a radiation schedule that maximizes the tumor control probability (TCP), subject to a constraint on the biologically effective dose (BED) of the early and late tissues . Mathematically, the problem is to choose T and {dt > 0, 0 < t < T} to maximize Subject to constraints
15. Results: We restrict our numerical study to fractionation schemes that have 10 fractions per week. Time t = 0 corresponds to the first fraction given on Monday morning, there are two fractions per day that are separated by eight hours (each fraction's duration is one minute), and there is no treatment on the weekends. First, the initial tumor radius Ro is set equal to 0.5 cm , which corresponds to a typical tumor at the time of presentation. We set the viable rim radius ro equal to 0.05 cm , which is about three times larger than the oxygen diffusion limit in tumor tissue in order to reflect the fact that a tumor of this size would be vascularized. This value leads to 27.1% of the tumor being viable initially. The loss rate for necrotic debris is taken to be
16. To assess the efficacy of the optimal solution, we compare it to the best static (i.e., fraction sizes do not vary over time) scheme, the hyperfractionation (HF) (70 fractions x 1.15 Gy) regimen and whose TCP is 0.7. The optimal solution to is displayed in Figure. This scheme administers a total of 66.81 Gy in six weeks , and achieves a TCP of 0.966 , which is a significant improvement over HF's TCP of 0.7. The resulting BED administered to the early and late tissues is 4.59 Gy and 98.5 Gy, respectively. Hence, the early constraint is binding under the optimal scheme but the late constraint has a slack of 13 Gy.
17. The optimal solution in Figure possesses several interesting features. The most pronounced effect is the large doses on Friday afternoons . These large fractions are primarily used to compensate for the weekend breaks. However, a secondary factor could be that tumors are also smaller on Friday afternoon than at other times of the week, and smaller tumors are more sensitive and may attract larger fractions . There is also a significant am-pm effect : 60.0% of the total dose on Monday through Thursdays is administered in the afternoons . These large afternoon fractions offset the repopulation during the 16-hour gap until the next morning's fraction. A third feature of Figure is the intensification of the Friday afternoon doses throughout the course of treatment.
18. Discussion: The foundation of the rationale for current fractionation schemes is the exploitation of the differences in radiation sensitivity and repopulation between the tumor and the normal (primarily late) tissue. Recent results show how the difference in repair rates can also be exploited by temporally optimizing the dose rate in accelerated protocols. The results in the present paper complement these ideas by suggesting that the therapeutic ratio can be further improved by exploiting two other factors : Irregular time intervals between doses caused by overnight and weekend breaks, and the changing radiosensitivity and repopulation rate of the tumor caused by reoxygenation.
19. The weekend break was the most pronounced effect in our numerical example, causing Friday afternoon doses to be about 3.5 times larger than the other doses. The overnight effect was also significant, with afternoon doses accounting for 60.0% of the total dose administered on Mondays through Thursdays. The tumor increased its radiosensitivity and repopulation rates throughout the course of treatment , leading to 16.8% larger Friday afternoon doses in the latter three weeks of treatment than in the first three weeks of treatment. The optimal fractionation scheme compensates for irregular time intervals between doses by administering larger doses before longer breaks and shorter doses before shorter breaks .
20. The optimal radiation policy exploits the reoxygenation process by taking into account the fact that as the tumor gets smaller , the tumor's sensitivity increases. Hence, giving large doses at the beginning of therapy is wasteful , since some of this dose can kill more cells if it is deferred until the tumor is smaller. Moreover, as the tumor shrinks, the growth fraction increases and the cell loss factor decreases, and consequently the repopulation rate increases . This provides an additional incentive to increase the dose rate (thereby reducing the length of treatment) when the tumor is smaller. In summary, an optimal radiation policy attempts to exercise patience when faced with a large tumor: it slowly and methodically chips away at the outer surface of the tumor, until the hypoxic core is sufficiently small, at which time the dose rate is increased until the end of treatment.
21. Clinical Relevance: Dose intensification throughout the course of treatment can also be seen in concomitant boost (CB) therapy , where daily 1.8 Gy fractions are given for six weeks to the standard large field, plus an additional 1.5 Gy fraction is delivered to a reduced field on a daily basis for the last 10-12 days of treatment. The boost appears to be more efficacious when administered late in treatment rather than early, which is consistent with our results .
22. Future Directions: Our results suggest that there is untapped potential for the use of dynamic fractionation schemes that incorporate the overnight effect, the weekend effect and the dose escalation effect . Our hope is that these types of models and analyses will provide a systematic way of generating and refining approaches to improve the therapeutic ratio of radiotherapy by temporal optimization of dose schedules.