# A Joint Modelling Approach to Analyze Risky Decisions by Means of Diffusion Tensor Imaging and Behavioural Data

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. The BART Data

#### 2.2. The Cognitive Model

#### 2.3. The Neural Model

#### 2.4. DTI Data Processing

#### 2.5. Joint Modelling

## 3. Results

## 4. Discussion

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

DTI | Diffusion Tensor Imaging |

BART | Balloon Analogue Risk task |

MNI | Montreal Neurological Institute |

## Appendix A

## References

- Turner, B.M.; Forstmann, B.U.; Wagenmakers, E.J.; Brown, S.D.; Sederberg, P.B.; Steyvers, M. A Bayesian framework for simultaneously modeling neural and behavioral data. NeuroImage
**2013**, 72, 193–206. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Hawkins, G.E.; Mittner, M.; Forstmann, B.U.; Heathcote, A. On the efficiency of neurally-informed cognitive models to identify latent cognitive states. J. Math. Psychol.
**2017**, 76, 142–155. [Google Scholar] [CrossRef] [Green Version] - Bridwell, D.A.; Cavanagh, J.F.; Collins, A.G.; Nunez, M.D.; Srinivasan, R.; Stober, S.; Calhoun, V.D. Moving beyond ERP components: A selective review of approaches to integrate EEG and behavior. Front. Human Neurosci.
**2018**, 12, 106. [Google Scholar] [CrossRef] [PubMed] - Lee, M.D.; Wagenmakers, E.J. Bayesian Cognitive Modeling: A practical Course; Cambridge University Press: Cambridge, UK, 2014. [Google Scholar]
- Lewandowsky, S.; Farrell, S. Computational Modeling in Cognition: Principles and Practice; SAGE Publications: Thousand Oaks, CA, USA, 2010. [Google Scholar]
- Lee, M. Special issue on hierarchical Bayesian models. J. Math. Psychol.
**2011**, 55, 1–118. [Google Scholar] [CrossRef] - Barber, D. Bayesian Reasoning and Machine Learning; Cambridge University Press: Cambridge, UK, 2012. [Google Scholar]
- Forstmann, B.U.; Wagenmakers, E.J.; Eichele, T.; Brown, S.; Serences, J.T. Reciprocal relations between cognitive neuroscience and formal cognitive models: opposites attract? Trends Cogn. Sci.
**2011**, 15, 272–279. [Google Scholar] [CrossRef] [Green Version] - Nunez, M.D.; Vandekerckhove, J.; Srinivasan, R. How attention influences perceptual decision making: Single-trial EEG correlates of drift-diffusion model parameters. J. Math. Psychol.
**2017**, 76, 117–130. [Google Scholar] [CrossRef] [Green Version] - Turner, B.M.; Rodriguez, C.A.; Norcia, T.M.; McClure, S.M.; Steyvers, M. Why more is better: Simultaneous modeling of EEG, fMRI, and behavioral data. NeuroImage
**2016**, 128, 96–115. [Google Scholar] [CrossRef] [Green Version] - Palestro, J.J.; Bahg, G.; Sederberg, P.B.; Lu, Z.L.; Steyvers, M.; Turner, B.M. A tutorial on joint models of neural and behavioral measures of cognition. J. Math. Psychol.
**2018**, 84, 20–48. [Google Scholar] [CrossRef] - Brouwer, G.J.; Heeger, D.J. Cross-orientation suppression in human visual cortex. J. Neurophys.
**2011**, 106, 2108–2119. [Google Scholar] [CrossRef] [Green Version] - Lu, Z.L.; Li, X.; Tjan, B.S.; Dosher, B.A.; Chu, W. Attention extracts signal in external noise: A BOLD fMRI study. J. Cogn. Neurosci.
**2011**, 23, 1148–1159. [Google Scholar] [CrossRef] [Green Version] - Kragel, J.E.; Morton, N.W.; Polyn, S.M. Neural activity in the medial temporal lobe reveals the fidelity of mental time travel. J. Neurosci.
**2015**, 35, 2914–2926. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Mack, M.L.; Preston, A.R.; Love, B.C. Decoding the brain’s algorithm for categorization from its neural implementation. Curr. Biol.
**2013**, 23, 2023–2027. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Van Ravenzwaaij, D.; Provost, A.; Brown, S.D. A confirmatory approach for integrating neural and behavioral data into a single model. J. Math. Psychol.
**2017**, 76, 131–141. [Google Scholar] [CrossRef] - Lejuez, C.W.; Read, J.P.; Kahler, C.W.; Richards, J.B.; Ramsey, S.E.; Stuart, G.L.; Strong, D.R.; Brown, R.A. Evaluation of a behavioral measure of risk taking: The balloon analogue risk task (BART). J. Exp. Psychol. Appl.
**2002**, 8, 75. [Google Scholar] [CrossRef] [PubMed] - Aklin, W.M.; Lejuez, C.; Zvolensky, M.J.; Kahler, C.W.; Gwadz, M. Evaluation of behavioral measures of risk taking propensity with inner city adolescents. Behav. Res. Ther.
**2005**, 43, 215–228. [Google Scholar] [CrossRef] [PubMed] - Goldenberg, D.; Telzer, E.H.; Lieberman, M.D.; Fuligni, A.J.; Galván, A. Greater response variability in adolescents is associated with increased white matter development. Soc. Cogn. Affect. Neurosci.
**2017**, 12, 436–444. [Google Scholar] [CrossRef] [Green Version] - Cazzell, M.; Li, L.; Lin, Z.J.; Patel, S.J.; Liu, H. Comparison of neural correlates of risk decision making between genders: An exploratory fNIRS study of the Balloon Analogue Risk Task (BART). Neuroimage
**2012**, 62, 1896–1911. [Google Scholar] [CrossRef] [PubMed] - Bornovalova, M.A.; Daughters, S.B.; Hernandez, G.D.; Richards, J.B.; Lejuez, C. Differences in impulsivity and risk-taking propensity between primary users of crack cocaine and primary users of heroin in a residential substance-use program. Exp. Clin. Psychopharm.
**2005**, 13, 311. [Google Scholar] [CrossRef] - Lejuez, C.; Aklin, W.M.; Jones, H.A.; Richards, J.B.; Strong, D.R.; Kahler, C.W.; Read, J.P. The balloon analogue risk task (BART) differentiates smokers and nonsmokers. Exp. Clin. Psychopharm.
**2003**, 11, 26. [Google Scholar] [CrossRef] - Van Ravenzwaaij, D.; Dutilh, G.; Wagenmakers, E.J. Cognitive model decomposition of the BART: Assessment and application. J. Math. Psychol.
**2011**, 55, 94–105. [Google Scholar] [CrossRef] - Poldrack, R.A.; Barch, D.M.; Mitchell, J.; Wager, T.; Wagner, A.D.; Devlin, J.T.; Cumba, C.; Koyejo, O.; Milham, M. Toward open sharing of task-based fMRI data: the OpenfMRI project. Front. Neuroinf.
**2013**, 7, 12. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Cohen, J.R.; Poldrack, R.A. Materials and Methods for OpenfMRI ds009: The Generality of Self Control. 2014. Available online: https://www.openfmri.org/media/ds000009/ds009_methods_0_CchSZHn.pdf (accessed on 1 December 2019).
- Wallsten, T.S.; Pleskac, T.J.; Lejuez, C.W. Modeling behavior in a clinically diagnostic sequential risk-taking task. Psychol. Rev.
**2005**, 112, 862. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Ferrari, S.; Cribari-Neto, F. Beta regression for modelling rates and proportions. J. Appl. Stat.
**2004**, 31, 799–815. [Google Scholar] [CrossRef] - Pierpaoli, C.; Basser, P.J. Toward a quantitative assessment of diffusion anisotropy. Magn. Reson. Med.
**1996**, 36, 893–906. [Google Scholar] [CrossRef] - Beppu, T.; Inoue, T.; Shibata, Y.; Kurose, A.; Arai, H.; Ogasawara, K.; Ogawa, A.; Nakamura, S.; Kabasawa, H. Measurement of fractional anisotropy using diffusion tensor MRI in supratentorial astrocytic tumors. J. Neurooncol.
**2003**, 63, 109–116. [Google Scholar] [CrossRef] - Kwon, M.S.; Vorobyev, V.; Moe, D.; Parkkola, R.; Hämäläinen, H. Brain structural correlates of risk-taking behavior and effects of peer influence in adolescents. PloS ONE
**2014**, 9, e112780. [Google Scholar] [CrossRef] - Lane, S.D.; Steinberg, J.L.; Ma, L.; Hasan, K.M.; Kramer, L.A.; Zuniga, E.A.; Narayana, P.A.; Moeller, F.G. Diffusion tensor imaging and decision making in cocaine dependence. PLoS ONE
**2010**, 5, e11591. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Kohno, M.; Morales, A.M.; Guttman, Z.; London, E.D. A neural network that links brain function, white-matter structure and risky behavior. Neuroimage
**2017**, 149, 15–22. [Google Scholar] [CrossRef] [PubMed] - Fukunaga, R.; Brown, J.W.; Bogg, T. Decision making in the Balloon Analogue Risk Task (BART): anterior cingulate cortex signals loss aversion but not the infrequency of risky choices. Cogn. Affect. Behav. Neurosci.
**2012**, 12, 479–490. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Krain, A.L.; Wilson, A.M.; Arbuckle, R.; Castellanos, F.X.; Milham, M.P. Distinct neural mechanisms of risk and ambiguity: A meta-analysis of decision-making. Neuroimage
**2006**, 32, 477–484. [Google Scholar] [CrossRef] - Krawitz, A.; Fukunaga, R.; Brown, J.W. Anterior insula activity predicts the influence of positively framed messages on decision making. Cogn. Affect. Behav. Neurosci.
**2010**, 10, 392–405. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Christopoulos, G.I.; Tobler, P.N.; Bossaerts, P.; Dolan, R.J.; Schultz, W. Neural correlates of value, risk, and risk aversion contributing to decision making under risk. J. Neurosci.
**2009**, 29, 12574–12583. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Kuhnen, C.M.; Knutson, B. The neural basis of financial risk taking. Neuron
**2005**, 47, 763–770. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Furman, D.J.; Hamilton, J.P.; Gotlib, I.H. Frontostriatal functional connectivity in major depressive disorder. Biol. Mood Anxiety Disord.
**2011**, 1, 11. [Google Scholar] [CrossRef] [Green Version] - Basser, P.J.; Pierpaoli, C. Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI. J. Magn. Reson. Ser. B
**1996**, 111, 209–219. [Google Scholar] [CrossRef] - Yeh, F.C.; Verstynen, T.D.; Wang, Y.; Fernández-Miranda, J.C.; Tseng, W.Y.I. Deterministic diffusion fiber tracking improved by quantitative anisotropy. PloS ONE
**2013**, 8, 713. [Google Scholar] [CrossRef] [Green Version] - Christidi, F.; Karavasilis, E.; Samiotis, K.; Bisdas, S.; Papanikolaou, N. Fiber tracking: A qualitative and quantitative comparison between four different software tools on the reconstruction of major white matter tracts. Eur. J. Radiol. Open
**2016**, 3, 153–161. [Google Scholar] [CrossRef] [Green Version] - Rolls, E.T.; Joliot, M.; Tzourio-Mazoyer, N. Implementation of a new parcellation of the orbitofrontal cortex in the automated anatomical labeling atlas. Neuroimage
**2015**, 122, 1–5. [Google Scholar] [CrossRef] - Desikan, R.S.; Ségonne, F.; Fischl, B.; Quinn, B.T.; Dickerson, B.C.; Blacker, D.; Buckner, R.L.; Dale, A.M.; Maguire, R.P.; Hyman, B.T.; et al. An automated labeling system for subdividing the human cerebral cortex on MRI scans into gyral based regions of interest. Neuroimage
**2006**, 31, 968–980. [Google Scholar] [CrossRef] - Yeh, F.C.; Panesar, S.; Fernandes, D.; Meola, A.; Yoshino, M.; Fernandez-Miranda, J.C.; Vettel, J.M.; Verstynen, T. A population-based atlas of the macroscale structural connectome in the human brain. bioRxiv
**2017**, 2017, 136473. [Google Scholar] - Turner, B.M.; Forstmann, B.U.; Love, B.C.; Palmeri, T.J.; Van Maanen, L. Approaches to analysis in model-based cognitive neuroscience. J. Math. Psychol.
**2017**, 76, 65–79. [Google Scholar] [CrossRef] [PubMed] - Welsh, A.; Richardson, A. Approaches to the Robust Estimation of Mixed Models Handbook of Statistics; Elsevier Science BV: Amsterdam, The Netherlands, 1997. [Google Scholar]
- Pinheiro, J.C.; Liu, C.; Wu, Y.N. Efficient Algorithms for Robust Estimation in Linear Mixed-Effects Models Using the Multivariate t Distribution. J. Comput. Graph. Stat.
**2001**, 10, 249–276. [Google Scholar] [CrossRef] - Gilks, W.R.; Richardson, S.; Spiegelhalter, D. Markov Chain Monte Carlo in Practice; Chapman and Hall/CRC: Boca Raton, FL, USA, 1995. [Google Scholar]
- Team, R.C. R: A Language and Environment for Statistical Computing; Tea, R Core: Vienna, Austria, 2013. [Google Scholar]
- Plummer, M. JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling. In Proceedings of the 3rd International Workshop on Distributed Statistical Computing, Vienna, Austria, 20–22 March 2003; Volume 124, pp. 1–10. [Google Scholar]
- Su, Y.S.; Yajima, M.; Su, M.Y.S. Package ‘R2jags’. R Package Version 0.03-08. 2015. Available online: http://CRAN.R-project.org/package=R2jags (accessed on 1 December 2019).
- Casella, G.; George, E.I. Explaining the Gibbs sampler. Am. Stat.
**1992**, 46, 167–174. [Google Scholar] - Gelman, A.; Rubin, D.B. Inference from iterative simulation using multiple sequences. Stat. Sci.
**1992**, 7, 457–472. [Google Scholar] [CrossRef] - Gelman, A.; Shalizi, C.R. Philosophy and the practice of Bayesian statistics. Br. J. Math. Stat. Psychol.
**2013**, 66, 8–38. [Google Scholar] [CrossRef] [Green Version] - Lee, M.D. How cognitive modeling can benefit from hierarchical Bayesian models. J. Math. Psychol.
**2011**, 55, 1–7. [Google Scholar] [CrossRef] - Dean, A.C.; Sugar, C.A.; Hellemann, G.; London, E.D. Is all risk bad? Young adult cigarette smokers fail to take adaptive risk in a laboratory decision-making test. Psychopharmacology
**2011**, 215, 801–811. [Google Scholar] [CrossRef] [Green Version] - Humphries, M.D.; Khamassi, M.; Gurney, K. Dopaminergic control of the exploration-exploitation trade-off via the basal ganglia. Front. Neurosci.
**2012**, 6, 9. [Google Scholar] [CrossRef] [Green Version] - Cohen-Adad, J.; Descoteaux, M.; Rossignol, S.; Hoge, R.D.; Deriche, R.; Benali, H. Detection of multiple pathways in the spinal cord using q-ball imaging. Neuroimage
**2008**, 42, 739–749. [Google Scholar] [CrossRef] - Zhan, L.; Leow, A.D.; Jahanshad, N.; Chiang, M.C.; Barysheva, M.; Lee, A.D.; Toga, A.W.; McMahon, K.L.; De Zubicaray, G.I.; Wright, M.J.; et al. How does angular resolution affect diffusion imaging measures? Neuroimage
**2010**, 49, 1357–1371. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**Pictures on the left show the regions of interest (ROIs) which constitute the networks. The network containing anterior cingulate (red), insula (yellow) and inferior frontal gyrus (blue) consists of the anterior cingulate cortex (ACC)–Insula–inferior frontal gyrus (IFG) Network (

**a**). The network containing thalamus (green), striatum (yellow) and dorsolateral prefrontal cortex (dlPFC) (blue) consists of the dlPFC–Thalamus–Striatum Network (

**b**). The central and rightmost pictures represent tracts of white matters connections for the first and the second network, respectively. For simplicity, figures show networks tracts for the left brain hemisphere, but the same applies to the opposite hemisphere. Network Fractional Anisotropy (FA) is intended to account for bilateral network tracts fractional anisotropy.

**Figure 2.**Covariance model’s architecture. Square and circular nodes indicate discrete and continous variables, respectively. Grey nodes indicate observed variables. Blue and red nodes represent behavioural and neural node parameters, respectively. Double-circled nodes represent deterministic nodes.

**Figure 3.**Trace plot of the (unnormalized) log posterior density computed for all the chains, for the first 6000 iterations. The burn-in period was removed to show the whole convergence dynamic. As can be noticed, the log posterior seems to show no trends.

**Figure 4.**Posterior predictive check. Black dots and boundaries represent mean pumps and standard deviations for each individual from the empirical dataset. Red dots and lines represent mean pumps and standard deviations of predicted synthetic individual datasets.

**Figure 5.**Marginal posterior distributions of the correlation parameters of interest in the covariance matrix.

**Table 1.**Marginal posterior distributions statistics: Posterior mean (${\mu}_{post}$), $95\%$ credible intervals $[{q}_{0.05},{q}_{0.975}]$, chains convergence ($\widehat{\mathrm{R}}$).

Parameter | ${\mathit{\mu}}_{\mathbf{post}}$ | ${\mathit{q}}_{0.05}$ | ${\mathit{q}}_{0.975}$ | $\widehat{\mathbf{R}}$ |
---|---|---|---|---|

${\mu}_{\gamma}$ | $0.442$ | $0.374$ | $0.474$ | 1.012 |

${\mu}_{\beta}$ | $1.471$ | $1.211$ | $1.571$ | 1.013 |

${\mu}_{{\alpha}_{0}}$ | $2.653$ | $2.460$ | $2.722$ | 1.001 |

${\mu}_{{\alpha}_{1}}$ | $-0.004$ | $-0.007$ | $-0.001$ | 1.001 |

${\rho}_{1}$ | $-0.341$ | $-0.85$ | $0.365$ | 1.019 |

${\rho}_{2}$ | $-0.483$ | $-0.86$ | $0.072$ | 1.010 |

${\rho}_{3}$ | $0.021$ | $-0.645$ | $0.750$ | 1.013 |

${\rho}_{4}$ | $-0.250$ | $-0.761$ | $0.371$ | 1.008 |

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**MDPI and ACS Style**

D’Alessandro, M.; Gallitto, G.; Greco, A.; Lombardi, L.
A Joint Modelling Approach to Analyze Risky Decisions by Means of Diffusion Tensor Imaging and Behavioural Data. *Brain Sci.* **2020**, *10*, 138.
https://doi.org/10.3390/brainsci10030138

**AMA Style**

D’Alessandro M, Gallitto G, Greco A, Lombardi L.
A Joint Modelling Approach to Analyze Risky Decisions by Means of Diffusion Tensor Imaging and Behavioural Data. *Brain Sciences*. 2020; 10(3):138.
https://doi.org/10.3390/brainsci10030138

**Chicago/Turabian Style**

D’Alessandro, Marco, Giuseppe Gallitto, Antonino Greco, and Luigi Lombardi.
2020. "A Joint Modelling Approach to Analyze Risky Decisions by Means of Diffusion Tensor Imaging and Behavioural Data" *Brain Sciences* 10, no. 3: 138.
https://doi.org/10.3390/brainsci10030138