Basic DREAM Model (BDM)

• The Basic DREAM Model (BDM) is a compact biomathematical framework that quantifies dream formation and spontaneous cognitive activity.
• It employs a system of ordinary differential equations to model interactions among variables tied to key neural regions such as the ACC, vmPFC, and hippocampus.
• Simulations show that BDM’s dynamics closely align with neuroimaging findings, supporting its role in studying dreaming, emotional regulation, and spontaneous cognition.

The Basic DREAM Model (BDM) is a compact, biomathematical framework formulated to quantitatively describe the neurodynamic processes underlying dream formation and spontaneous cognitive activity. Developed by Tavangari et al., BDM integrates dissatisfaction, acceptance, forgetting, and mental activity into a system of ordinary differential equations (ODEs), with explicit correspondence to neural systems, and simulates the interactions among these latent cognitive states to produce dream-like internal imagery (Tavangari et al., 25 Apr 2025). BDM’s architecture enables formal mapping of theoretical constructs to neuroimaging data, leveraging both continuous mathematical modeling and empirical validation.

1. Model Structure and Neurocognitive Variables

The BDM consists of six principal variables:

• Dissatisfaction $D(t)$: Encodes negative affect and conflict monitoring, primarily mapping to dorsal anterior cingulate cortex (ACC) and anterior insula activation.
• Acceptance $P(t)$: Models regulatory top-down vmPFC (ventromedial prefrontal cortex) activity, serving to down-regulate limbic and ACC signals.
• Dream Intensity $R(t)$: Quantifies the vividness/depth of experiential dream imagery, associated with hippocampus, prefrontal cortex, and amygdala function.
• Cumulative Dream Content $H(t)$: Aggregates the effects of prior influences, aligning with extended BOLD signals in associative cortices during dream periods.
• Mental Activity $M(t)$: Represents spontaneous, high-frequency (gamma) DMN oscillations, predominantly in mPFC/PCC.
• Forgetting $F(t)$: Reflects hippocampal suppression/deactivation, particularly in memory down-regulation conditions.

$M(t)$ and $F(t)$ are modeled as exogenous, slow oscillators that impose modulation but are not themselves dynamically updated by the system.

2. System of Differential Equations

BDM is formalized by a system of four coupled ODEs:

$$\begin{align*} \frac{dR}{dt} &= -\alpha\,P(t) + \beta\,F(t) \ \frac{dD}{dt} &= -\gamma\,P(t) + \delta\,F(t) - \epsilon\,M(t) \ \frac{dP}{dt} &= \eta\,R(t) - \zeta\,D(t) \ \frac{dH}{dt} &= \eta_1\,D(t) + \eta_2\,F(t) + \eta_3\,M(t) - \eta_4\,P(t) \end{align*}$$

with $M(t) = 0.5 + 0.2\sin(0.1t)$ and $F(t) = 0.3 + 0.1\cos(0.1t)$ acting as prescribed inputs.

Parameter interpretation and typical ranges are as follows:

Parameter	Effect	Typical Range	Neural Mapping/Interpretation
$\alpha$	P→R suppression (vmPFC→hippocampus)	0.1–1.0	Emotional regulation strength
$\beta$	F→R facilitation (hippocampus)	0.05–0.5	Degree of memory replay/disinhibition
$\gamma$	P→D inhibition (vmPFC→ACC)	0.1–1.0	Downregulation of negative affect
$\delta$	F→D increase	0.05–0.3	Conflict from memory suppression
$\epsilon$	M→D reduction (DMN-ACC)	0.1–0.4	Mental restructuring/distraction
$\eta$	R→P enhancement	0.05–0.5	Reward, positive imagery impact
$\zeta$	D→P disruption	0.1–0.6	Negative affect interfering
$\eta_1$…$\eta_4$	H equation weights	$\sim$0.1–0.3	Aggregation coefficients for D, F, M, P

Variables are continuous and bounded ($0 \leq D,P,R,H \leq 1$). Initial conditions are e.g. $D(0)=0.8,\;P(0)=0.2,\;R(0)=0.1,\;H(0)=0.0$.

3. Mapping of Variables to Neural Systems

Each BDM state variable is directly mapped to candidate empirical substrates:

• $D(t)$: dorsal ACC and anterior insula, measured via fMRI BOLD and reflecting negative affect/conflict.
• $P(t)$: vmPFC BOLD, associated with emotional regulation and resilience mechanisms.
• $R(t)$: integration of hippocampal, amygdalar, and prefrontal signal (dream vividness/cognitive imagery).
• $H(t)$: summative BOLD/EEG in associative cortex during dreaming.
• $M(t)$: mPFC and PCC gamma, corresponding to DMN spontaneous activity.
• $F(t)$: hippocampal suppression, corresponding to memory suppression or recombination.

This explicit mapping supports translation to neuroimaging experimental settings, allowing simulation-observable correspondence and parameter fitting from empirical data.

4. Analytical Properties and Steady-State Solutions

With $M$ and $F$ held constant, the BDM admits analytical steady-state solutions by setting derivatives to zero:

$$\begin{align*} 0 &= -\alpha\,P^* + \beta\,F \ 0 &= -\gamma\,P^* + \delta\,F - \epsilon\,M \ 0 &= \eta\,R^* - \zeta\,D^* \end{align*}$$

This yields:

$$R^* = \sqrt{\frac{\beta\,\zeta}{\alpha\,\eta}}\,F, \ P^* = \frac{\eta}{\zeta} R^*, \ D^* = \frac{\delta\,F - \epsilon\,M}{\gamma}$$

Local linear stability analysis via the Jacobian indicates, for biologically plausible parameters (all couplings $< 1$), a locally attracting node or focus in state space (trace $< 0$, determinant $>0$).

5. Simulation Results and Empirical Validation

BDM simulations over $t \in [0,100]$ with prescribed $M(t)$ and $F(t)$ and typical parameter choices produce cognitive dynamics aligning with empirical observations:

• $D(t)$ declines smoothly as $P(t)$ (acceptance) rises, consistent with documented ACC–vmPFC anticorrelation in fMRI.
• $P(t)$ stabilizes at a plateau, matching vmPFC BOLD trajectories in emotional regulation tasks.
• $R(t)$ exhibits oscillations in synchrony with $F(t)$, with modulation by $P(t)$, capturing the temporal profile of dream intensity and gamma-band EEG activity.
• $H(t)$ accumulates steadily, consistent with sustained associative cortex activity during REM.
• Joint plots of $H$ against $D$ and $M$ mirror positive correlations observed in mind-wandering and spontaneous cognition studies (e.g., Christoff et al. 2009; Smallwood & Schooler 2015).

6. Model Assumptions, Limitations, and Extensions

BDM assumes all state variables are continuous, differentiable, and normalized. $M(t)$ and $F(t)$ are treated as exogenous rhythmic modulators without endogenous feedback. The model currently omits explicit noise or nonlinearity terms, but can be extended to include stochastic terms or saturating nonlinear dynamics for increased biological realism. The simplicity of four ODEs enables computational tractability and interpretability, but abstracted representations may not capture all complex, multiscale features of real neural circuits.

7. Significance and Applications

BDM offers a reduced, mechanistically interpretable platform for investigating the dynamical underpinnings of dreaming, emotional regulation, and spontaneous cognitive activity. By providing explicit links between abstract ODE states and neurophysiological variables, it enables hypothesis generation and testing against neuroimaging (EEG, fMRI) data. The model’s alignments with empirical ACC/DMN/hippocampus/vmPFC signatures validate its plausibility for modeling spontaneous cognition and the emergence of dream imagery. Potential applications include computational psychiatry, sleep science, and the paper of memory consolidation and affect regulation during unstructured mental activity.