A second-order, unconditionally positive, mass-conserving integration scheme for biochemical systems.

Biochemical systems are bound by two mathematically-relevant restrictions. First, state variables in such systems represent non-negative quantities, such as concentrations of chemical compounds. Second, biochemical systems conserve mass and energy. Both properties must be reflected in results of an integration scheme applied to biochemical models. This paper first presents a mathematical framework for biochemical problems, which includes an exact definition of biochemical conservation: elements and energy, rather than state variable units, are conserved. We then analyze various fixed-step integration schemes, including traditional Euler-based schemes and the recently published modified Patankar schemes, and conclude that none of these deliver unconditional positivity and biochemical conservation in combination with higher-order accuracy. Finally, we present two new fixed-step integration schemes, one first-order and one second-order accurate, which do guarantee positivity and (biochemical) conservatio

Numerical continuation of equilibria of physiologically structured population models

The paper introduces a new numerical method for continuation of equilibria of models describing physiologically structured populations. To describe such populations, we use integral equations coupled with each other via interaction (or feedback) variables. Additionally we allow interaction with unstructured populations, described by ordinary differential equations. The interaction variables are chosen such that if they are given functions of time, each of the resulting decoupled equations becomes linear. Our numerical procedure to approximate an equilibrium will use heavily this special form of the underlying equations. We also establish a method for local stability analysis of equilibria in dependence on parameters

Does Diabetes Accelerate the Progression of Aortic Stenosis through Enhanced Inflammatory Response within Aortic valves?

Diabetes predisposes to aortic stenosis (AS). We aimed to investigate if diabetes affects the expression of selected coagulation proteins and inflammatory markers in AS valves. Twenty patients with severe AS and concomitant type 2 diabetes mellitus (DM) and 40 well-matched patients without DM scheduled for valve replacement were recruited. Valvular tissue factor (TF), TF pathway inhibitor (TFPI), prothrombin, C-reactive protein (CRP) expression were evaluated by immunostaining and TF, prothrombin, and CRP transcripts were analyzed by real-time PCR. DM patients had elevated plasma CRP (9.2 [0.74–51.9] mg/l vs. 4.7 [0.59–23.14] mg/l, p = 0.009) and TF (293.06 [192.32–386.12] pg/ml vs. 140 [104.17–177.76] pg/ml, p = 0.003) compared to non-DM patients. In DM group, TF−, TFPI−, and prothrombin expression within valves was not related to demographics, body mass index, and concomitant diseases, whereas increased expression related to DM was found for CRP on both protein (2.87 [0.5–9]% vs. 0.94 [0–4]%, p = 0.01) and transcript levels (1.3 ± 0.61 vs. 0.22 ± 0.43, p = 0.009). CRP-positive areas were positively correlated with mRNA TF (r = 0.84, p = 0.036). Diabetes mellitus is associated with enhanced inflammation within AS valves, measured by CRP expression, which may contribute to faster AS progression

Reasons for not reaching or using web-based self-management applications, and the use and evaluation of Oncokompas among cancer survivors, in the context of a randomised controlled trial

Introduction: The web-based self-management application Oncokompas was developed to support cancer survivors to monitor health-related quality of life and symptoms (Measure) and to provide tailored information (Learn) and supportive care options (Act). In a previously reported randomised controlled trial (RCT), 68% of 655 recruited survivors were eligible, and of those 45% participated in the RCT. Among participants of the RCT that were randomised to the intervention group, 52% used Oncokompas as intended. The aim of this study was to explore reasons for not participating in the RCT, and reasons for not using Oncokompas among non-users, and the use and evaluation of Oncokompas among users. Methods: Reasons for not participating were assessed with a study-specific questionnaire among 243 survivors who declined participation. Usage was investigated among 320 participants randomised to the intervention group of the RCT via system data and a study-specific questionnaire that was assessed during the 1 week follow-up (T1) assessment. Results: Main reasons for not participating were not interested in participation in scientific research (40%) and not interested in scientific research and Oncokompas (28%). Main reasons for not being interested in Oncokompas were wanting to leave the period of being ill behind (29%), no symptom burden (23%), or lacking internet skills (18%). Out of the 320 participants in the intervention group 167 (52%) used Oncokompas as intended. Among 72 non-users, main reasons for not using Oncokompas were no symptom burden (32%) or lack of time (26%). Among 248 survivors that activated their account, satisfaction and user-friendliness were rated with a 7 (scale 0–10). Within 3 (IQR 1–4) sessions, users selected 32 (IQR 6–37) topics. Main reasons for not using healthcare options in Act were that the information in Learn was already sufficient (44%) or no supportive care needs (32%). Discussion: Main reasons for not reaching or using Oncokompas were no symptom burden, no supportive care needs, or lack of time. Users selected many cancer-generic and tumour-specific topics to address, indicating added value of the wide range of available topics