Getting ones head around beer science Andr Heck
Getting one’s head around beer science André Heck, University of Amsterdam METMAS seminar Aspects of mathematical education at technical schools and universities, Brno, December 7, 2015
Getting one’s head around beer science Video analysis and modelling in authentic student research
Getting one’s head around beer science Goals of student activities • Bring reality into the classroom • Learn math & science with food and drink • Connect experimentation and mathematical modelling • Give opportunity to work professionally with a computer, in particular the COACH environment, as an instrument to o carry out experiments and collect data o control of apparatus and processes o measure on digital images and video clips o process and analyse data o work with and build computer models o work with and build computer animations • Do not merely follow standard recipes, but engage in the full process: ‘Students act as real scientists and practitioners’
Getting one’s head around beer science A model of quantitative mathematical modelling Always look at the descriptive, predictive and explanatory qualtity of a model
Getting one’s head around beer science Two remaining parts in the talk 1. Collapse of the head of a beer (before & during drinking) 2. Intake and clearance of alcohol in humans (during & after drinking)
Collapse of the head of a beer: Preferences of head and lacing What kind of head and lacing do you prefer? Smythe & Bamforth (2003). Food Quality and Preference, 14, 567– 572.
Collapse of the head of a beer: Video analysis Heck (2009). Teaching Mathematics and its Applications, 28(4), 164 179. Video analysis as a tool to collect and analyse data: Change of the head of a beer (low speed video)
Collapse of the head of a beer: Various experimental models Experimental modelling: regression analysis using • exponential decay of foam height (Wet. Foam. H) • limited exponential growth of liquid height (Beer. H) • bi exponential models of foam height and liquid height • exponential decay of Dry. Beer. H defined as Dry. Foam. H = Wet. Foam. H – (Final. Beer. H) in: Hackbarth, J. (2006). Journal of the Institute of Brewing, 112(1), 17 24 Next step: modelling based on systems of differential equations in a graphical system dynamics based approach
Collapse of the head of a beer : Graphical models based on system dynamics Graphical system dynamics based modelling of foam height
Collapse of the head of a beer: Graphical models based on system dynamics Graphical system dynamics based modelling of beer height
Collapse of the head of a beer: Graphical models based on system dynamics Mixed model
Collapse of the head of a beer: Important phases in creation, retention and collapse of beer foam: 1. Bubble formation (oversaturation CO 2 at 4 °C; nuclei needed) 2. Creaming (bubble creation and rise in beer) 3. Drainage (of liquid from foam to beer) 4. Disproportionation (gas moving from small to large bubbles) 5. Lacing (adherence of foam to the side of the glass) Steps modelled by exponential decay: 3 and 4 Neglected step in modelling: 5
Collapse of the head of a beer: Advanced model of beer and foam height Advanced model
Intake and clearance of alcohol in humans: Getting drunk and sober again • Facts & figures • Simple models • Advanced models • Conclusions • References 14
Intake and clearance of alcohol in humans: Some facts about alcohol use of Dutch pupils (dated 2006) • First alcohol drink between the age of 11 and 14. • At age 15: • 90% ever drank alcohol • 50% drink weekly • 63% got drunk once (33% every month) • 67% prefer alcoholic drinks • 6% children between age 12 and 17 are heavy drinkers. • Binge drinking is not unusual. (during weekends and holidays, average = 17 glasses) • Annually, 500 1000 children (especially girls, 12 14 yrs) are hospitalized because of alcohol poisoning (average promillage: 1. 84 ‰; 3 hours of lost consciousness) • 25% of young pupils think that it takes at least 10 glasses to get drunk; only 11% say that 4 glasses of less suffice.
Intake and clearance of alcohol in humans: Trends • Number of emergency treatments because of alcohol intoxication + gender and age distribution
Intake and clearance of alcohol in humans: Basics • Blood Alcohol Concentration (BAC) = amount of alcohol : total amount of body water • Most of alcohol is metabolized in the liver via enzymes • 2 5% of unmodified alcohol is excreted in breath, sweat and urine • Individual differences: gender, weight, height, physical condition, medication, full or empty stomach, activities, … • Standard unit = 10 gram ethanol
Intake and clearance of alcohol in humans: Measurement and modelling • Modeling is more than understanding the model. Focus on understanding the phenomenon investigated. Comparison of model with real, measured data is important. Equipment used: Dräger Alcotest 6510 (accuracy: 0. 017‰) Legal limits in the Netherlands: 0. 5 ‰ (g/L = mg/m. L), 0. 2 ‰ (since 1/1/2006) for moped rider < 24 yrs and car driver with license < 5 yrs.
Intake and clearance of alcohol in humans: Some aspects of modeling • Modeling process: – Simplify and create a model – Estimate parameters – Evaluate the model, preferably by comparison with real data – Adapt the model (undo simplifications, take more factors into account) – Play with the model (what ifs) • Promotion of a critical attitude of students by looking at various models of the same phenomenon • Students use the same theoretical framework, methods and techniques as practicing professionals. • Most pharmacokinetic models are compartmental models • Lesson materials: Swilling, shooting and swallowing
Intake and clearance of alcohol in humans: Simple compartmental models • Widmark model – Open 1 compartmental model with 0 th order elimination • Wagner model – Open 1 compartmental mode with enzymatic kinetics
Intake and clearance of alcohol in humans: Widmark model Theoretical BAC curve after drinking 2 standard units: Computer simulation
Intake and clearance of alcohol in humans: Widmark model BAC curve, drinking 8 standard units at regular intervals. Comparing model and reality in a computer simulation.
Intake and clearance of alcohol in humans: Wagner model Theoretical BAC curve after drinking 3 standard units. Computer simulation
Intake and clearance of alcohol in humans: Adding compartments to the model • Norberg model – 2 compartmental model – central compartment (blood plasma, kidneys, liver) – peripheral compartment (other tissues)
Intake and clearance of alcohol in humans: Pieters 3 -compartment model empty stomach (a<0), full stomach (a>0)
Intake and clearance of alcohol in humans: Simulation of Pieters 3 -compartment model BAC curve, drinking 3 standard units at once after fasting. Comparing model and reality in a computer simulation.
Intake and clearance of alcohol in humans: Physiologically based 5 -compartment model of Umulis et al (2005) The liver is divided into segments that each contribute to alcohol metabo lism
Intake and clearance of alcohol in humans: Simulation of the Umulis model
Intake and clearance of alcohol in humans: Clinical trial real data, empty stomach. What if full stomach?
Intake and clearance of alcohol in humans: Conclusions • The subject of alcohol intake and clearance is attractive. • Graphical modelling allows pupils to implement and apply models that are really used in (research) practice. • Pupils’ critical attitude can be stimulated by – comparing models with reality; – looking at more than one model of the same phenomenon. • Compartmental modelling is a general purpose method that also applies to many other processes.
Intake and clearance of alcohol in humans: References • http: //staff. fnwi. uva. nl/a. j. p. heck • Heck (2007). Getting Drunk and Sober Again. Electronic Proceedings of Modeling in Physics and Physics Education, GIREP 2006 Conference, University of Amsterdam. • Heck (2007). Modelling Intake and Clearance of Alcohol in Humans. Electronic Journal of Mathematics and Technology, Vol. 1, No. 3. • Pieters, Wedel, & Schaafsma (1990). Parameter estimation in a three compart ment model for blood alcohol curves. Alcohol & Alcoholism 25 (1) 17 24. • Norberg, Å (2001). Clinical Pharmacokinetics of Intravenous Ethanol: Relationship Between the Ethanol Space and Total Body Water. Ph. D thesis. Karolinska University: Stockholm, Sweden. https: //openarchive. ki. se/xmlui/bitstream/handle/10616/40010/thesis. pdf? sequence=1
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