Choosing Models

This guide helps you select the appropriate neural mass model for your research question.

Decision Tree

Need physiological realism?
├─ YES → Physiological Models
│  ├─ Modeling EEG/MEG? → JansenRitModel
│  ├─ Modeling fMRI BOLD? → WongWangModel
│  ├─ E-I population dynamics? → WilsonCowanModel
│  └─ Mean-field spiking? → QIFModel (MontbrioPazoRoxin)
│
└─ NO → Phenomenological Models
   ├─ Studying oscillations? → HopfOscillator or StuartLandauOscillator
   ├─ Studying excitability? → FitzHughNagumoModel
   ├─ Phase synchronization? → KuramotoNetwork
   └─ Fast/simple dynamics? → ThresholdLinearModel

Model Categories

Phenomenological Models

When to use:

• Studying generic dynamical phenomena (bifurcations, synchronization)

• Computational efficiency is critical

• Detailed biophysical mechanisms are not required

Hopf Oscillator

• Best for: Onset of oscillations, rhythm generation

• Key feature: Supercritical Hopf bifurcation

• Variables: 2 (x, y)

• Example use: Studying how oscillatory activity emerges

hopf = brainmass.HopfOscillator(
    in_size=90,
    omega=2 * jnp.pi * 10 * u.Hz,  # 10 Hz alpha rhythm
    a=0.1,  # >0 for limit cycle
)

FitzHugh-Nagumo

• Best for: Excitable systems, spike generation

• Key feature: Type II excitable, fast-slow dynamics

• Variables: 2 (v, w)

• Example use: Studying transitions from rest to spiking

Kuramoto Network

• Best for: Phase synchronization in oscillator networks

• Key feature: Order parameter for collective synchrony

• Variables: 1 (θ)

• Example use: Studying synchronization patterns

Physiological Models

When to use:

• Linking models to empirical neuroimaging data

• Biophysical realism is important

• Modeling specific neural populations

Jansen-Rit Model

• Best for: EEG signal generation, alpha rhythms

• Key feature: 3 neural populations (pyramidal, excitatory, inhibitory)

• Variables: 6 states

• Example use: Simulating EEG from cortical columns

jr = brainmass.JansenRitModel(
    in_size=68,  # number of cortical sources
)

Wilson-Cowan Model

• Best for: Excitatory-inhibitory population dynamics

• Key feature: Classic E-I model, firing rate equations

• Variables: 2 (rE, rI)

• Example use: Studying E-I balance, oscillations

Wong-Wang Model

• Best for: Resting-state fMRI, decision-making tasks

• Key feature: Reduced spiking network with NMDA/GABA synapses

• Variables: 2 (S_E, S_I)

• Example use: Whole-brain resting-state fMRI simulations

QIF Model (Montbrio-Pazo-Roxin)

• Best for: Mean-field reduction of spiking networks

• Key feature: Exact reduction of QIF neuron networks

• Variables: 2 (r, v)

• Example use: Linking spiking and rate dynamics

Model Comparison

Model	Complexity	Speed	Realism	Typical Application
ThresholdLinear	Low	Very Fast	Low	Fast exploratory simulations
Hopf	Low	Fast	Low	Oscillation emergence
FitzHugh-Nagumo	Low	Fast	Medium	Excitability, spikes
Kuramoto	Low	Fast	Low	Phase synchronization
Wilson-Cowan	Medium	Medium	Medium	E-I dynamics, general purpose
Jansen-Rit	High	Slow	High	EEG/MEG modeling
Wong-Wang	High	Slow	High	fMRI BOLD, decision making
QIF	Medium	Medium	High	Mean-field spiking networks

Use Case Examples

Resting-State fMRI Study

Goal: Simulate spontaneous BOLD fluctuations matching empirical FC

Recommended: WongWangModel or WilsonCowanModel

Why: - Slow synaptic dynamics (NMDA) match BOLD timescales - Captures E-I dynamics generating realistic fluctuations - Well-validated for resting-state simulations

nodes = brainmass.WongWangModel(in_size=90)  # AAL90 atlas
bold = brainmass.BOLDSignal(in_size=90)

# Add structural coupling from DTI
coupling = brainmass.DiffusiveCoupling(conn=SC_matrix, k=0.2)

EEG Source Modeling

Goal: Simulate EEG signals from cortical sources

Recommended: JansenRitModel

Why:

• Explicitly models pyramidal neuron membrane potentials (EEG source)

• Validated against empirical EEG spectra

• Generates realistic alpha rhythms

jr = brainmass.JansenRitModel(in_size=68)  # cortical parcels
eeg_fwd = brainmass.EEGLeadFieldModel(
    in_size=68,
    out_size=64,  # electrodes
    L=leadfield_matrix,
)

Synchronization Study

Goal: Study emergence of network synchronization

Recommended: HopfOscillator or KuramotoNetwork

Why:

• Simple, interpretable dynamics

• Well-studied analytically

• Fast for large networks

# Kuramoto for phase-only
kuramoto = brainmass.KuramotoNetwork(
    in_size=100,
    omega_mean=10 * u.Hz,
    omega_std=1 * u.Hz,
)

# Hopf for amplitude + phase
hopf = brainmass.HopfOscillator(in_size=100, omega=10 * u.Hz, a=0.1)

Parameter Fitting Study

Goal: Fit model parameters to empirical data

Recommended: Start simple, then increase complexity

Strategy:

1. Start with HopfOscillator or WilsonCowanModel (fewer parameters)

2. Validate parameter estimates

3. If needed, move to JansenRitModel or WongWangModel

Why:

• Simpler models have fewer local minima

• Easier to interpret fitted parameters

• Can always add complexity later

Common Pitfalls

Using Complex Models Too Early

• More parameters = harder optimization

• Start simple, add complexity only if needed

Ignoring Model Timescales

• Jansen-Rit: τ ~ 10 ms → good for EEG (ms resolution)

• Wong-Wang: τ ~ 100 ms → good for fMRI (second resolution)

• Match model timescale to data modality

Not Considering Computational Cost

• Jansen-Rit: 6 variables per region → 6× slower than Hopf

• For exploratory work, use faster models

Mismatched Observable

• EEG: Use models with explicit membrane potentials (Jansen-Rit)

• fMRI BOLD: Use models with slow synaptic dynamics (Wong-Wang)

• MEG: Similar to EEG

Mixing Models

You can use different models for different regions:

# Thalamus: fast dynamics
thalamus = brainmass.HopfOscillator(in_size=N_thal, omega=40 * u.Hz)

# Cortex: slower dynamics
cortex = brainmass.WilsonCowanModel(in_size=N_cort)

# Couple them
def network_step(i):
    thal_out = thalamus.update()
    cort_out = cortex.update(rE_inp=thal_out.mean())  # thalamic drive
    return cort_out

Model Extensions

All models support:

• Noise: Add stochastic fluctuations

• Coupling: Connect in networks

• Batching: Run multiple parameter sets in parallel

• Optimization: Fit parameters with gradient descent

See corresponding tutorials for details.

Summary Recommendations

Your Goal	Recommended Model
Learn brainmass basics	HopfOscillator or WilsonCowanModel
EEG/MEG modeling	JansenRitModel
fMRI BOLD modeling	WongWangModel or WilsonCowanModel
Fast exploratory work	Hopf Oscillator or ThresholdLinearModel
Excitable dynamics	FitzHughNagumoModel
Spiking network reduction	QIFModel
Synchronization studies	KuramotoNetwork or HopfOscillator

Next Steps

• Building Multi-Region Networks - Create multi-region networks with your chosen model

• Neural Mass Models - Detailed documentation for each model

• Examples - See models in action

See Also

• Deco et al. (2008). “The Dynamic Brain” for model selection guidance

• Parameter Fitting for fitting model parameters