A 3D Mathematical Model of Coupled Stem Cell-Nutrient Dynamics in Myocardial Regeneration Therapy

2022 ◽  
pp. 111023
Author(s):  
D. Andreucci ◽  
A.M. Bersani ◽  
E. Bersani ◽  
F.J. León Trujillo ◽  
S. Marconi
2015 ◽  
Author(s):  
david miguez

The understanding of the regulatory processes that orchestrate stem cell maintenance is a cornerstone in developmental biology. Here, we present a mathematical model based on a branching process formalism that predicts average rates of proliferative and differentiative divisions in a given stem cell population. In the context of vertebrate spinal neurogenesis, the model predicts complex non-monotonic variations in the rates of pp, pd and dd modes of division as well as in cell cycle length, in agreement with experimental results. Moreover, the model shows that the differentiation probability follows a binomial distribution, allowing us to develop equations to predict the rates of each mode of division. A phenomenological simulation of the developing spinal cord informed with the average cell cycle length and division rates predicted by the mathematical model reproduces the correct dynamics of proliferation and differentiation in terms of average numbers of progenitors and differentiated cells. Overall, the present mathematical framework represents a powerful tool to unveil the changes in the rate and mode of division of a given stem cell pool by simply quantifying numbers of cells at different times.


Stem Cells ◽  
2020 ◽  
pp. 17-50
Author(s):  
Violetta A. Maltabe ◽  
Theofilos M. Kolettis ◽  
Panos Kouklis

Blood ◽  
2013 ◽  
Vol 122 (21) ◽  
pp. 2709-2709
Author(s):  
Rick Proschmann ◽  
Meinolf Suttorp ◽  
Andreas Hochhaus ◽  
Christian Thiede ◽  
Ingo Roeder ◽  
...  

Abstract Introduction Treatment of chronic myeloid leukemia (CML) with imatinib (IM) has replaced stem cell transplantation as first line therapy also in pediatric patients (pts). Although CML is rare in the first 2 decades of life, pediatric studies published recently have indicated that like in adults most pts achieve prolonged molecular response (MR). In adults it could be demonstrated that IM monotherapy induces a biphasic decline of BCR-ABL1 transcript levels, characterized by an initially steep decline (α-slope) documenting the rapid initial depletion of actively cycling BCR-ABL1–positive cells, followed by a 2nd moderate decline (β-slope), most likely indicating the slow elimination of residual leukemic stem cells (rLSK) with low turnover. In adults regular monitoring of the BCR-ABL1/ABL1 ratio during IM therapy allowed detailed mathematical modelling to predict the abundance of rLSK, which is a major determinant to access the relapse risk after treatment cessation (Horn et al, Blood 2013). A similar assessment of individual relapse risk is even more important in children because long-term IM exposure is associated with longitudinal growth retardation and may increase the risk for cardiac failure at younger age. Therefore, we sought to evaluate and adapte the existing mathematical model as established for adult German pts from the IRIS and CML IV trial to children and teenagers. Methods For statistical analysis of IM treatment response in children (trial CML-PAED-II) and adults (German arm IRIS) we required a minimal essential data set of >=7 consecutive BCR-ABL1 level measurements over at least a follow-up interval >1.5 years. Early non-responders within that interval were excluded. Data from 56 pediatric pts (male/female: 34/22; median age 12 years, range 1-18; median follow up 30.7 mos) and 60 adult pts (male/female 43/17; median age 51.5years, range 21-69, median follow up 57.4 mos) were included. For comparison of pediatric and adult cohorts a segmented linear regression model was applied to characterise the pt-specific decline of BCR-ABL1/ABL1-ratios. Five parameters were analyzed in a comparative fashion: i) the α-slope; ii) the β-slope; iii) backwards extrapolation of the α-slope (corresponding to an estimation of the BCR-ABL1 level at diagnosis); and at the breakpoint of α- and β-curves: iv) the transcript ratio as well as, v) the time point (months on IM treatment). For the corresponding modelling approach, we use an established single cell-based model of CML dynamics under IM treatment to estimate the fraction of rLSK (Roeder et al, Nat Med 2006). Results In 42/56 pediatric and in 54/60 adult pts a biphasic slope of transcript decline patterns was identified. A comparison of median response curves documented a slightly higher, however, not significant reduction of transcript ratios in the pediatric cohort with a tendency to achieve lower ratios at the breakpoint of the biphasic decline (mean BCR-ABL1 ratio adults vs pediatric: 0.103 %/ 0.051 %). This effect is attributed to a significantly increased heterogeneity in the initial IM response (SD of mean ratio adults versus pediatric: 0.63/1.2 log scales). For the α- and β-slopes no statistically significant difference was observed between the cohorts. We used the available data to adapt our mathematical model for pediatric CML, in which the slightly increased reduction in BCR-ABL1 levels in children can be attributed to an increased sensitivity to IM or an increased stem cell turnover. However, the increased heterogeneity in the initial IM response in children limits the model’s ability to provide refined risk estimators for treatment cessation and calls for the integration of further parameters. Conclusions Statistical analysis revealed distinct features of pediatric CML with respect to the dynamic response to IM treatment. In particular, we observed an increased heterogeneity in the IM response pointing towards a subgroup of pediatric pts that achieves MR4 during the initial decline (11 out of 42 children versus 2 out of 54 adults). We will further adapt our mathematical modelling approach for pediatric CML to estimate whether relapse-free treatment cessation is achieved more likely in these pts. Thereby, the model-based analysis and predictions on CML dynamics demonstrated to become useful for optimization of treatment strategies also in pediatric pts. Disclosures: Hochhaus: Novartis: Consultancy, Honoraria, Research Funding, Travel Other; BMS: Consultancy, Honoraria, Research Funding; Pfizer: Consultancy, Honoraria; Ariad: Consultancy, Honoraria.


Heart Disease ◽  
2002 ◽  
Vol 4 (4) ◽  
pp. 205 ◽  
Author(s):  
William H. Frishman ◽  
Piero Anversa

2001 ◽  
Vol 43 (7) ◽  
pp. 47-54 ◽  
Author(s):  
W. Zeng ◽  
M. B. Beck

A mathematical model (Sediment-Transport-Associated Nutrient Dynamics - STAND) has been developed for the study of sediment-associated water quality issues. The model is intended to simulate changes of water composition associated with sediment behavior. It has a 3-level structure. The first level accounts for the hydraulics of open-channel flow. The second computes sediment transport potential and actual rates based on the information provided by the first level. A non-equilibrium approach is used. In the third level, changes of nutrient concentrations along a studied river are computed with the consideration of nutrient transport, adsorption/desorption, and release. In order to calibrate the model, field data were collected from the Oconee River, a major tributary of the Altamaha River in Georgia, USA. Two stations, approximately 17 km distant from each other, were established along the river for the purpose of data collection. Observations of the river's hydraulics, suspended sediment, and water quality (mainly ortho-phosphate, nitrate, temperature, specific conductivity, oxidation-reduction potential, dissolved oxygen, and pH) were collected at the two stations. Another data set collected along a major tributary of the Yellow River in China was also used for calibration of the model's hydraulics and sediment transport parts. Calibration and validation results are encouraging, which suggests STAND may be a useful tool for the thorough study and understanding of nutrient dynamics associated with sediment behaviour.


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