scholarly journals Optimal Interval for Detection of Molecular Relapse after Stop of TKI in Ph+ ALL Calculating By MRD Kinetics

Blood ◽  
2018 ◽  
Vol 132 (Supplement 1) ◽  
pp. 5291-5291
Author(s):  
Koichi Miyamura ◽  
Satoshi Nishiwaki
Keyword(s):  
Mathematical Model ◽  
Growth Rate ◽  
Doubling Time ◽  
Detection Threshold ◽  
The Body ◽  
Leukemia Cells ◽  
Intervention Threshold ◽  
Detection Level ◽  
Optimal Intervention ◽  
As If

Abstract In the era of new-generation tyrosine kinase inhibitors (TKIs), prognosis of Ph+ leukemia (CML/ALL) has dramatically improved. Furthermore the number of CML patients who have stopped TKI is increasing. Usually TKI is stopped in patients who have sustained a deep molecular response. The MRD monitoring interval and threshold of restarting TKI is mostly established in CML. In Ph+ALL patients, prophylactic/maintenance administrations of TKI are used during post hematopoietic stem cell transplantation (HSCT) as well as post chemotherapy. Unlike CML, currently there are no standard methods of detection BCR-ABL in Ph+ALL and no established selection of patients who can stop TKI. In addition, after TKI stopped, there is no consensus about how often to monitor to detect molecular relapse and threshold of restart for TKI. In the current study, we tried to determine the optimal frequency of MRD monitor after the cessation of TKI in Ph+ALL using a mathematical model. In this model, we determined several agreed items. Mimicking CML, we defined BCR-ABL/ABL ratio of 0.1% as"MR3" and undetectable levels of BCR-ABL transcript as "MR5". We estimate that patients with MR3 and MR5 have 109 and 107 Ph+ cells in the body, respectively. In this perspective, we defined "MR3" and "MR5" as "optimal intervention threshold" and "detection threshold". From the literatures, we determined that growth rate of leukemia is distributed between 1%/day and 100%/day (doubling time of leukemic cells is 1 day). Also, we assumed that single cell have a relapse potency and the growth rate is constant during observation in each patient. The number of Ph+ cells in a MR5 patient is distributed between 1 cell and 1 x 107 (MR5). "Success" is defined as if molecular relapse is detected between MR3 and MR5 and "Failure" is defined as if detected more than MR3. Table shows the interval from single leukemia cell to MR5 leukemia burden (1 x 107 cells) and the interval from MR5 to MR3 (X100) according to growth rate. Figure is a graph of Table. We calculated using most extreme cases. In the highest growing speed (100%/day), if the number of Ph+ cells is just below detection level (MR5) , it will take 6.6 days to reach MR3 (optimal intervention threshold). Also, if the number of Ph+ cells is only 1 cell, it will take 23.3 days to reach MR5. The other ultimate condition is that the number of leukemia cells is only one in the body and has the slowest growth rate (1%/day). In this case it will take 1620 days (4.4 years) to reach MR5. It was reported that the growth rate of Ph+ cells in the blastic phase of CML is approximately 8% (doubling time 9 days) (Branford. Blood. 2012;119:4264). Applying this value to our model, it will take 209 days to reach MR5 (detection threshold) from single Ph+ cell. If the number of leukemia cells is just below the detection level (MR5), it will take 60 days to reach MR3 (optimal intervention threshold). In this patient a 2 months interval can detect MRD before it reaches to MR3 (Success). If 1 Ph+ cell remains when TKI is stopped, it will reach the MRD detection level (MR5) in 269 days. If Ph+ cells does not appear until this time, this patient is supposed to be cured in this model. In the clinical setting, growth rate is unknown. Thus in the beginning, a highest growth rate of 100% is applied. (Figure) Monitoring should be performed every 6.6 days for avoiding MRD is detected over MR3 (Failure). If Ph+ cells does not appear until 23.3 days after stop of TKI, which indicate growth rate of 100% is neglected. Because MRD does not increase from MR5 to MR3 during 23.3 days, the growth rate is less than 21.8% from the Table and Graph. At this point, interval MRD monitoring can be prolonged from 6.6 to 23.3 days until 82 days after stop of TKI. Similarly, if Ph+ cells does not appear at 82 days, growth rate is calculated less than 5.8% and interval can be prolonged from 23.3 to 82 days until 290 days. Again if Ph+ cells does not appear, now growth rate is estimated less than 1.6%. Taken together, soon after stop of TKI, frequent monitoring of MRD is needed. The interval can be prolonged with the passage of time. After allogeneic HSCT, the growth rate of leukemia may be down regulated to some extent according to the GVL effect. At the detection of MRD, interventions such as TKI, donor lymphocyte infusion or chemotherapy are started as soon as possible. Thus the tight monitoring according to the mathematical model is important. The current strategy may be applied to other leukemia in which MRD monitoring by PCR is established. Figure. Figure. Disclosures No relevant conflicts of interest to declare.

Optimal Interval for Detection of Molecular Relapse after Stop of Tyrosine Kinase Inhibitor (TKI) in Philadelphia Chromosome Positive Acute Lymphoblastic Leukemia (Ph+ALL) Caliculated By Kinetics of BCR-ABL Transcripts

Blood ◽  
2020 ◽  
Vol 136 (Supplement 1) ◽  
pp. 21-21
Author(s):  
Koichi Miyamura ◽  
Masahide Osaki ◽  
Tatsunori Goto ◽  
Takanobu Morishita ◽  
Yukiyasu Ozawa
Keyword(s):  
Mathematical Model ◽  
Growth Rate ◽  
Clinical Data ◽  
Kinetic Data ◽  
Doubling Time ◽  
Tumor Burden ◽  
Molecular Response ◽  
Optimal Frequency ◽  
Optimal Interval ◽  
As If

Background In Ph+ALL patients, prophylactic/maintenance administrations of TKI are used after the protocol treatment. Unlike Chronic myelogenous leukemia (CML), after TKI stopped, there is no consensus about how often to monitor to detect molecular relapse. In the current study, from clinical data of 31 patients we tried to determine the optimal frequency of MRD monitor for better prognosis using a mathematical model. Methods Doubling time (DT) and Growth rate (GR) were retrospectively calculated by the increase of BCR-ABL from 99 kinetic data from 31 patients with Ph+ALL at molecular relapse. Measurement of amount BCR-ABL was performed by RQ-PCR. Mimicking CML, we defined BCR-ABL/ABL ratio of 0.1% as "MR3 (Major molecular response)" and undetectable levels of BCR-ABL transcript as "MR5 (Complete molecular response)". In order to investigate the relationship between tumor burden (BCR/ABL) at the time of MRD detection and prognosis, it was divided into 3 groups, BCR/ABL<0.1% (MR3), 0.1%<BCR/ABL<1% (MR2) and BCR/ABL>1% (MR1). This study was approved by the institutional review committee. Results The doubling time was 1.3 days (GR 0.7%/day) to 95.4 days (70.8%/day) with a median of 12.3 days (5.8%). The rate of increase was compared by three groups of tumor burden. The DT among patients in MR1 was shorter than those in MR3 and MR2 (7.7 days vs 15.2 days in median, t-test p<0.01). There were no differences of DT in sex, age, treatments and BCR/ABL mutation. Most patient had multiple kinetic data and the smallest amount of BCR/ABL was used in each patient. Among 8 patients who showed MR3 (MR3pt) and 11 who showed MR2 (MR2pt), 14 are alive at this analysis, while among 10 patients who showed MR1 (MR1pt), only 1 patient is alive.(Log-rank test, p<0.1) (Figure) Median survival time is 882 days, 330 days and 16 days in MR3pt, Mr2pt and MR1pt, respectively. All patients died of progression of the disease. Finding molecular relapse before MR2 may related to better results. Optimal interval of MRD detection We set several hypotheses to determine the optimal frequency to detect early recurrence of leukemia. We estimated that patients with MR2 and MR5 have 1010 and 107 Ph+ cells in body, respectively. We defined "MR2" and "MR5" as "optimal intervention threshold" and "detection threshold". From our clinical data, we tentatively determined that doubling time of leukemia growth is distributed between 1 day (GR 100%/day) and 100days (0.7%). Also, we assumed that single cell has a relapse potency and the GR is constant during observation in each patient. The number of Ph+ cells in a MR5 patient who would potentially relapse might be distributed between 1 cell and 1 x 107 (MR5). "Success" was defined as if molecular relapse is detected between M5 and MR2 and "Failure" was defined as if detected more than MR2. According to the daily clinical practice, the optimal examination interval is tentatively every 7 days, every 14 days, every 28 days, every 56 days, every 84 days, every 6 months, and every year. First, in order to calculate the growth rate that would be successful at 7-day intervals, the rate of 168%/day for 1 cell to increase 107 (MR5) in 7 days was calculated. This rate is faster than the maximum rate of 100%/day in this study, so an interval of 7 days is good for the initial period. Similarly, at 14-day intervals, 68%/day is calculated, and in this case, it requires 32 days to increase 107 (MR5) from 1 cell. As a result, after 32.7 days, 14-day intervals are acceptable. Similarly, the calculated results for 28 days, 56 days, 84 days, 6 months, and 1 year are shown in the Table. MRD can be found before M3 (success) with 28-day intervals after 65 days, 56-day intervals after 131 days, 84-day intervals after 196 days, 6-month intervals after 419 days and 1-year intervals after 852 days. Conclusion Taken together, soon after stop of TKI, more frequent monitoring of MRD than in "treatment free remission" in CML is needed. The interval can be prolonged with the passage of time. In several patients, hematopoietic stem cell transplantation (HSCT) was possible due to early intervention by changing TKI and chemotherapy. After HSCT, TKI combined with rapid reduction of immune-suppressants and donor lymphocyte infusion successfully related with long term survival. (data will be shown in ASH) Thus, the tight monitoring according to the mathematical model is important. The current strategy may be applied to other leukemia in which MRD monitoring by PCR is established. Disclosures Miyamura: Bristol-Myers Squibb Co., Ltd.:Honoraria;Celgene Co., Ltd.:Honoraria;Daiichi-Sankyo Co., Ltd.:Honoraria;Otsuka Co., Ltd.:Honoraria;Pfizer Co., Ltd.:Honoraria;Novartis Co., Ltd.:Honoraria.Goto:Takeda Pharmaceutical Co., Ltd:Honoraria;Novartis Pharma Co., Ltd.:Honoraria.Morishita:Bristol-Myers Squibb Co., Ltd.:Honoraria.Ozawa:Novartis Co., Ltd.:Honoraria.

Impact of Electric Vehicle Lateral Dynamics on the Battery Pack

2014 ◽  
Vol 590 ◽  
pp. 451-457
Author(s):  
Sen Nan Song ◽  
Fa Chao Jiang ◽  
Hong Shi
Keyword(s):  
Mathematical Model ◽  
Angular Acceleration ◽  
Simulation Software ◽  
The Body ◽  
Battery Pack ◽  
Vehicle Body ◽  
Rolling Motion ◽  
Rolling Angle ◽  
On The Road ◽  
The Mathematical Model

The present work is concerned with the rolling motion of the battery pack when EV travelling on the road. First McPherson suspension system was regarded as the research object with detailed analysis of its structural features and motion characteristics. Establish the mathematical model which could apply to calculating the rolling motion of the vehicle body. Through MATLAB/Simulink simulation software, we could calculate the rolling angle on passive suspension. On this basis, assume that the battery pack mounted on the vehicle body and make it passive connection and PID connection. When the body rolls, the battery pack will produce a certain angle then. Next establish the mathematical model to summarize the relationship between the two variables. Then we set the parameters and calculate the roll angle of battery pack in both cases for comparison. Simulation results show that road irregularities will make battery rotate an angle and PID controller can effectively reduce the angle, especially angular acceleration. This paper put forward a new idea that battery is connected with body by active control on EV, and proves the superiority in reducing the rolling angle.

scholarly journals The ameliorative effect of selenium on Azolla caroliniana grown under UV-B stress

2015 ◽  
Vol 95 (1) ◽  
pp. 20-26 ◽  
Author(s):  
E.M. Mostafa ◽  
A.M.A. Hassan
Keyword(s):  
Growth Rate ◽  
Protein Content ◽  
Doubling Time ◽  
The Other ◽  
Total Glutathione ◽  
Nutrient Media ◽  
Relative Growth ◽  
Other Hand ◽  
Ameliorative Effect ◽  
Glutathione Redox

Exposure ofAzollaplants to UV-B radiation for 6 h resulted in a decrease in biomass and relative growth rate (RGR), which coincided with an increase in doubling time (DT) as compared with the control. Also, the protein content decreased. On the other hand, hydrogen peroxyde (H2O2) and malondialdehyde (MDA) accumulated significantly in UV-treatedAzollaplants. Conversely, the addition of selenium (Se) at 1 ppm resulted in a significant increase in biomass and protein content of untreated and UV-treatedAzollaplants, and a significant reduction in both H2O2and MDA. Moreover, the addition of Se to UV-treated and untreatedAzollaplants resulted in a significant increase in total ascorbate and total glutathione (GSH) contents compared with the control and UV-stressedAzollaplants. Also, glutathione redox potential (GSH/TG) increased significantly in UV-treatedAzollaplants in the presence of Se. There also was a significant increase (38%) in ascorbate peroxidase (APX) activity in UV-treated plants compared with the control. APX activity in the presence of Se did not change significantly compared with the control. Glutathione reductase (GR) activity increased significantly in UV-treatedAzolla, while glutathione peroxidase (GSH-PX) activity did not. On the other hand, both GSH-PX and GR activity in untreated and UV-treatedAzollaplants were significantly enhanced by the application of Se to the nutrient media at a concentration of 1 ppm. Therefore, we can conclude that Se protectsAzollaplants from UV-B stress.

The physical basis of mollusk shell chiral coiling

2021 ◽  
Vol 118 (48) ◽  
pp. e2109210118
Author(s):  
Régis Chirat ◽  
Alain Goriely ◽  
Derek E. Moulton
Keyword(s):  
Mathematical Model ◽  
The Body ◽  
Symmetric Body ◽  
Model Organisms ◽  
Physical Interaction ◽  
Mechanical Forces ◽  
Hard Shell ◽  
Left Right Asymmetry ◽  
Development And Evolution ◽  
Mollusk Shell

Snails are model organisms for studying the genetic, molecular, and developmental bases of left–right asymmetry in Bilateria. However, the development of their typical helicospiral shell, present for the last 540 million years in environments as different as the abyss or our gardens, remains poorly understood. Conversely, ammonites typically have a bilaterally symmetric, planispiraly coiled shell, with only 1% of 3,000 genera displaying either a helicospiral or a meandering asymmetric shell. A comparative analysis suggests that the development of chiral shells in these mollusks is different and that, unlike snails, ammonites with asymmetric shells probably had a bilaterally symmetric body diagnostic of cephalopods. We propose a mathematical model for the growth of shells, taking into account the physical interaction during development between the soft mollusk body and its hard shell. Our model shows that a growth mismatch between the secreted shell tube and a bilaterally symmetric body in ammonites can generate mechanical forces that are balanced by a twist of the body, breaking shell symmetry. In gastropods, where a twist is intrinsic to the body, the same model predicts that helicospiral shells are the most likely shell forms. Our model explains a large diversity of forms and shows that, although molluscan shells are incrementally secreted at their opening, the path followed by the shell edge and the resulting form are partly governed by the mechanics of the body inside the shell, a perspective that explains many aspects of their development and evolution.

Numerical modelling of swirling momentumless turbulent wake dynamics

2018 ◽  
pp. 37-48
Author(s):  
Андрей Геннадьевич Деменков ◽  
Геннадий Георгиевич Черных
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Equations Of Motion ◽  
Turbulent Wake ◽  
The Body ◽  
Jet Flows ◽  
Reynolds Stresses ◽  
Bodies Of Revolution ◽  
Averaged Equations

С применением математической модели, включающей осредненные уравнения движения и дифференциальные уравнения переноса нормальных рейнольдсовых напряжений и скорости диссипации, выполнено численное моделирование эволюции безымпульсного закрученного турбулентного следа с ненулевым моментом количества движения за телом вращения. Получено, что начиная с расстояний порядка 1000 диаметров от тела течение становится автомодельным. На основе анализа результатов численных экспериментов построены упрощенные математические модели дальнего следа. Swirling turbulent jet flows are of interest in connection with the design and development of various energy and chemical-technological devices as well as both study of flow around bodies and solving problems of environmental hydrodynamics, etc. An interesting example of such a flow is a swirling turbulent wake behind bodies of revolution. Analysis of the known works on the numerical simulation of swirling turbulent wakes behind bodies of revolution indicates lack of knowledge on the dynamics of the momentumless swirling turbulent wake. A special case of the motion of a body with a propulsor whose thrust compensates the swirl is studied, but there is a nonzero integral swirl in the flow. In previous works with the participation of the authors, a numerical simulation of the initial stage of the evolution of a swirling momentumless turbulent wake based on a hierarchy of second-order mathematical models was performed. It is shown that a satisfactory agreement of the results of calculations with the available experimental data is possible only with the use of a mathematical model that includes the averaged equations of motion and differential equations for the transfer of normal Reynolds stresses along the rate of dissipation. In the present work, based on the above mentioned mathematical model, a numerical simulation of the evolution of a far momentumless swirling turbulent wake with a nonzero angular momentum behind the body of revolution is performed. It is shown that starting from distances of the order of 1000 diameters from the body the flow becomes self-similar. Based on the analysis of the results of numerical experiments, simplified mathematical models of the far wake are constructed. The authors dedicate this work to the blessed memory of Vladimir Alekseevich Kostomakha.

The Shroud of Turin

1997 ◽  
Vol 9 (1) ◽  
pp. 121-140
Author(s):  
Thaddeus J. Trenn ◽  
Keyword(s):  
Body Image ◽  
Scientific Evidence ◽  
The Body ◽  
Religious Art ◽  
Satisfactory Explanation ◽  
Marshall Mcluhan ◽  
Modern Age ◽  
Shroud Of Turin ◽  
High Degree ◽  
As If

The Shroud of Turin, a linen cloth with but a faint image, continues to capture the interest of many people of diverse beliefs. Although the measured age of the cloth is relatively recent, other scientific findings indicate an earlier provenance. Any firm conclusions regarding the cloth's history remain premature. No satisfactory explanation has been found as yet for how the image on the cloth was produced structurally or stylistically. Iconographic evidence suggests that the image was the source of facial peculiarities found in early works of religious art. The body image bears a striking yet preternatural correlation with Scriptural accounts of wounds. Curiously, the image on the cloth functions as a photographic negative, exhibiting a high degree of resolution, as if the original were produced in pixels. Despite serious efforts to discover some artistic origin md medium, scientific evidence points in the direction that it was not produced by hands. If it is tme that the medium is the message, as Marshall McLuhan wrote, then the Turin Shroud may be a parable for the modern age.

Simulation of cancer treatment using the MATLAB SimBiology application

2021 ◽  
Vol 14 (3) ◽  
pp. 90-96
Author(s):  
Anastasia Goncharova ◽  
Maria Vil'
Keyword(s):  
Mathematical Model ◽  
Cancer Treatment ◽  
Interference Competition ◽  
The Body ◽  
Continuous Treatment ◽  
Constant Concentration ◽  
Application Package ◽  
The Mathematical Model ◽  
Cancerous Cells

The paper presents the implementation of the mathematical model of cancer taking into account interference competition and the model of continuous treatment with a constant concentration of the drug in the patient's blood. The implementation was carried out using the MATLAB SimBiology application package. The principle of implementation of different stages of the course of the disease within the framework of one model is described. On the basis of the constructed models and SimBiology tools, a modification was carried out that implements the discrete administration of doses of the drug in courses and takes into account its dynamics in the body, taking into account the assumption that the drug is consumed only to suppress cancerous cells.

XXIV. Observations on the Chariots of the antient Britains. By the Rev. Mr. Pegge. In a Letter to the Rev. Mr. Norris

Archaeologia ◽  
1785 ◽  
Vol 7 ◽  
pp. 211-213
Author(s):  
Pegge
Keyword(s):  
The Body ◽  
Common Mistake ◽  
Proper Name ◽  
The Common ◽  
As If

Besides the common mistake of the annalists and historians in regard to this passage in Juvenal,Regem aliquem capies, aut de temone BritannoExcidet Arviragus—Juvenal IV. 126.By taking Arviragus for the proper name of a person, and not of an officer; the words of the satyrist are memorable in another respect, as serving to inform us, by the word temone, of a singular mode of fighting amongst the Britons; as if by leaving his carriage, and running upon the pole, the combatant from thence, or from the yoke, engaged the enemy, as long as he thought prudent and convenient, and then retreated back into the body of the vehicle.

scholarly journals Magnetic behaviour of supraconducting tin spheres

1935 ◽  
Vol 151 (873) ◽  
pp. 316-333 ◽  
Author(s):  
K. Mendelssohn ◽  
J. D. Babbitt ◽  
Frederick Alexander Lindemann
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Magnetic Force ◽  
Magnetic Behaviour ◽  
The Body ◽  
Whole Body ◽  
Measured Field ◽  
Lines Of Force ◽  
As If ◽  
Field Strengths

Until a year ago it was generally accepted that if a body is made supraconducting while in a magnetic field the lines of magnetic force were "frozen in," i. e ., whatever lines of force passed through the body at the time when it became supraconducting remained there afterwards, unaffected by any change in the external field, so long as the body was supraconducting. Meissner and Ochsenfeld, however, showed that this supposition was not true. They measured field strengths in the immediate neighbourhood of cylinders which had been cooled to supraconductivity in an external magnetic field, and found that the field of force was then of the same nature as that to be expected in the neighbourhood of perfectly diamagnetic bodies. Thus it appeared that when a body becomes supraconducting in a magnetic field the lines of force are all pressed out of the body, and the induction inside the body falls to zero. At the same time, however, these authors report on another experiment, the result of which appears to us not entirely in accordance with the assumption that the induction in the whole body became zero. They measured the field strengths inside and outside a hollow cylinder, after it had become supraconducting in a field perpendicular to its axis, and found again that the field strength outside was as if the cylinder were almost perfectly diamagnetic, but the field inside was appreciably the same as if the cylinder were non-supraconducting. We therefore made a number of experiments, hoping to find out more exactly the nature of the phenomenon.

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