breed [symptoms symptom] symptoms-own [ symptom-present? ;; if true, the symptom is a present symptom b ;; the threshold of regression a ;; the steepness of the probability function activation ;; =0 if symptom-absent, =1 if symptom-present total-activation ;; total activation from network chance-to-become-activated ;; calculates the likelihood with logistic function to become active individual-stress Act ] links-own [ weight-edge ] globals [ mood shock ] ;;;;;;;;;;;;;;;;;;;;;;;; ;;; Setup Procedures ;;; ;;;;;;;;;;;;;;;;;;;;;;;; to setup clear-all setup-symptoms ask symptom 0 [set b 0.8473446 set a 2.191685 set label "Depmood"] ask symptom 1 [set b 1.1534109 set a 1.908611 set label "Lossint"] ask symptom 2 [set b 1.7241530 set a 1.803834 set label "Wloss"] ask symptom 3 [set b 2.1434912 set a 1.423235 set label "Wgain"] ask symptom 4 [set b 1.7898552 set a 1.489656 set label "Dapp"] ask symptom 5 [set b 1.7924182 set a 1.692587 set label "Iapp"] ask symptom 6 [set b 2.0968795 set a 1.219107 set label "Insom"] ask symptom 7 [set b 1.7218456 set a 1.856848 set label "Hypersom"] ask symptom 8 [set b 1.4080463 set a 1.712685 set label "Pagit"] ask symptom 9 [set b 2.0744478 set a 1.532739 set label "Pretar"] ask symptom 10 [set b 1.6176604 set a 1.519489 set label "Fatigue"] ask symptom 11 [set b 2.4087651 set a 1.449846 set label "Worthless"] ask symptom 12 [set b 2.4090998 set a 1.385965 set label "Conc"] ask symptom 13 [set b 1.8460433 set a 2.006484 set label "Death"] setup-network set mood [] reset-ticks end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;; Setup symptoms: creates symptoms with a nice layout ;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to setup-symptoms create-symptoms 14 [ set shape "circle"] layout-circle (sort symptoms) max-pxcor - 1 ask symptoms [ setxy (xcor * 0.70) (ycor * 0.70) become-symptom-absent ] end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;; Setup network: creates fully connected network, assigns ;; ;; weights to the links ;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to setup-network ask symptom 0 [create-link-with symptom 1] ask symptom 0 [create-link-with symptom 6] ask symptom 0 [create-link-with symptom 10] ask symptom 0 [create-link-with symptom 11] ask symptom 1 [create-link-with symptom 11] ask symptom 1 [create-link-with symptom 12] ask symptom 2 [create-link-with symptom 4] ask symptom 3 [create-link-with symptom 5] ask symptom 4 [create-link-with symptom 6] ask symptom 6 [create-link-with symptom 8] ask symptom 6 [create-link-with symptom 10] ask symptom 7 [create-link-with symptom 10] ask symptom 8 [create-link-with symptom 12] ask symptom 9 [create-link-with symptom 10] ask symptom 9 [create-link-with symptom 12] ask symptom 11 [create-link-with symptom 12] ask symptom 11 [create-link-with symptom 13] ask link 0 1 [set weight-edge 1 set color 1] ask link 0 6 [set weight-edge 1 set color 1] ask link 0 10 [set weight-edge 1 set color 1] ask link 0 11 [set weight-edge 1 set color 1] ask link 1 11 [set weight-edge 1 set color 1] ask link 1 12 [set weight-edge 1 set color 1] ask link 2 4 [set weight-edge 1 set color 1] ask link 3 5 [set weight-edge 1 set color 1] ask link 4 6 [set weight-edge 1 set color 1] ask link 6 8 [set weight-edge 1 set color 1] ask link 6 10 [set weight-edge 1 set color 1] ask link 7 10 [set weight-edge 1 set color 1] ask link 8 12 [set weight-edge 1 set color 1] ask link 9 10 [set weight-edge 1 set color 1] ask link 9 12 [set weight-edge 1 set color 1] ask link 11 12 [set weight-edge 1 set color 1] ask link 11 13 [set weight-edge 1 set color 1] ask links [ if weight-edge = 1 [ set color 3 ] ] end to go spread-activation list-mood tick update-plot set shock 1 make-histogram end to administer-shock set shock 0 ; ask links ; [ ; set weight-edge 0 ; ] end ;;;;;;;;;;;;;;;;;;;;;;; ;;; Main Procedures ;;; ;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;; Spread activation: The likelihood is calculated and drawing a random number between a uniform distribution of 0 and 1 ;; ;; determines whether the symptom will actually be activated or deactivated ;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to spread-activation ask symptoms with [symptom-present?] [ calculate-chance-to-become-activated if random 1000 / 1000 > chance-to-become-activated [ become-symptom-absent ] ] ask symptoms with [not symptom-present?] [ calculate-chance-to-become-activated if random 1000 / 1000 < chance-to-become-activated [ become-symptom-present ] ] end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;; Calculates the likelihood with a logistic function ;; ;; Makes a list with the actual activation values of the symptoms ;; ;; Makes a matrix from list-activation-all to perform matrix algebra ;; ;; and calculates the chance to become activated in a random order ;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to calculate-chance-to-become-activated ind-stress ask symptoms [ set total-activation 0 let j 0 while [j < count symptoms] [ if link who j != nobody [ if who < j [ let temptot-activation ([weight-edge] of link who j * [activation] of symptom j * connection-strength) set total-activation total-activation + temptot-activation ] if who > j [ let temptot-activation ([weight-edge] of link j who * [activation] of symptom j * connection-strength) set total-activation total-activation + temptot-activation ] ] set j j + 1 ] set Act total-activation + external-activation + individual-stress set chance-to-become-activated (1 / (1 + exp (a * (b - Act)))) * shock ] end to ind-stress ask symptom 0 [set individual-stress Depmood] ask symptom 1 [set individual-stress Lossint] ask symptom 2 [set individual-stress Wloss] ask symptom 3 [set individual-stress Wgain] ask symptom 4 [set individual-stress Dapp] ask symptom 5 [set individual-stress Iapp] ask symptom 6 [set individual-stress Insom] ask symptom 7 [set individual-stress Hypersom] ask symptom 8 [set individual-stress Pagit] ask symptom 9 [set individual-stress Pretar] ask symptom 10 [set individual-stress Fatigue] ask symptom 11 [set individual-stress Worthless] ask symptom 12 [set individual-stress Conc] ask symptom 13 [set individual-stress Death] end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;; procedures to activate and deactivate symptoms ;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to become-symptom-absent set symptom-present? false set activation 0 set shape "circle 2" set size 1 end to become-symptom-present set symptom-present? true set activation 1 set shape "circle" set color red set size 2 end to list-mood set mood lput (count symptoms with [symptom-present?]) mood if length mood > 1000 [ set mood butfirst mood ] end ;;;;;;;;;;;;;;;;;;;;;;; ;;; Plots ;;; ;;;;;;;;;;;;;;;;;;;;;;; to update-plot set-current-plot "Network Status" set-current-plot-pen "cut-off" ;; we don't want the "auto-plot" feature to cause the ;; plot's x range to grow when we draw the axis. so ;; first we turn auto-plot off temporarily auto-plot-off plotxy 0 7 plotxy 1000000000 7 auto-plot-on set-current-plot-pen "symptom-present" plot (count symptoms with [symptom-present?]) set-current-plot-pen "external-activation" plot ((external-activation + 8) / 2) set-current-plot-pen "connection-strength" plot (connection-strength * 5) set-current-plot "Hysteresis plot" set-current-plot-pen "symptom-present" plotxy (external-activation) (count symptoms with [symptom-present?]) end to make-histogram set-current-plot "Histogram" set-current-plot-pen "mood" histogram mood end ; *** NetLogo 4.0.3 Model Copyright Notice *** ; ; Copyright 2008 by Uri Wilensky. All rights reserved. ; ; Permission to use, modify or redistribute this model is hereby granted, ; provided that both of the following requirements are followed: ; a) this copyright notice is included. ; b) this model will not be redistributed for profit without permission ; from Uri Wilensky. ; Contact Uri Wilensky for appropriate licenses for redistribution for ; profit. ; *** End of NetLogo 4.0.3 Model Copyright Notice *** @#$#@#$#@ GRAPHICS-WINDOW 222 10 555 344 16 15 9.8 1 10 1 1 1 0 0 0 1 -16 16 -15 15 0 0 1 ticks 30.0 BUTTON 19 11 97 47 NIL setup NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 105 11 187 48 NIL go T 1 T OBSERVER NIL NIL NIL NIL 1 PLOT 457 357 932 532 Network Status time number of nodes 0.0 0.0 0.0 14.0 true true "" "" PENS "symptom-present" 1.0 0 -2674135 true "" "" "external-activation" 1.0 0 -10899396 true "" "" "connection-strength" 1.0 0 -7500403 true "" "" "cut-off" 1.0 0 -16777216 true "" "" SLIDER 4 56 203 89 connection-strength connection-strength 0.1 3 1 .05 1 NIL HORIZONTAL SLIDER 4 101 203 134 external-activation external-activation -8 8 0 .1 1 NIL HORIZONTAL PLOT 9 357 444 531 Hysteresis plot external activation (stress) sum of symptoms 0.0 10.0 0.0 14.0 true true "" "" PENS "symptom-present" 1.0 0 -2674135 true "" "" PLOT 9 194 209 344 Histogram NIL NIL 0.0 15.0 0.0 10.0 true false "" "" PENS "mood" 1.0 1 -13791810 true "" "" BUTTON 37 144 161 177 NIL administer-shock NIL 1 T OBSERVER NIL NIL NIL NIL 1 SLIDER 569 37 741 70 Depmood Depmood -5 5 0 1 1 NIL HORIZONTAL SLIDER 569 76 741 109 Lossint Lossint -5 5 0 1 1 NIL HORIZONTAL SLIDER 569 120 741 153 Wloss Wloss -5 5 0 1 1 NIL HORIZONTAL SLIDER 570 162 742 195 Wgain Wgain -5 5 0 1 1 NIL HORIZONTAL SLIDER 570 207 742 240 Dapp Dapp -5 5 0 1 1 NIL HORIZONTAL SLIDER 570 251 742 284 Iapp Iapp -5 5 0 1 1 NIL HORIZONTAL SLIDER 572 291 744 324 Insom Insom -5 5 0 1 1 NIL HORIZONTAL SLIDER 757 37 929 70 Hypersom Hypersom -5 5 0 1 1 NIL HORIZONTAL SLIDER 757 78 929 111 Pagit Pagit -5 5 0 1 1 NIL HORIZONTAL SLIDER 758 121 930 154 Pretar Pretar -5 5 0 1 1 NIL HORIZONTAL SLIDER 758 163 930 196 Fatigue Fatigue -5 5 0 1 1 NIL HORIZONTAL SLIDER 759 204 931 237 Worthless Worthless -5 5 0 1 1 NIL HORIZONTAL SLIDER 758 249 930 282 Conc Conc -5 5 0 1 1 NIL HORIZONTAL SLIDER 759 292 931 325 Death Death -5 5 0 1 1 NIL HORIZONTAL @#$#@#$#@ ## WHAT IS IT? This model is a representation of major depression. The nodes in this model represent the symptoms of major depression. According to the DSM-IV (APA, 2000) there are nine symptoms: (1) depressed mood, (2) loss of interest, (3) weight loss, (4) weight gain, (5) decreased appetite, (6) increased appetite, (7) insomnia, (8) hypersomnia, (9) psychomotor agitation, (10) psychomotor retardation, (11) fatigue, (12) worthlessness or guilt, (13) concentration problems, and (14) suicidal thoughts. In this model, a recently emerging view on the relations between symptoms is illustrated. It is based on the hypothesis that symptoms of mental disorders have direct causal relations with one another and is called the causal network perspective (Borsboom, 2008; Cramer, Waldorp, van der Maas & Borsboom, 2010; Schmittmann, Cramer, Waldorp, Epskamp, Kievit & Borsboom, 2011; Cramer, Borsboom, Aggen, & Kendler, 2012). For instance, if one develops a symptom of major depression (e.g., insomnia) then this increases the likelihood of developing other symptoms (e.g., fatigue, lack of concentration). Conversely, if one of the symptoms disappears, this increases the likelihood that other symptoms disappear as well. It is hypothesized that if someone is vulnerable to depression (i.e., symptoms are strongly connected), mild stress could be enough to trigger a cascade of symptoms that can eventually lead to a full-blown depressive episode (Cramer et al., submitted). This model is made to illustrate this effect of vulnerability. This means that this model predicts that a person that is vulnerable and develops a depression due to, for example, severe marital problems, will not recover automatically when the marital problems are solved. More is needed to trigger recovery from depression. Conversely, for someone that is resilient to depression (i.e., symptoms are weakly connected), mild stress cannot trigger a cascade of symptoms. Severe stress can lead to a full-blown depression, but when the stress subsides, the depression will subside too. This effect is also known as the hysteresis effect. ## HOW IT WORKS The model is based on two parameters for the whole network that can be controlled by the sliders: CONNECTION-STRENGTH, EXTERNAL-ACTIVATION. Furthermore, the stress levels can be varied per symptom with the sliders on the right of the monitor. The network architecture is based on partial correlations between symptoms of a dataset on psychiatric and substance use disorders (VATSPUD; Prescott, Aggen & Kendler, 2000; Kendler & Prescott, 2006). At each time step (tick), the probability of a symptom being developed (turning red), is calculated for each symptom. This probability depends on certain parameters as well as the total activation of its neighbors at the previous tick. These parameters are regression parameters (a threshold and a slope) for each symptom by fitting a logistic regression model on the VATSPUD data in which each symptom was regressed on the total score of its neighbors). The probability to become activated for symptom i is represented as: 1 / 1 + e^(a(b - A)) Here, A is the total amount of stress on symptom i. The amount of stress consists of the individual stress level of symptom i (the value on the slider of symptom i), the amount of external activation (the amount of stress on the whole network, indicated by the slider EXTERNAL-ACTIVATION) and the influence of the activation of the neighbors of symptom i. The influence of the neighbors depends on whether or not they are activated and on the strength of the connection between the activated neighbor and symptom i. The strength of the connections determines the degree to which the activation signal of a symptom is sent to the other symptoms and is controlled by the CONNECTION-STRENGTH slider. The external activation can be seen as influences from the environment (e.g., stressful life events like a romantic breakup or the loss of a loved one), controlled by the EXTERNAL-ACTIVATION slider. Parameter a is a symptom-specific parameter that controls the steepness of the probability function. When a is high, a change in A results larger change in the probability of becoming infected. Parameter b is a symptom-specific parameter for the threshold of a symptom; a symptom with a higher threshold needs more activation (from its neighbors for example) to become infected than symptoms with a lower threshold. ## HOW TO USE IT Use the sliders CONNECTION-STRENGTH and EXTERNAL-ACTIVATION to choose the initial settings for the model. Press SETUP to create the network. To run the model, press the GO button. If you want to start a new simulation press SETUP again. The CONNECTION-STRENGTH and EXTERNAL-ACTIVATION sliders can be adjusted before pressing GO, or while the model is running. The NETWORK STATUS plot shows the number of activated symptoms over time (per tick). As the EXTERNAL-ACTIVATION slider is adjusted, the green line moves up or down accordingly. The same goes for the CONNECTION_STRENGTH slider and the grey line. In the HYSTERESIS PLOT, the hysteresis effect can be demonstrated. At a certain fixed connection-strength and changing external activation, it will be made visible that the shifts from depressed to healthy states and vice versa generally follow a non-linear pattern (hysteresis). The HISTOGRAM represents the frequency of the number of activated symptoms per tick of the last 1000 ticks. ## THINGS TO NOTICE The network can be regarded as disordered when the total number of active symptoms is larger than 7. In the NETWORK STATUS plot this is when the network is above the black line. Conversely, the network is regarded healthy when there are 7 or less symptoms activated (below the black line). ## THINGS TO TRY Press SETUP and then GO. When you let the network run for a while, notice that, with the initial settings (CONNECTION-STRENGTH 1.20, EXTERNAL-ACTIVATION 0.0 and stress levels of all symptoms 0), the activation of the network is around the black line in the NETWORK STATUS plot. Change the EXTERNAL-ACTIVATION and see how that affects the activity of the network. Then increase the CONNECTION-STRENGTH and see if the influence of the EXTERNAL-ACTIVATION is altered. To demonstrate a hysteresis effect, choose a CONNECTION-STRENGTH. Now, increase the EXTERNAL-ACTIVATION slowly at a constant pace. At what level of external activation does the network switch to a depressed state? And when you decrease the external activation at the same pace: at what level does the network switch into a healthy state? Go back and forth with the EXTERNAL-ACTIVATION slider a couple of times. Can you find a way to make the hysteresis effect bigger? With the ADMINISTER-SHOCK button, you can deactivate all symptoms at once. It is as if you give the network an electric shock that resets all the symptoms. Try to find a setting of the CONNECTION-STRENGTH and EXTERNAL-ACTIVATION that creates a disordered network (above the black line in the NETWORK STATUS plot) whereby administering a shock, makes the system healthy again. With the stress sliders per symptom, you can intervene on a specific symptom by ‘curing’ that symptom (by lowering the stress level). Can you make a disordered network and make it healthy again by focusing your treatment on a few symptoms? What symptoms are most effective to intervene on? ## EXTENDING THE MODEL The model could be extended by incorporating the kindling effect (Kraepelin, 1921). The kindling effect is the phenomenon that stressful life events play the greatest role in the first onset of Major Depression. Subsequent episodes are elicited by less and less severe life events (Monroe, Torres, Guillaumot, Harkness, Roberts, Frank & Kupfer, 2006). This could be incorporated in the model by making the connections between the symptoms stronger after every depressive episode. So, each time the network status goes above the black line (or after a certain amount of times in a certain period), the connections become a bit stronger. ## NETLOGO FEATURES ## CREDITS AND REFERENCES APA (2000). Diagnostic and Statistical Manual of Mental Disorders, 4th edition, text revision. American Psychiatric Association: Washington, DC. Borsboom, D. (2008). Psychometric perspectives on diagnostic systems. Journal of Clinical Psychology, 64, 1089-1108. Cramer, A. O. J., Waldorp, L. J., Van der Maas, H. L. J., and Borsboom, D. (2010). Comorbidity: A network perspective. Behavioral and Brain Sciences, 33, 137-193. Cramer, A. O. J., Giltay, E. J., Van Borkulo, C. D., Van der Maas, H. J., Kendler, K. S., Scheffer, M., and Borsboom, D. (submitted). I feel sad therefore I do not sleep: Major depression as a complex system. Kendler, K. S., & Prescott, C. A. (2006). Genes, environment, and psychopathology: Understanding the causes of psychiatric and substance use disorders. Guilford Press. Kraepelin E: Manic-depressive insanity and paranoia. Edinburgh, Scotland: E. & S. Livingstone, 1921 Monroe SM, Torres LD, Guillaumot J, Harkness KL, Roberts JE, Frank E, Kupfer D: Life stress and the long-term treatment course of recurrent depression: III. nonsevere life events predict recurrence for medicated patients over 3 years. J Consult Clin Psychol 2006; 74:112-120 Prescott CA, Aggen SH, Kendler KS: Sex-specific genetic influences on the comorbidity of alcoholism and major depression in a population-based sample of US twins. Arch Gen Psychiatry 2000; 57:803-811 Prescott, C. A., Aggen, S. H., & Kendler, K. S. (2000). Sex-specific genetic influences on the comorbidity of alcoholism and major depression in a population-based sample of US twins. Archives of General Psychiatry, 57, 803-811. Schmittman, V. D., Cramer, A. O. J., Waldorp, L. J., Epskamp, S., Kievit, R. A., and Borsboom, D. Deconstructing the construct: A network perspective on psychological phenomena. New Ideas in Psychology (2011), doi:10.1016/j.newideapsych.2011.02.007 ## HOW TO CITE If you mention this model in an academic publication, we ask that you include these citations for the model itself and for the NetLogo software: - Van Borkulo, C.D., Van der Maas, H.L.J., Borsboom, D., and Cramer, A.O.J. (2013). NetLogo Vulnerability_to_Depression. http://ccl.northwestern.edu/netlogo/models/community/Vulnerability_to_Depression. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. - Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. In other publications, please use: - Copyright 2013 Claudia D. van Borkulo, Han L. J. van der Maas, Denny Borsboom, and Angelique O. J. Cramer. All rights reserved. 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