Stochastic Norton-Simon-Massagu\ue9 Tumor Growth Modeling: Controlled and Mixed-Effects Uncontrolled Analysis

Tumorigenesis is a complex process that is heterogeneous and affected by numerous sources of variability. This study presents a stochastic extension of a biologically grounded tumor growth model, referred to as the Norton-Simon-Massagu\ue9 (NSM) tumor growth model. We first study the uncontrolled version of the model where the effect of chemotherapeutic drug agent is absent. Conditions on the model\u2019s parameters are derived to guarantee the positivity of the tumor volume and hence the validity of the proposed stochastic NSM model. To calibrate the proposed model we utilize a maximum likelihood- based estimation algorithm and population mixed-effect modeling formulation. The algorithm is tested by fitting previously published tumor volume mice data. Then, we study the controlled version of the model which includes the effect of chemotherapy treatment. Analysis of the influence of adding the control drug agent into the model and how sensitive it is to the stochastic parameters is performed both in open-loop and closed-loop viewpoints through different numerical simulations

The Australasian Resuscitation In Sepsis Evaluation : fluids or vasopressors in emergency department sepsis (ARISE FLUIDS), a multi-centre observational study describing current practice in Australia and New Zealand

Objectives: To describe haemodynamic resuscitation practices in ED patients with suspected sepsis and hypotension. Methods: This was a prospective, multicentre, observational study conducted in 70 hospitals in Australia and New Zealand between September 2018 and January 2019. Consecutive adults presenting to the ED during a 30-day period at each site, with suspected sepsis and hypotension (systolic blood pressure <100 mmHg) despite at least 1000 mL fluid resuscitation, were eligible. Data included baseline demographics, clinical and laboratory variables and intravenous fluid volume administered, vasopressor administration at baseline and 6- and 24-h post-enrolment, time to antimicrobial administration, intensive care admission, organ support and in-hospital mortality. Results: A total of 4477 patients were screened and 591 were included with a mean (standard deviation) age of 62 (19) years, Acute Physiology and Chronic Health Evaluation II score 15.2 (6.6) and a median (interquartile range) systolic blood pressure of 94 mmHg (87–100). Median time to first intravenous antimicrobials was 77 min (42–148). A vasopressor infusion was commenced within 24 h in 177 (30.2%) patients, with noradrenaline the most frequently used (n = 138, 78%). A median of 2000 mL (1500–3000) of intravenous fluids was administered prior to commencing vasopressors. The total volume of fluid administered from pre-enrolment to 24 h was 4200 mL (3000–5661), with a range from 1000 to 12 200 mL. Two hundred and eighteen patients (37.1%) were admitted to an intensive care unit. Overall in-hospital mortality was 6.2% (95% confidence interval 4.4–8.5%). Conclusion: Current resuscitation practice in patients with sepsis and hypotension varies widely and occupies the spectrum between a restricted volume/earlier vasopressor and liberal fluid/later vasopressor strategy

Scaling relations and critical exponents for two dimensional two parameter maps

In this paper we calculate the critical scaling exponents describing the variation of both the positive Lyapunov exponent, λ+, and the mean residence time, $\langle$τ$\rangle$, near the second order phase transition critical point for dynamical systems experiencing crisis-induced intermittency. We study in detail 2-dimensional 2-parameter nonlinear quadratic mappings of the form: Xn+1 = f1(Xn, Yn; A, B) and Yn+1 = f2(Xn, Yn; A, B) which contain in their parameter space (A, B) a region where there is crisis-induced intermittent behaviour. Specifically, the Henon, the Mira 1, and Mira 2 maps are investigated in the vicinity of the crises. We show that near a critical point the following scaling relations hold: $\langle$τ$\rangle$ ~ |A – Ac|-γ, (λ+ – λc+) ~ |A – Ac|βA and (λ+ – λc+) ~ |B – Bc|βB. The subscript c on a quantity denotes its value at the critical point. All these maps exhibit a chaos to chaos second order phase transition across the critical point. We find these scaling exponents satisfy the scaling relation γ = βB($\frac{1}{\beta_{A}}$ – 1), which is analogous to Widom's scaling law. We find strong agreement between the scaling relationship and numerical results

Scaling relations and critical exponents for two dimensional two parameter maps

In this paper we calculate the critical scaling exponents describing the variation of both the positive Lyapunov exponent, λ + , and the mean residence time, $\langle$ τ $\rangle$ , near the second order phase transition critical point for dynamical systems experiencing crisis-induced intermittency. We study in detail 2-dimensional 2-parameter nonlinear quadratic mappings of the form: X n+1 =f 1 (X n , Y n ; A, B) and Y n+1 =f 2 (X n , Y n ; A, B) which contain in their parameter space (A, B) a region where there is crisis-induced intermittent behaviour. Specifically, the Henon, the Mira 1, and Mira 2 maps are investigated in the vicinity of the crises. We show that near a critical point the following scaling relations hold: $\langle$ τ $\rangle$ ~ |A – A c | -γ , (λ + – λ c + ) ~ |A – A c | βA and (λ + – λ c + ) ~ |B – B c | βB . The subscript c on a quantity denotes its value at the critical point. All these maps exhibit a chaos to chaos second order phase transition across the critical point. We find these scaling exponents satisfy the scaling relation γ=β B ( $\frac{1}{\beta_{A}}$ – 1), which is analogous to Widom’s scaling law. We find strong agreement between the scaling relationship and numerical results. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010

The Australasian Resuscitation In Sepsis Evaluation: Fluids or vasopressors in emergency department sepsis (ARISE FLUIDS), a multi-centre observational study describing current practice in Australia and New Zealand

OBJECTIVES: To describe haemodynamic resuscitation practices in ED patients with suspected sepsis and hypotension. METHODS: This was a prospective, multicentre, observational study conducted in 70 hospitals in Australia and New Zealand between September 2018 and January 2019. Consecutive adults presenting to the ED during a 30-day period at each site, with suspected sepsis and hypotension (systolic blood pressure <100 mmHg) despite at least 1000 mL fluid resuscitation, were eligible. Data included baseline demographics, clinical and laboratory variables and intravenous fluid volume administered, vasopressor administration at baseline and 6- and 24-h post-enrolment, time to antimicrobial administration, intensive care admission, organ support and in-hospital mortality. RESULTS: A total of 4477 patients were screened and 591 were included with a mean (standard deviation) age of 62 (19) years, Acute Physiology and Chronic Health Evaluation II score 15.2 (6.6) and a median (interquartile range) systolic blood pressure of 94 mmHg (87-100). Median time to first intravenous antimicrobials was 77 min (42-148). A vasopressor infusion was commenced within 24 h in 177 (30.2%) patients, with noradrenaline the most frequently used (n = 138, 78%). A median of 2000 mL (1500-3000) of intravenous fluids was administered prior to commencing vasopressors. The total volume of fluid administered from pre-enrolment to 24 h was 4200 mL (3000-5661), with a range from 1000 to 12 200 mL. Two hundred and eighteen patients (37.1%) were admitted to an intensive care unit. Overall in-hospital mortality was 6.2% (95% confidence interval 4.4-8.5%). CONCLUSION: Current resuscitation practice in patients with sepsis and hypotension varies widely and occupies the spectrum between a restricted volume/earlier vasopressor and liberal fluid/later vasopressor strategy