Biological Dynamics of Stress Response

At ISDC 2018, we gave the Dana Meadows Award for best student paper to Gizem Aktas, for Modeling the Biological Mechanisms that Determine the Dynamics of Stress Response of the Human Body (with Yaman Barlas)This is a very interesting paper that elegantly synthesizes literature on stress, mood, and hormone interactions. I plan to write more about it later, but for the moment, here’s the model for your exploration.

The dynamic stress response of the human body to stressors is produced by nonlinear interactions among its physiological sub-systems. The evolutionary function of the response is to enable the body to cope with stress. However, depending on the intensity and frequency of the stressors, the mechanism may lose its function and the body can go into a pathological state. Three subsystems of the body play the most essential role in the stress response: endocrine, immune and neural systems. We constructed a simulation model of these three systems to imitate the stress response under different types of stress stimuli. Cortisol, glucocorticoid receptors, proinflammatory cytokines, serotonin, and serotonin receptors are the main variables of the model. Using both qualitative and quantitative physiological data, the model is structurally and behaviorally well-validated. In subsequent scenario runs, we have successfully replicated the development of major depression in the body. More interestingly, the model can present quantitative representation of some very well acknowledged qualitative hypotheses about the stress response of the body. This is a novel quantitative step towards the comprehension of stress response in relation with other disorders, and it provides us with a tool to design and test treatment methods.

The original is a STELLA model; here I’ve translated it to Vensim and made some convenience upgrades. I used the forthcoming XMILE translation in Vensim to open the model. You get an ugly diagram (due to platform differences and XMILE’s lack of support for flow-clouds), but it’s functional enough to browse. I cleaned up the diagrams and moved them into multiple views to take better advantage of Vensim’s visual approach.

The model ran right away, though I had to add one MAX statement to handle a uniflow (not supported in Vensim, and something I remain allergic to). There’s actually an important lesson on model replication and calibration in this.

When I first translated the model, I ran a few scenarios, using the comprehensive replication instructions in the supplemental material for the paper. I built up a Vensim command script to make it easy to replicate all the scenarios in the paper. To do that, I had to modify the equations a bit, so that manual equation editing (in STELLA) could be replaced by automatic parameter changes.

Then I ran my script and eyeballed a few graphs. Things looked pretty good:

The same, right? Not so fast! If you look closely, you’ll find that the Vensim version (bottom) has 9 peaks instead of 10, due to my replacement of a cascade of IF … ELSE test inputs with a simpler PULSE TRAIN. When you fix the count, there are still issues, because the duration parameter for each pulse (0.2) is not an integral multiple of the TIME STEP. (Incidentally, differences arising from PULSE implementations are tricky – see Yutaka Takahashi’s poster from ISDC 2018).

It took me several iterations to work out what was going wrong. I found that, to really verify that the translation (plus my initially erroneous upgrades) was OK, I had to export a run from STELLA, import it as a dataset in Vensim, and compare behavior hour by hour. That’s how I discovered the subtle but important uniflow difference.

The fact that tiny differences in test input implementations matter highlights the extreme numerical sensitivity of the model. This is a feature, not a bug. It arises from positive feedback that creates sensitive thresholds in stress response: 5% more episodic stress can be the difference between routine recovery and total collapse.

For example, here’s a sensitivity experiment with external stress at 10, 20, 30, 40, 50 & 60 units:

Notice that for external stress <= 40, recovery is quick – hours to days. But somewhere above 40 is a nonlinear threshold, beyond which recovery takes weeks.

This .zip archive contains:

  • An updated source model (.stmx) from the author, used for the translation.
  • The translated model (.mdl and .vpm). This version won’t work in PLE because it uses macros, but you can use the free Model Reader to run it.
  • Command scripts for replicating the paper’s scenarios, plus the vector of stress levels above.

StressResponseModel_converted 7.zip

Update: StressResponseModel_converted 7b.zip fixes a unit error in a test input (my mistake) – this version is closest to the original in the paper.

Update 2: StressResponseModel_converted 8.zip has an improved control panel and runs 4x faster. It departs from the original to improve sensitivity analysis capability and pulse test stability, but remains dynamically identical (as far as I can determine).

The original paper and supplementary material should be in the conference submission system.

Stay tuned for more on this topic! Here’s a detailed critique & analysis.

Dynamic Cohorts

This is the model library entry for my ISDC 2017 plenary paper with Larry Yeager on dynamic cohorts in Ventity:

Dynamic cohorts: a new approach to managing detail

While it is desirable to minimize the complexity of a model, some problems require the detailed representation of heterogeneous subgroups, where nonlinearities prevent aggregation or explicit chronological aging is needed. It is desirable to have a representation that avoids burdening the modeler or user computationally or cognitively. Eberlein & Thompson (2013) propose continuous cohorting, a novel solution to the cohort blending problem in population modeling, and test it against existing aging chain and cohort-shifting approaches. Continuous cohorting prevents blending of ages and other properties, at at some cost in complexity.

We propose another new solution, dynamic cohorts, that prevents blending with a comparatively low computational burden. More importantly, the approach simplifies the representation of distinct age, period and cohort effects and representation of dynamics other than the aging process, like migration and attribute coflows. By encapsulating the lifecycle of a representative cohort in a single entity, rather than dispersing it across many states over time, it makes it easier to develop and explain the model structure.

Paper: Dynamic Cohorts P1363.pdf

Models: Dynamic Cohorts S1363.zip

Presentation slides: Dynamic Cohorts Fid Ventana v2b.pdf

I’ve previously written about this here.

The Beer Game

The Beer Game is the classic business game in system dynamics, demonstrating just how tricky it can be to manage a seemingly-simple system with delays and feedback. It’s a great icebreaker for teams, because it makes it immediately clear that catastrophes happen endogenously and fingerpointing is useless.

The system demonstrates amplification, aka the bullwhip effect, in supply chains. John Sterman analyzes the physical and behavioral origins of underperformance in the game in this Management Science paper. Steve Graves has some nice technical observations about similar systems in this MSOM paper.

Here are two versions that are close to the actual board game and the Sterman article:

Beer Game Fiddaman NoSubscripts.zip

This version doesn’t use arrays, and therefore should be usable in Vensim PLE. It includes a bunch of .cin files that implement the (calibrated) decision heuristics of real teams of the past, as well as some sensitivity and optimization control files.

Beer Game Fiddaman Array.zip

This version does use arrays to represent the levels of the supply chain. That makes it a little harder to grasp, but much easier to modify if you want to add or remove levels from the system or conduct optimization experiments. It requires Vensim Pro or DSS, or the Model Reader.

Thyroid Dynamics

Quite a while back, I posted about the dynamics of the thyroid and its interactions with other systems.

That was a conceptual model; this is a mathematical model. This is a Vensim replication of:

Marisa Eisenberg, Mary Samuels, and Joseph J. DiStefano III

Extensions, Validation, and Clinical Applications of a Feedback Control System Simulator of the Hypothalamo-Pituitary-Thyroid Axis

Background:We upgraded our recent feedback control system (FBCS) simulation model of human thyroid hormone (TH) regulation to include explicit representation of hypothalamic and pituitary dynamics, and up-dated TH distribution and elimination (D&E) parameters. This new model greatly expands the range of clinical and basic science scenarios explorable by computer simulation.

Methods: We quantified the model from pharmacokinetic (PK) and physiological human data and validated it comparatively against several independent clinical data sets. We then explored three contemporary clinical issues with the new model: …

… These results highlight how highly nonlinear feedback in the hypothalamic-pituitary-thyroid axis acts to maintain normal hormone levels, even with severely reduced TSH secretion.

THYROID
Volume 18, Number 10, 2008
DOI: 10.1089=thy.2007.0388

This version is a superset of the authors’ earlier 2006 model, and closely reproduces that with a few parameter changes.

L-T4 Bioequivalence and Hormone Replacement Studies via Feedback Control Simulations

THYROID
Volume 16, Number 12, 2006

The model is used in:

TSH-Based Protocol, Tablet Instability, and Absorption Effects on L-T4 Bioequivalence

THYROID
Volume 19, Number 2, 2009
DOI: 10.1089=thy.2008.0148

This works with any Vensim version:

thyroid 2008 d.mdl

thyroid 2008 d.vpm

The Dynamics of Initiative Success

This is a new replication of a classic model, for the library. The model began in Nelson Repenning’s thesis, and was later published in Organization Science:

A Simulation-Based Approach to Understanding the Dynamics of Innovation Implementation

The history of management practice is filled with innovations that failed to live up to the promise suggested by their early success. A paradox currently facing organizational theory is that the failure of these innovations often cannot be attributed to an intrinsic lack of efficacy. To resolve this paradox, in this paper I study the process of innovation implementation. Working from existing theoretical frameworks, I synthesize a model that describes the process through which participants in an organization develop commitment to using a newly adopted innovation. I then translate that framework into a formal model and analyze it using computer simulation. The analysis suggests three new constructs—reversion, regeneration, and the motivation threshold—characterizing the dynamics of implementation. Taken together, the constructs provide an internally consistent theory of how seemingly rational decision rules can create the apparent paradox of innovations that generate early results but fail to produce sustained benefit.

An earlier version is online here.

This is another nice example of tipping points. In this case, an initiative must demonstrate enough early success to grow its support base. If it succeeds, word of mouth takes its commitment level to 100%. If not, the positive feedbacks run as vicious cycles, and the initiative fails.

When initiatives compete for scarce resources, this creates a success to the successful dynamic, in which an an initiative that demonstrates early success attracts more support, grows commitment faster, and thereby demonstrates more success.

This version is in Ventity, in order to make it easier to handle multiple competing initiatives, with each as a discrete entity. One initialization dataset for the model creates initiatives at random intervals, with success contingent on the environment (other initiatives) prevailing at the time of launch:

This archive contains two versions of the model: “Intervention2” is the first in the paper, with no resource competition. “Intervention5” is the second, with multiple competing initiatives.

Innovation2+5.zip

Feedback and project schedule performance

Yasaman Jalili and David Ford look take a deeper look at project model dynamics in the January System Dynamics Review. An excerpt:
projectloops

Quantifying the impacts of rework, schedule pressure, and ripple effect loops on project schedule performance

Schedule performance is often critical to construction project success. But many times projects experience large unforeseen delays and fail to meet their schedule targets. The failure of large construction projects has enormous economic consequences. …

… the persistence of large project delays implies that their importance has not been fully recognized and incorporated into practice. Traditional project management methods do not explicitly consider the effects of feedback (Pena-Mora and Park, 2001). Project managers may intuitively include some impacts of feedback loops when managing projects (e.g. including buffers when estimating activity durations), but the accuracy of the estimates is very dependent upon the experience and judgment of the scheduler (Sterman, 1992). Owing to the lack of a widely used systematic approach to incorporating the impacts of feedback loops in project management, the interdependencies and dynamics of projects are often ignored. This may be due to a failure of practicing project managers to understand the role and significance of commonly experienced feedback structures in determining project schedule performance. Practitioners may not be aware of the sizes of delays caused by feedback loops in projects, or even the scale of impacts. …

In the current work, a simple validated project model has been used to quantify the schedule impacts of three common reinforcing feedback loops (rework cycle, “haste makes waste”, and ripple effects) in a single phase of a project. Quantifying the sizes of different reinforcing loop impacts on project durations in a simple but realistic project model can be used to clearly show and explain the magnitude of these impacts to project management practitioners and students, and thereby the importance of using system dynamics in project management.

This is a more formal and thorough look at some issues that I raised a while ago, here and here.

I think one important aspect of the model outcome goes unstated in the paper. The results show dominance of the rework parameter:

The graph shows that, regardless of the value of the variables, the rework cycle has the most impact on project duration, ranging from 1.2 to 26.5 times more than the next most influential loop. As the high level of the variables increases, the impact of “haste makes waste” and “ripple effects” loops increases.

projectcauses

Yes, but why? I think the answer is in the nonlinear relationships among the loops. Here’s a simplified view (omitting some redundant loops for simplicity):

projectrework

Project failure occurs when it crosses the tipping point at which completing one task creates more than one task of rework (red flows). Some rework is inevitable due to the error rate (“rework fraction” – orange), i.e. the inverse of quality. A high rework fraction, all by itself, can torpedo the project.

The ripple effect is a little different – it creates new tasks in proportion to the discovery of rework (blue). This is a multiplicative relationship,

ripple work ≅ rework fraction * ripple strength

which means that the ripple effect can only cause problems if quality is poor to begin with.

Similarly, schedule pressure (green) only contributes to rework when backlogs are large and work accomplished is small relative to scheduled ambitions. For that to happen, one of two things must occur: rework and ripple effects delay completion, or the schedule is too ambitious at the outset.

With this structure, you can see why rework (quality) is a problem in itself, but ripple and schedule effects are contingent on the rework trigger. I haven’t run the simulations to prove it, but I think that explains the dominance of the rework parameter in the results. (There’s a followup article here!)

Update, H/T Michael Bean:

Update II

There’s a nice description of the tipping point dynamics here.

Samuelson’s Multiplier Accelerator

This is a fairly direct implementation of the multiplier-accelerator model from Paul Samuelson’s classic 1939 paper,

“Interactions between the Multiplier Analysis and the Principle of Acceleration” PA Samuelson – The Review of Economics and Statistics, 1939 (paywalled on JSTOR, but if you register you can read a limited number of publications for free)

SamuelsonDiagramB

This is a nice example of very early economic dynamics analyses, and also demonstrates implementation of discrete time notation in Vensim. Continue reading “Samuelson’s Multiplier Accelerator”

Environmental Homeostasis

Replicated from

The Emergence of Environmental Homeostasis in Complex Ecosystems

The Earth, with its core-driven magnetic field, convective mantle, mobile lid tectonics, oceans of liquid water, dynamic climate and abundant life is arguably the most complex system in the known universe. This system has exhibited stability in the sense of, bar a number of notable exceptions, surface temperature remaining within the bounds required for liquid water and so a significant biosphere. Explanations for this range from anthropic principles in which the Earth was essentially lucky, to homeostatic Gaia in which the abiotic and biotic components of the Earth system self-organise into homeostatic states that are robust to a wide range of external perturbations. Here we present results from a conceptual model that demonstrates the emergence of homeostasis as a consequence of the feedback loop operating between life and its environment. Formulating the model in terms of Gaussian processes allows the development of novel computational methods in order to provide solutions. We find that the stability of this system will typically increase then remain constant with an increase in biological diversity and that the number of attractors within the phase space exponentially increases with the number of environmental variables while the probability of the system being in an attractor that lies within prescribed boundaries decreases approximately linearly. We argue that the cybernetic concept of rein control provides insights into how this model system, and potentially any system that is comprised of biological to environmental feedback loops, self-organises into homeostatic states.

See my related blog post for details.

Continue reading “Environmental Homeostasis”

Wonderland

Wonderland model by Sanderson et al.; see Alexandra Milik, Alexia Prskawetz, Gustav Feichtinger, and Warren C. Sanderson, “Slow-fast Dynamics in Wonderland,” Environmental Modeling and Assessment 1 (1996) 3-17.

Here’s an excerpt from my 1998 critique of this model: Continue reading “Wonderland”

Early warnings of catastrophe

Catastrophic Collapse Can Occur without Early Warning: Examples of Silent Catastrophes in Structured Ecological Models (PLOS ONE – open access)

Catastrophic and sudden collapses of ecosystems are sometimes preceded by early warning signals that potentially could be used to predict and prevent a forthcoming catastrophe. Universality of these early warning signals has been proposed, but no formal proof has been provided. Here, we show that in relatively simple ecological models the most commonly used early warning signals for a catastrophic collapse can be silent. We underpin the mathematical reason for this phenomenon, which involves the direction of the eigenvectors of the system. Our results demonstrate that claims on the universality of early warning signals are not correct, and that catastrophic collapses can occur without prior warning. In order to correctly predict a collapse and determine whether early warning signals precede the collapse, detailed knowledge of the mathematical structure of the approaching bifurcation is necessary. Unfortunately, such knowledge is often only obtained after the collapse has already occurred.

This is a third-order ecological model with juvenile and adult prey and a predator:

See my related blog post on the topic, in which I also mention a generic model of critical slowing down.

The model, with changes files (.cin) implementing some of the experiments: CatastropheWarning.zip