diff --git a/.DS_Store b/.DS_Store new file mode 100644 index 0000000..b1bc858 Binary files /dev/null and b/.DS_Store differ diff --git a/docs/.DS_Store b/docs/.DS_Store index feca861..9a874b5 100644 Binary files a/docs/.DS_Store and b/docs/.DS_Store differ diff --git a/docs/Project.toml b/docs/Project.toml index f7d5dbc..b334ed5 100644 --- a/docs/Project.toml +++ b/docs/Project.toml @@ -1,5 +1,6 @@ [deps] CSV = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b" +CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0" DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0" DifferentialEquations = "0c46a032-eb83-5123-abaf-570d42b7fbaa" Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4" diff --git a/docs/make.jl b/docs/make.jl index 1662eba..eec3484 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -3,6 +3,8 @@ using Documenter cp("./docs/Manifest.toml", "./docs/src/assets/Manifest.toml", force = true) cp("./docs/Project.toml", "./docs/src/assets/Project.toml", force = true) +#cp("./Manifest.toml", "./src/assets/Manifest.toml", force = true) +#cp("./Project.toml", "./src/assets/Project.toml", force = true) DocMeta.setdocmeta!(Neuroblox, :DocTestSetup, :(using Neuroblox); recursive = true) diff --git a/docs/pages.jl b/docs/pages.jl index ce58fbd..4e41aa7 100644 --- a/docs/pages.jl +++ b/docs/pages.jl @@ -3,7 +3,15 @@ pages = ["index.md", "Getting Started" => "getting_started.md", "Tutorials" => Any[ - "tutorials/resting_state_wb.md" + "tutorials/beginner_tutorial.md", + "tutorials/resting_state_wb.md", + #"tutorials/resting_state_wb_delays.md" + #"tutorials/DCM.md" + #"tutorials/Adam_basal_ganglia.md" + #"tutorial/winner_takes_all.md" + "tutorials/neural_assembly.md" + #"tutorial/reinforcement_learning.md" + #"tutorial/cortical.md" ], #"Manual" => Any[], "API" => "api.md", diff --git a/docs/src/.DS_Store b/docs/src/.DS_Store index c0851a2..8f960f9 100644 Binary files a/docs/src/.DS_Store and b/docs/src/.DS_Store differ diff --git a/docs/src/data/image_example.csv b/docs/src/data/image_example.csv new file mode 100644 index 0000000..0d90b0f --- /dev/null +++ b/docs/src/data/image_example.csv @@ -0,0 +1,1027 @@ 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+,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, +,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, +,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, +,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, +,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, +,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, +,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, +,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, 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6cd857d..3e16252 100644 --- a/docs/src/getting_started.md +++ b/docs/src/getting_started.md @@ -2,16 +2,34 @@ This tutorial will introduce you to simulating brain dynamics using Neuroblox. -## Example 1 : Building an oscillating circuit from two Wilson-Cowan Neural Mass Models +## Example 1: Creating a Simple Neural Circuit -The Wilson–Cowan model describes the dynamics of interactions between populations of excitatory and inhibitory neurons. Each Wilson-Cowan Blox is described by the follwoing equations: +In this example, we'll create a simple oscillating circuit using two Wilson-Cowan neural mass models [1]. The Wilson-Cowan model is one of the most influential models in computational neuroscience [2], describing the dynamics of interactions between populations of excitatory and inhibitory neurons. + +### The Wilson-Cowan Model + +Each Wilson-Cowan neural mass is described by the following equations: + +```math +\begin{align} +\nonumber +\frac{dE}{dt} &= \frac{-E}{\tau_E} + S_E(c_{EE}E - c_{IE}I + \eta\textstyle\sum{jcn})\\[10pt] +\nonumber +\frac{dI}{dt} &= \frac{-I}{\tau_I} + S_I\left(c_{EI}E - c_{II}I\right) +\end{align} +``` + +where $E$ and $I$ denote the activity levels of the excitatory and inhibitory populations, respectively. The terms $\frac{dE}{dt}$ and $\frac{dI}{dt}$ describe the rate of change of these activity levels over time. The parameters $\tau_E$ and $\tau_I$ are time constants analogous to membrane time constants in single neuron models, determining how quickly the excitatory and inhibitory populations respond to changes. The coefficients $c_{EE}$ and $c_{II}$ represent self-interaction (or feedback) within excitatory and inhibitory populations, while $c_{IE}$ and $c_{EI}$ represent the cross-interactions between the two populations. The term $\eta\sum{jcn}$ represents external input to the excitatory population from other brain regions or external stimuli, with $\eta$ acting as a scaling factor. While $S_E$ and $S_I$ are sigmoid functions that represent the responses of neuronal populations to input stimuli, defined as: ```math -\frac{dE}{dt} = \frac{-E}{\tau_E} + \frac{1}{1 + \text{exp}(-a_E*(c_{EE}*E - c_{IE}*I - \theta_E + \eta*(\sum{jcn}))}\\[10pt] -\frac{dI}{dt} = \frac{-I}{\tau_I} + \frac{1}{1 + exp(-a_I*(c_{EI}*E - c_{II}*I - \theta_I)} +S_k(x) = \frac{1}{1 + exp(-a_kx - \theta_k)} ``` -Our first example is to simply combine two Wilson-Cowan Blox to build an oscillatory circuit +where $a_k$ and $\theta_k$ determine the steepness and threshold of the response, respectively. + +### Building the Circuit + +Let's create an oscillating circuit by connecting two Wilson-Cowan neural masses: ```@example Wilson-Cowan using Neuroblox @@ -20,27 +38,41 @@ using Graphs using MetaGraphs using Plots +# Create two Wilson-Cowan blox @named WC1 = WilsonCowan() @named WC2 = WilsonCowan() +# Create a graph to represent our circuit g = MetaDiGraph() add_blox!.(Ref(g), [WC1, WC2]) -adj = [-1 6; 6 -1] +# Define the connectivity between the neural masses +adj = [-1 7; 4 -1] create_adjacency_edges!(g, adj) ``` -First, we create the two Wilson-Cowan Blox: WC1 and WC2. Next, we add the two Blox into a directed graph as nodes and then we are creating weighted edges between the two nodes using an adjacency matrix. +Here, we've created two Wilson-Cowan Blox and connected them as nodes in a directed graph. The `adj` matrix defines the weighted edges between these nodes. Each entry `adj[i,j]` represents how the output of blox `j` influences the input of blox `i`: + +- Diagonal elements (`adj[1,1]` and `adj[2,2]`): Self-connections, adding feedback to each blox. +- Off-diagonal elements (`adj[1,2]` and `adj[2,1]`): Inter-blox connections, determining how each blox influences the other. -Now we are ready to build the ModelingToolkit System. Structural simplify creates the final set of equations in which all substiutions are made. +By default, the output of each Wilson-Cowan blox is its excitatory activity (E). The negative self-connections (-1) provide inhibitory feedback, while the positive inter-blox connections (6) provide strong excitatory coupling. This setup creates an oscillatory dynamic between the two Wilson-Cowan units. + +### Creating the Model + +Now, let's build the complete model: ```@example Wilson-Cowan @named sys = system_from_graph(g) sys = structural_simplify(sys) ``` -To solve the system, we first create an ODEProblem and then solve it over the tspan of (0,100) using a stiff solver. The solution is saved every 0.1ms. The unit of time in Neuroblox is 1ms. +This creates a differential equations system from our graph representation using ModelingToolkit and symbolically simplifies it for efficient computation. + +### Simulating the Model + +Finally, let's simulate our model. The following code creates and solves an `ODEProblem` for our system, simulating 100 time units of activity. In Neuroblox, the default time unit is milliseconds. We use `Rodas4`, a solver efficient for stiff problems. The solution is saved every 0.1 ms, allowing us to observe the detailed evolution of the system's behavior. ```@example Wilson-Cowan prob = ODEProblem(sys, [], (0.0, 100), []) @@ -48,51 +80,86 @@ sol = solve(prob, Rodas4(), saveat=0.1) plot(sol) ``` +[[1] Wilson, H. R., & Cowan, J. D. (1972). Excitatory and inhibitory interactions in localized populations of model neurons. Biophysical journal, 12(1), 1-24.](https://www.cell.com/biophysj/fulltext/S0006-3495(72)86068-5) + +[[2] Destexhe, A., & Sejnowski, T. J. (2009). The Wilson–Cowan model, 36 years later. Biological cybernetics, 101(1), 1-2.](https://link.springer.com/article/10.1007/s00422-009-0328-3) + + + ## Example 2 : Building a Brain Circuit from literature using Neural Mass Models -In this example, we will construct a Parkinsons model from eight Jansen-Rit Neural Mass Models as described in Liu et al. (2020). DOI: 10.1016/j.neunet.2019.12.021. The Jansen-Rit Neural Mass model is defined by the following differential equations: +In this example, we'll construct a model of Parkinson's disease using eight Jansen-Rit Neural Mass Models, based on the work of Liu et al. (2020) [1]. + +### The Jansen-Rit Neural Mass Model + +The Jansen-Rit model [2] is another popular neural mass model that, like the Wilson-Cowan model from [Example 1](#example-1-creating-a-simple-neural-circuit), describes the average activity of neural populations. Each Jansen-Rit unit is defined by the following differential equations: + +```math +\begin{align} +\frac{dx}{dt} &= y-\frac{2}{\tau}x \\[10pt] +\frac{dy}{dt} &= -\frac{x}{\tau^2} + \frac{H}{\tau} \left[2\lambda S(\textstyle\sum{jcn}) - \lambda\right] +\end{align} +``` + +where $x$ represents the average postsynaptic membrane potential of the neural population, $y$ is an auxiliary variable, $\tau$ is the membrane time constant, $H$ is the maximum postsynaptic potential amplitude, $\lambda$ determines the maximum firing rate, and $\sum{jcn}$ represents the sum of all synaptic inputs to the population. The sigmoid function $S(x)$ models the population's firing rate response to input and is defined as: ```math -\frac{dx}{dt} = y-\frac{2}{\tau}x -\frac{dy}{dt} = -\frac{x}{\tau^2} + \frac{H}{\tau} [\frac{2\lambda}{1+\text{exp}(-r*\sum{jcn})} - \lambda] +S(x) = \frac{1}{1 + \text{exp}(-rx)} ``` +where $r$ controls the steepness of the sigmoid, affecting the population's sensitivity to input. + +### Setting Up the Model + +Let's start by importing the necessary libraries and defining our neural masses: + ```@example Jansen-Rit using Neuroblox using DifferentialEquations using Graphs using MetaGraphs using Plots -``` -The original paper units are in seconds we therefore need to multiply all parameters with a common factor -```@example Jansen-Rit +# Convert time units from seconds to milliseconds τ_factor = 1000 +# Define Jansen-Rit neural masses for different brain regions @named Str = JansenRit(τ=0.0022*τ_factor, H=20/τ_factor, λ=300, r=0.3) -@named GPE = JansenRit(τ=0.04*τ_factor, cortical=false) # all default subcortical except τ +@named GPE = JansenRit(τ=0.04*τ_factor, cortical=false) # all default subcortical except τ @named STN = JansenRit(τ=0.01*τ_factor, H=20/τ_factor, λ=500, r=0.1) -@named GPI = JansenRit(cortical=false) # default parameters subcortical Jansen Rit blox +@named GPI = JansenRit(cortical=false) # default parameters subcortical Jansen Rit blox @named Th = JansenRit(τ=0.002*τ_factor, H=10/τ_factor, λ=20, r=5) @named EI = JansenRit(τ=0.01*τ_factor, H=20/τ_factor, λ=5, r=5) -@named PY = JansenRit(cortical=true) # default parameters cortical Jansen Rit blox +@named PY = JansenRit(cortical=true) # default parameters cortical Jansen Rit blox @named II = JansenRit(τ=2.0*τ_factor, H=60/τ_factor, λ=5, r=5) + blox = [Str, GPE, STN, GPI, Th, EI, PY, II] ``` -Again, we create a graph and add the Blox as nodes + +Here, we've created eight Jansen-Rit neural masses representing different brain regions involved in Parkinson's disease. The `τ_factor` is used to convert time units from seconds (as in the original paper) to milliseconds (Neuroblox's default time unit). + +### Building the Circuit + +Now, let's create a graph representing our brain circuit: ```@example Jansen-Rit g = MetaDiGraph() add_blox!.(Ref(g), blox) +``` + +We've created a MetaDiGraph and added our neural masses as nodes. Next, we'll define the connections between these nodes based on the known anatomy of the basal ganglia-thalamocortical circuit. + +ModelingToolkit allows us to create parameters that can be passed into the equations symbolically: +```@example Jansen-Rit +# Define connection strength parameters params = @parameters C_Cor=60 C_BG_Th=60 C_Cor_BG_Th=5 C_BG_Th_Cor=5 ``` -ModelingToolkit allows us to create parameters that can be passed into the equations symbolically. -We add edges as specified in Table 2 of Liu et al. -We only implemented a subset of the nodes and edges to describe a less complex version of the model. Edges can also be created using an adjacency matrix as in the previous example. +As an alternative to creating edges with an adjacency matrix (as shown in the previous example), here we demonstrate a different approach by adding edges one by one. In this case, we set the connections specified in Table 2 of Liu et al. [1], although we only implement a subset of the nodes and edges to describe a simplified version of the model: ```@example Jansen-Rit +# Add connections between brain regions add_edge!(g, 2, 1, Dict(:weight => -0.5*C_BG_Th)) add_edge!(g, 2, 2, Dict(:weight => -0.5*C_BG_Th)) add_edge!(g, 2, 3, Dict(:weight => C_BG_Th)) @@ -116,23 +183,27 @@ add_edge!(g,3,2,:weight, C_BG_Th) add_edge!(g,4,3,:weight, -0.5*C_BG_Th) add_edge!(g,4,4,:weight, C_BG_Th_Cor) ``` -Now we are ready to build the ModelingToolkit System and apply structural simplification to the equations. + +### Creating the Model + +Let's build the complete model: ```@example Jansen-Rit @named final_system = system_from_graph(g) final_system_sys = structural_simplify(final_system) ``` -Our Jansen-Rit model allows delayed edges, and we therefore need to collect those delays (in our case all delays are zero). Then we build a Delayed Differential Equations Problem (DDEProblem). + +This creates a differential equations system from our graph representation using ModelingToolkit and symbolically simplifies it for efficient computation. + +### Simulating the Model + +Lastly, we create the `ODEProblem` for our system, select an algorithm, in this case `Tsit5()`, and simulate 1 second of brain activity. + ```@example Jansen-Rit sim_dur = 1000.0 # Simulate for 1 second -prob = ODEProblem(final_system_sys, - [], - (0.0, sim_dur)) -``` -We select an algorithm and solve the system -```@example Jansen-Rit -alg = Tsit5() -sol_dde_no_delays = solve(prob, alg, saveat=1) -plot(sol_dde_no_delays) +prob = ODEProblem(final_system_sys, [], (0.0, sim_dur)) +sol = solve(prob, Tsit5(), saveat=1) +plot(sol) ``` -In a later tutorial, we will show how to introduce edge delays. + +[[1] Liu, C., Zhou, C., Wang, J., Fietkiewicz, C., & Loparo, K. A. (2020). The role of coupling connections in a model of the cortico-basal ganglia-thalamocortical neural loop for the generation of beta oscillations. Neural Networks, 123, 381-392.](https://doi.org/10.1016/j.neunet.2019.12.021) \ No newline at end of file diff --git a/docs/src/index.md b/docs/src/index.md index af03c67..0c1d001 100644 --- a/docs/src/index.md +++ b/docs/src/index.md @@ -1,14 +1,27 @@ # Neuroblox ## About -Neuroblox.jl is designed for computational neuroscience and psychiatry applications. Our tools range from control circuit system identification to brain circuit simulations bridging scales from spiking neurons to fMRI-derived circuits, parameter-fitting models to neuroimaging data, interactions between the brain and other physiological systems, experimental optimization, and scientific machine learning. +### Overview +Neuroblox is designed for computational neuroscience and psychiatry applications. Our tools range from brain circuit simulations to control circuit system identification, bridging scales from spiking neurons to fMRI-derived circuits, interactions between the brain and other physiological systems, experimental optimization, and scientific machine learning. -## Description -Neuroblox.jl is based on a library of modular computational building blocks (“blox”) in the form of systems of symbolic dynamic differential equations that can be combined to describe large-scale brain dynamics. Once a model is built, it can be simulated efficiently and fit electrophysiological and neuroimaging data. Moreover, the circuit behavior of multiple model variants can be investigated to aid in distinguishing between competing hypotheses. -We employ ModelingToolkit.jl to describe the dynamical behavior of blox as symbolic (stochastic/delay) differential equations. Our libraries of modular blox consist of individual neurons (Hodgkin-Huxley, IF, QIF, LIF, etc.), neural mass models (Jansen-Rit, Wilson-Cowan, Lauter-Breakspear, Next Generation, microcanonical circuits etc.) and biomimetically-constrained control circuit elements. A GUI designed to be intuitive to neuroscientists allows researchers to build models that automatically generate high-performance systems of numerical ordinary/stochastic differential equations from which one can run stimulations with parameters fit to experimental data. Our benchmarks show that the increase in speed for simulation often exceeds a factor of 100 as compared to neural mass model implementation by the Virtual Brain (python) and similar packages in MATLAB. For parameter fitting of brain circuit dynamical models, we use Turing.jl to perform probabilistic modeling, including Hamilton-Monte-Carlo sampling and Automated Differentiation Variational Inference. +### Features +Neuroblox is based on a library of modular computational building blocks (“blox”) in the form of systems of symbolic dynamic differential equations, which can be flexibly combined to describe large-scale brain dynamics. Our libraries of modular blox consist of individual neurons (Hodgkin-Huxley, IF, QIF, LIF, etc.), neural mass models (Jansen-Rit, Wilson-Cowan, Lauter-Breakspear, Next Generation, microcanonical circuits, etc.), and biomimetically-constrained control circuit elements. + +Once a model is built, it can be simulated efficiently and used to fit electrophysiological and neuroimaging data. Moreover, the circuit behavior of multiple model variants can be investigated to aid in distinguishing between competing hypotheses. + +### Interface +Users can interface with Neuroblox either via Julia code or using a simple drag-and-drop GUI designed to be intuitive to neuroscientists. Both interfaces allow researchers to automatically generate high-performance models from which one can run stimulations with parameters fit to experimental data. + +### Performance +The Neuroblox back-end (Neuroblox.jl) is built using [Julia](https://julialang.org/), an open-source, high-level scripting language designed for high-performance in computation-intensive applications. Our benchmarks show greater than 100x increase in speed over neural mass model implementations using the Virtual Brain (Python) and similar packages in MATLAB. + +### Implementation +Under the hood, we employ ModelingToolkit.jl to describe the dynamical behavior of blox as symbolic (stochastic/delay) differential equations. For parameter fitting of brain circuit dynamical models, we use Turing.jl to perform probabilistic modeling, including Hamilton-Monte-Carlo sampling and Automated Differentiation Variational Inference. ## Installation +Neuroblox requires a valid [Julia](https://julialang.org/downloads/) installation and [JuliaHub](https://juliahub.com/ui/Home) user account. Using Neuroblox via the GUI does *not* require any programming knowledge, but interested users can learn more about Julia [here](https://julialang.org/learning/). + To install Neuroblox.jl, first add the JuliaHubRegistry and then use the Julia package manager: ```julia @@ -22,6 +35,6 @@ Pkg.add("Neuroblox") ## Licensing -Neuroblox is free for non-commerical and academic use. For full details of the license, please see +Neuroblox is free for non-commerical and academic use. For full details of the license, please see [the Neuroblox EULA](https://github.com/Neuroblox/NeurobloxEULA). For commercial use, get in contact with sales@neuroblox.org. diff --git a/docs/src/tutorials/QIF_movie.jl b/docs/src/tutorials/QIF_movie.jl new file mode 100644 index 0000000..53ca5c0 --- /dev/null +++ b/docs/src/tutorials/QIF_movie.jl @@ -0,0 +1,28 @@ +using Neuroblox +using MetaGraphs +using DifferentialEquations +using Random +using Plots +using Statistics + +qif1 = QIFNeuron(name=Symbol("qif1"), I_in=0.5) +g = MetaDiGraph() +add_blox!.(Ref(g), [qif1]) + +@named sys = system_from_graph(g) +sys = structural_simplify(sys) +length(unknowns(sys)) + +prob = ODEProblem(sys, [], (0.0, 1000), []) +sol = solve(prob, Vern7(), saveat=0.1) +plot(sol.t,sol[1,:],xlims=(0,1000),xlabel="time (ms)",ylabel="mV") +pI_in = parameters(sys)[findall(x->contains(string(x),"I_in"),parameters(sys))][1] + +I = 0:0.01:0.1 +anim = @animate for i in I + @show i + prob_new = remake(prob,p=[pI_in => i]) + sol_new = solve(prob_new, Vern7(), saveat=0.1) + plot_qif = plot(sol_new.t,sol_new[1,:],xlims=(0,1000),xlabel="time (ms)",ylabel="mV",label="I_in=$(i)",legend=:top) +end +gif(anim, "anim_fps5.gif", fps = 5) \ No newline at end of file diff --git a/docs/src/tutorials/beginner_tutorial.md b/docs/src/tutorials/beginner_tutorial.md new file mode 100644 index 0000000..5593472 --- /dev/null +++ b/docs/src/tutorials/beginner_tutorial.md @@ -0,0 +1,229 @@ +# [Julia Basics and how to model a single neuron](@id beginner_tutorial) + +This initial tutorial will introduce Julia's basic structures and how to model the Izhikevich model of neuronal spiking. + +## Julia's basic structures + +In Julia, we assign a variable simply by calling it by its name and assigning a value to it using the `=` symbol: + +```@example beginner_tutorial +my_variable = 42 +``` + +For basic math operations, we can just use the following operators: + +```@example beginner_tutorial +sum = 3 + 2 +product = 3 * 2 +difference = 3 - 2 +quotient = 3 / 2 +power = 3 ^ 2 +modulus = 3 % 2 +``` + +To define a function in Julia, we first write `function` followed by the function's name, its arguments, the commands and `end`: + +```@example beginner_tutorial +function tutorial(argument) + # Your code goes here + println("The input was ", argument, ".") +end +``` + +And we can simply call it by its name: + +```@example beginner_tutorial +tutorial("Neuroblox") +#This should print "The input was Neuroblox." +``` + +## Plotting graphs + +We can plot graphs in Julia using the `Plots.jl` package. To add this package we use the terminal: + +```@example beginner_tutorial +using Pkg +Pkg.add("Plots") +# This will use the package manager to explicitely add the Plots.jl package + +using Plots +# This will load the package +``` + +Inside this package, there are several built-in functions. First, we have to tell Plots.jl which backend we will be using for rendering plots. + +In this tutorial we will be using `GR backend`, but there are several others and you can find them here: https://docs.juliaplots.org/latest/backends/ + +To call GR, we simply call it as the parameterless function `gr()`. After that, we need an interval and a data set to generate a graph. In general, we'll have something like this: + +```@example beginner_tutorial +using Plots + +# Set GR as the backend for Plots.jl +gr() + +# Create some data (an interval and a random 10-element vector) +x = 1:10 +y = rand(10) + +# Plot the data +plot(x, y, label="Random Data", xlabel="X-axis", ylabel="Y-axis", title="Example") +``` + +You can try running the code above in your Julia terminal using your own data to see how it works. + +## Solving differential equations + +An essential package we'll be using is `DifferentialEquations.jl`, a library designed to solve various types of differential equations, such as ODEs, SDEs and PDEs. + +To use the `DifferentialEquations` library, we need to define a differential equation as a function, solve it and then plot it (we know how to do the last part). + +Another useful library we'll be using is `ModelingToolkit.jl`, a Julia package designed to make our lives easiear when dealing with complex models and performing tasks such as model simplification, parameter estimation and code generation. + +Let's solve the ODE $\frac{du}{dt}=-a \cdot u$ using this package. First we need to define what are our variables and what are our parameters. For this, we'll use the `@variables`and `@parameters` macros from `ModelingToolkit`: + +```@example beginner_tutorial +# Install and import these packages +using Pkg +Pkg.add("ModelingToolkit") +Pkg.add("DifferentialEquations") +using ModelingToolkit +using DifferentialEquations + +# Define the time variable +@variables t + +# Define the time-dependent variable u +@variables u(t) + +# Define the parameter a +@parameters a +``` + +We also have to define our differential operator (it'll work as a function). We just need to declare it using the function `Differential(independent_variable)`: + +```@example beginner_tutorial +# Define the differential operator +D = Differential(t) +``` + +Finally, when using `ModelingToolkit`, the `~` symbol is used as the equal sign when writing an equation: + +```@example beginner_tutorial +# Define the differential equation du/dt = -a * u +equation = D(u) ~ -a * u +``` + +Now, in order to build the ODE system, we use the `@named` macro to name the system and the `ODESystem` function: + +```@example beginner_tutorial +# Build the ODE system and assign it a name +@named system = ODESystem(equation, t) +``` + +We also have to define our system's initial conditions and parameter values. We use the following syntax: + +```@example beginner_tutorial +# Define the initial conditions and parameters +u0 = [u => 1.0] +p = [a => 2.0] +tspan = (0.0 , 5.0) +``` + +Finally, using the functions `ODEProblem` and `solve` from `DifferentialEquations` we convert our system to a numerical problem and solve it: + +```@example beginner_tutorial +# Set up the problem +problem = ODEProblem(complete(system), u0, tspan, p) + +# Solve the problem +solution = solve(problem) +``` + +Finally, we can graph the solution using what we've already learned: + +```@example beginner_tutorial +using Plots + +plot(solution, xlabel="Time", ylabel="u(t)", title="Solution to du/dt=-a*u") +``` + +## The Izhikevich model + +The Izhikevich model is described by the following two-dimensional system of ordinary differential equations: + +```math +\begin{align} +\frac{dv}{dt} &= 0.04 v^2 + 5 v + 140 - u + I \\ +\frac{du}{dt} &= a(bv - u) +\end{align} +``` + +with the auxiliary after-spike resetting + +```math +\begin{align} +\text{if }v \geq 30\text{ mV, then }\begin{cases}v\rightarrow c\\ u \rightarrow u + d \end{cases} +\end{align} +``` + +In order to create this model in Julia, we first need to create an ODE using what we've already learned: + +```@example beginner_tutorial +using ModelingToolkit +using DifferentialEquations + +@variables t v(t) u(t) +@parameters a b c d I +D = Differential(t) + +equation = [D(v) ~ 0.04 * v ^ 2 + 5 * v + 140 - u + I + D(u) ~ a * (b * v - u)] +``` + +Now, we need to create the event that generates the spikes. For this, we create a continuous event to represent the discontinuity in our functions. Those should be written in the following format: + +```julia +name_of_event = [[event_1] => [effect_1] + [event_2] => [effect_2] + ... + [event_n] => [effect_n]] +``` + +In our case, it'll be: + +```@example beginner_tutorial +event = [[v ~ 30.0] => [u ~ u + d] + [v ~ 30.0] => [v ~ c]] +``` + +and now, using the `ODESystem` function, we'll create our system of ODE's. We need to declare our independent variable, dependent variables and parameters when creating this system, and if it exists (in this case, it does exist), we also need to declare our events: + +```@example beginner_tutorial +@named izh_system = ODESystem(equation, t, [v, u], [a, b, c, d, I]; continuous_events = event) +``` + Finally, we define our parameters and solve our system: + + ```@example beginner_tutorial + # Those below can change; I'm using the parameters for a chattering dynamic +p = [a => 0.02, b => 0.2, c => -50.0, d => 2.0, I => 10.0] + +u0 = [v => -65.0, u => -13.0] + +tspan = (0.0, 100.0) + +izh_prob = ODEProblem(complete(izh_system), u0, tspan, p) +izh_sol = solve(izh_prob) +``` + +Now that our problem is solved, we just have to plot it: + +```@example beginner_tutorial +using Plots +gr() + +# The "vars" below is used to plot only the "v" variable +plot(izh_sol, vars = [v], xlabel="Time (ms)", ylabel="Membrane Potential (mV)", title="Izhikevich Neuron Model") +``` + +We're done! You've just plotted a single neuron model. diff --git a/docs/src/tutorials/decision_making.jl b/docs/src/tutorials/decision_making.jl new file mode 100644 index 0000000..0cf0835 --- /dev/null +++ b/docs/src/tutorials/decision_making.jl @@ -0,0 +1,102 @@ +# # Introduction +# Describe what the tutorial will do, e.g. we are implementing a decision-making circuit model from Wang 2002 [1] +# Show some graph of the model (eventually this could be a GUI screenshot with the circuit, even for code tutorials). + +# # Model definition +## (Mention in comment why we are using every non-Neuroblox package) +using Neuroblox +using MetaGraphs ## use its MetaGraph type to build the circuit (actually we can avoid using Metagraph explicitly, Neuroblox can @reexport relevant structs) +using OrdinaryDiffEq ## to build the ODE problem and solve it, gain access to multiple solvers from this (AFAIK this is lighter than using DifferentialEquations) +using Distributions ## for statistical distributions +using Plots ## for displaying plots (plotting recipes will be internal to Neuroblox in an extension and load when CairoMakie or Plots is imported by the user) + +## Describe what the local variables you define are for +global_ns = :g ## global name for the circuit. All components should be inside this namespace. + +tspan = (0, 1000) ## Simulation time span [ms] +spike_rate = 2.4 ## spikes / ms + +f = 0.15 ## ratio of selective excitatory to non-selective excitatory neurons +N_E = 24 ## total number of excitatory neurons +N_I = Int(ceil(N_E / 4)) ## total number of inhibitory neurons +N_E_selective = Int(ceil(f * N_E)) ## number of selective excitatory neurons +N_E_nonselective = N_E - 2 * N_E_selective ## number of non-selective excitatory neurons + +w₊ = 1.7 +w₋ = 1 - f * (w₊ - 1) / (1 - f) + +## Use scaling factors for conductance parameters so that our abbreviated model +## can exhibit the same competition behavior between the two selective excitatory populations +## as the larger model in Wang 2002 does. +exci_scaling_factor = 1600 / N_E +inh_scaling_factor = 400 / N_I + +coherence = 0 # random dot motion coherence [%] +dt_spike_rate = 50 # update interval for the stimulus spike rate [ms] +μ_0 = 40e-3 # mean stimulus spike rate [spikes / ms] +ρ_A = ρ_B = μ_0 / 100 +μ_A = μ_0 + ρ_A * coherence +μ_B = μ_0 + ρ_B * coherence +σ = 4e-3 # standard deviation of stimulus spike rate [spikes / ms] + +spike_rate_A = Normal(μ_A, σ) => dt_spike_rate # spike rate distribution for selective population A +spike_rate_B = Normal(μ_B, σ) => dt_spike_rate # spike rate distribution for selective population B + +# Blox definitions +@named background_input = PoissonSpikeTrain(spike_rate, tspan; namespace = global_ns, N_trains=1); + +@named stim_A = PoissonSpikeTrain(spike_rate_A, tspan; namespace = global_ns); +@named stim_B = PoissonSpikeTrain(spike_rate_B, tspan; namespace = global_ns); + +@named n_A = LIFExciCircuitBlox(; namespace = global_ns, N_neurons = N_E_selective, weight = w₊, exci_scaling_factor, inh_scaling_factor); +@named n_B = LIFExciCircuitBlox(; namespace = global_ns, N_neurons = N_E_selective, weight = w₊, exci_scaling_factor, inh_scaling_factor) ; +@named n_ns = LIFExciCircuitBlox(; namespace = global_ns, N_neurons = N_E_nonselective, weight = 1.0, exci_scaling_factor, inh_scaling_factor); +@named n_inh = LIFInhCircuitBlox(; namespace = global_ns, N_neurons = N_I, weight = 1.0, exci_scaling_factor, inh_scaling_factor); + +bloxs = [background_input, stim_A, stim_B, n_A, n_B, n_ns, n_inh]; +## This is a convenience step so that we can later add edges to the graph using the Blox names. +## (We should replace add_edge! with a nicer interface to avoid this eventually) +d = Dict(b => i for (i,b) in enumerate(bloxs)); + +g = MetaDiGraph() +add_blox!.(Ref(g), bloxs) + +add_edge!(g, d[background_input], d[n_A], Dict(:weight => 1)) +add_edge!(g, d[background_input], d[n_B], Dict(:weight => 1)) +add_edge!(g, d[background_input], d[n_ns], Dict(:weight => 1)) +add_edge!(g, d[background_input], d[n_inh], Dict(:weight => 1)) + +add_edge!(g, d[stim_A], d[n_A], Dict(:weight => 1)) +add_edge!(g, d[stim_B], d[n_B], Dict(:weight => 1)) + +add_edge!(g, d[n_A], d[n_B], Dict(:weight => w₋)) +add_edge!(g, d[n_A], d[n_ns], Dict(:weight => 1)) +add_edge!(g, d[n_A], d[n_inh], Dict(:weight => 1)) + +add_edge!(g, d[n_B], d[n_A], Dict(:weight => w₋)) +add_edge!(g, d[n_B], d[n_ns], Dict(:weight => 1)) +add_edge!(g, d[n_B], d[n_inh], Dict(:weight => 1)) + +add_edge!(g, d[n_ns], d[n_A], Dict(:weight => w₋)) +add_edge!(g, d[n_ns], d[n_B], Dict(:weight => w₋)) +add_edge!(g, d[n_ns], d[n_inh ], Dict(:weight => 1)) + +add_edge!(g, d[n_inh], d[n_A], Dict(:weight => 1)) +add_edge!(g, d[n_inh], d[n_B], Dict(:weight => 1)) +add_edge!(g, d[n_inh], d[n_ns], Dict(:weight => 1)) + +## Build the ODE system from the model graph +@named sys = system_from_graph(g); +## Simplify the ODE system +sys_simpl = structural_simplify(sys); +## Build an ODE Problem object out of the system +prob = ODEProblem(sys_simpl, [], tspan); +## Solve the ODE Problem by choosing a solver +sol = solve(prob, Vern7(lazy=false)) + +# # Simulation results +# (Such plotting commands will be replaced with recipes) +plot(sol[1:end]; idxs = [n_A.odesystem.neuron1.V]) +plot(sol[1:end]; idxs = [n_B.odesystem.neuron1.V]) +plot(sol[1:end]; idxs = [n_inh.odesystem.neuron1.V]) +# Briefly describe the results in a paragraph. diff --git a/docs/src/tutorials/neural_assembly.jl b/docs/src/tutorials/neural_assembly.jl new file mode 100644 index 0000000..2856941 --- /dev/null +++ b/docs/src/tutorials/neural_assembly.jl @@ -0,0 +1,280 @@ +# # Tutorial on bottom-up approach to building a neural assembly + + +# ## Single spiking neuron from Hodgkin-Huxley model + +# Hodgkin-Huxley (HH) formalism to describe membrane potential of a single neuron + + #md ```math + #md \begin{align} + #md C_m\frac{dV}{dt} &= -g_L(V-V_L) - {g}_{Na}m^3h(V-V_{Na}) -{g}_Kn^4(V-V_K) + I_{in} - I_{syn} \\ + #md \frac{dm}{dt} &= \alpha_{m}(V)(1-m) + \beta_{m}(V)m \\ + #md \frac{dh}{dt} &= \alpha_{h}(V)(1-h) + \beta_{h}(V)h \\ + #md \frac{dn}{dt} &= \alpha_{n}(V)(1-n) + \beta_{n}(V)n + #md \end{align} + #md ``` + + +using Neuroblox +using MetaGraphs ## use its MetaGraph type to build the circuit +using DifferentialEquations ## to build the ODE problem and solve it, gain access to multiple solvers from this +using Random ## for generating random variables +using Plots ## Plotting timeseries +using CairoMakie ## for customized plotting recipies for blox +using CSV ## to read data from CSV files +using DataFrames ## to format the data into DataFrames + +# define a single excitatory neuron 'blox' with steady input current I_bg = 0.5 microA/cm2 +nn1 = HHNeuronExciBlox(name=Symbol("nrn1"), I_bg=0.5) + +# add the single neuron 'blox' as a single node in a graph +g = MetaDiGraph() ## defines a graph +add_blox!.(Ref(g), [nn1]) ## adds the defined blocks into the graph + + +# create an ODESystem from the graph +@named sys = system_from_graph(g) +sys = structural_simplify(sys) +length(unknowns(sys)) ## shows the number of variables in the simplified system + +# To solve the system, we first create an Ordinary Differential Equation Problem and then solve it over the tspan of (0,1e) using a Vern7() solver. The solution is saved every 0.1ms. The unit of time in Neuroblox is 1ms. + + +prob = ODEProblem(sys, [], (0.0, 1000), []) +sol = solve(prob, Vern7(), saveat=0.1) + +# acessing the voltage timeseries from the neuron block and plotting the voltage +v = voltage_timeseries(n_inh,sol) +Plots.plot(sol.t,v,xlims=(0,1000),xlabel="time (ms)",ylabel="mV") +# ``` + + +# ## Connecting three neurons through synapses to make a small local circuit + +## While creating a system of multiple components (neurons in this case), each component should be defined within the same namespace. So first +## we define a global namespace. +global_namespace=:g + +## define three neurons, two excitatory and one inhibitory + +nn1 = HHNeuronExciBlox(name=Symbol("nrn1"), I_bg=0.4,namespace=global_namespace) +nn2 = HHNeuronInhibBlox(name=Symbol("nrn2"), I_bg=0.1,namespace=global_namespace) +nn3 = HHNeuronExciBlox(name=Symbol("nrn3"), I_bg=1.4,namespace=global_namespace) +assembly = [nn1,nn2,nn3] + +## add the three neurons as nodes in a graph +g = MetaDiGraph() +add_blox!.(Ref(g), assembly) + +## connect the nodes with the edges (synapses in this case), with the synaptic weights specified as arguments +add_edge!(g, 1, 2, Dict(:weight => 1)) ##connection from node 1 to node 2 (nn1 to nn2) +add_edge!(g, 2, 3, Dict(:weight => 0.2)) ##connection from node 2 to node 3 (nn2 to nn3) + +## create an ODESystem from the graph and then solve it using an ODE solver +@named sys = system_from_graph(g) +sys = structural_simplify(sys) +prob = ODEProblem(sys, [], (0.0, 1000), []) +sol = solve(prob, Vern7(), saveat=0.1) + +## plotting membrane voltage activity of all neurons in a stacked form + +voltage_stack([nn1,nn2,nn3],sol) ## voltage_stack(, sol) + + + +# ## Creating a lateral inhibition circuit (the "winner-takes-all" circuit) in superficial cortical layer + +global_namespace=:g +N_exci = 5; ##number of excitatory neurons + +n_inh = HHNeuronInhibBlox(name = Symbol("inh"), namespace=global_namespace, G_syn = 4.0, τ = 70) ##feedback inhibitory interneuron neuron + +##creating an array of excitatory pyramidal neurons +n_excis = [HHNeuronExciBlox( + name = Symbol("exci$i"), + namespace=global_namespace, + G_syn = 3.0, + τ = 5, + I_bg = 5*rand(), + ) for i = 1:N_exci] + +g = MetaDiGraph() +add_blox!(g, n_inh) +for i in Base.OneTo(N_exci) + add_blox!(g, n_excis[i]) + add_edge!(g, 1, i+1, :weight, 1.0) + add_edge!(g, i+1, 1, :weight, 1.0) +end + +@named sys = system_from_graph(g) +sys = structural_simplify(sys) +prob = ODEProblem(sys, [], (0.0, 1000), []) +sol = solve(prob, Vern7(), saveat=0.1) +voltage_stack(n_excis,sol) + +# ## Creating lateral inhibition "winner-take-all" circuit (WTA) blocks from the inbuilt functions and connecting two WTA circuit blocks + + +global_namespace=:g +N_exci = 5 ##number of excitatory neurons in each WTA circuit +wta1 = WinnerTakeAllBlox(name=Symbol("wta1"), I_bg=5.0, N_exci=N_exci, namespace=global_namespace) ##for a single valued input current, each neuron of the WTA circuit will recieve a uniformly distributed random input from 0 to I_bg +wta2 = WinnerTakeAllBlox(name=Symbol("wta2"), I_bg=4.0, N_exci=N_exci, namespace=global_namespace) + +g = MetaDiGraph() +add_blox!.(Ref(g), [wta1, wta2]) +add_edge!(g, 1, 2, Dict(:weight => 1, :density => 0.5)) ##density keyword sets the connection probability from each excitatory neuron of source WTA circuit to each excitatory neuron of target WTA circuit + +sys = system_from_graph(g, name=global_namespace) +sys = structural_simplify(sys) +prob = ODEProblem(sys, [], (0.0, 1000), []) +sol = solve(prob, Vern7(), saveat=0.1) + +voltage_stack([wta1,wta2],sol) + +# ## Creating a single cortical superficial layer block (SCORT in Pathak et. al. 2024) by connecting multiple WTA circuits + +global_namespace=:g +N_wta=20 ## number of WTA circuits +## parameters +N_exci=5 ##number of pyramidal neurons in each lateral inhibition (WTA) circuit +G_syn_exci=3.0 ##maximal synaptic conductance in glutamatergic (excitatory) synapses +G_syn_inhib=4.0 ## maximal synaptic conductance in GABAergic (inhibitory) synapses from feedback interneurons +G_syn_ff_inhib=3.5 ## maximal synaptic conductance in GABAergic (inhibitory) synapses from feedforward interneurons +I_bg=5.0 ##background input +density=0.01 ##connection density between WTA circuits + +##creating array of WTA ciruits +wtas = [WinnerTakeAllBlox(; + name=Symbol("wta$i"), + namespace=global_namespace, + N_exci=N_exci, + G_syn_exci=G_syn_exci, + G_syn_inhib=G_syn_inhib, + I_bg = I_bg + ) for i = 1:N_wta] + +##feed-forward interneurons (get input from other pyramidal cells and from the ascending system, largely controls the rhythm) +n_ff_inh = HHNeuronInhibBlox(; + name=Symbol("ff_inh"), + namespace=global_namespace, + G_syn=G_syn_ff_inhib + ) + +g = MetaDiGraph() +add_blox!.(Ref(g), vcat(wtas, n_ff_inh)) + +## connecting WTA circuits to each other with given connection density, and feedforward interneuron connects to each WTA circuit +for i in 1:N_wta + for j in 1:N_wta + if j != i + add_edge!(g, i, j, Dict(:weight => 1, :density => density)) + end + end + add_edge!(g, N_wta+1, i, Dict(:weight => 1)) +end + +sys = system_from_graph(g, name=global_namespace) +sys = structural_simplify(sys) +prob = ODEProblem(sys, [], (0.0, 1000), []) +sol = solve(prob, Vern7(), saveat=0.1) + +voltage_stack(vcat(wtas, n_ff_inh),sol) + + +# ## Creating an ascending system block (ASC1 in Pathak et. al. 2024), a single inbuilt cortical superficial layer block (SCORT in Pathak et. al. 2024) and connecting them. + +global_namespace=:g + +## define ascending system block using a Next Generation Neural Mass model as described in Byrne et. al. 2020. +## the parameters are fixed to generate a 16 Hz modulating frequency in the cortical neurons +@named ASC1 = NextGenerationEIBlox(;namespace=global_namespace, Cₑ=2*26,Cᵢ=1*26, Δₑ=0.5, Δᵢ=0.5, η_0ₑ=10.0, η_0ᵢ=0.0, v_synₑₑ=10.0, v_synₑᵢ=-10.0, v_synᵢₑ=10.0, v_synᵢᵢ=-10.0, alpha_invₑₑ=10.0/26, alpha_invₑᵢ=0.8/26, alpha_invᵢₑ=10.0/26, alpha_invᵢᵢ=0.8/26, kₑₑ=0.0*26, kₑᵢ=0.6*26, kᵢₑ=0.6*26, kᵢᵢ=0*26) + +## define the superficial layer cortical block using inbuilt function +## Number if WTA circuits = N_wta=45; number of pyramidal neurons in each WTA circuit = N_exci = 5; +@named CB = CorticalBlox(N_wta=45, N_exci=5, density=0.01, weight=1,I_bg_ar=5;namespace=global_namespace) + +## define graph and add both blox in the graph +g = MetaDiGraph() +add_blox!.(Ref(g), [ASC1,CB]) +## connect ASC1->CB +add_edge!(g, 1, 2, Dict(:weight => 44)) + +## solve the system for time 0 to 1000 ms +sys = system_from_graph(g, name=global_namespace) +sys = structural_simplify(sys) +prob = ODEProblem(sys, [], (0.0, 1000), []) ## tspan = (0,1000) +sol = solve(prob, Vern7(), saveat=0.1) + +# plot neuron time series +voltage_stack(CB,sol) + +# plot the meanfield of all cortical block neurons (mean membrane voltage) +mnv = meanfield_timeseries(CB,sol) +Plots.plot(sol.t,mnv,xlabel="time (ms)",ylabel="mV") + +# plot power spectrum of the meanfield +powerspectrumplot(CB,sol) + +# Notice the peak at 16 Hz, representing beta oscillations. + + +# ## Creating simulation of visual stimulus response in cortical blocks (add Hebbian learning later) + +# create cortical blocks for visual area cortex (VAC), anterior cortex (AC) and ascending system block (ASC1) +global_namespace=:g +## cortical blox +@named VAC = CorticalBlox(N_wta=45, N_exci=5, density=0.01, weight=1,I_bg_ar=0;namespace=global_namespace) +@named AC = CorticalBlox(N_wta=20, N_exci=5, density=0.01, weight=1,I_bg_ar=0;namespace=global_namespace) +## ascending system blox, modulating frequency set to 16 Hz +@named ASC1 = NextGenerationEIBlox(;namespace=global_namespace, Cₑ=2*26,Cᵢ=1*26, Δₑ=0.5, Δᵢ=0.5, η_0ₑ=10.0, η_0ᵢ=0.0, v_synₑₑ=10.0, v_synₑᵢ=-10.0, v_synᵢₑ=10.0, v_synᵢᵢ=-10.0, alpha_invₑₑ=10.0/26, alpha_invₑᵢ=0.8/26, alpha_invᵢₑ=10.0/26, alpha_invᵢᵢ=0.8/26, kₑₑ=0.0*26, kₑᵢ=0.6*26, kᵢₑ=0.6*26, kᵢᵢ=0*26) + +# create an image source block which takes image data from a .csv file and gives input to visual cortex + +fn = joinpath(@__DIR__, "../data/image_example.csv") ## image data file +image_set = CSV.read(fn, DataFrame) ## reading data into DataFrame format +image_sample = 10 ## set which image to input (from 1 to 1000) + +## plot the image that the visual cortex 'sees' +pixels=Array(image_set[image_sample,1:end-1])## access the desired image sample from respective row +pixels=reshape(pixels,15,15)## reshape into 15 X 15 square image matrix +Plots.plot(Gray.(ar),xlims=(0.5,15.5),ylims=(0.5,15.5)) ## plot the grayscale image + +## define stimulus source blox +## t_stimulus: how long the stimulus is on (in msec) +## t_pause : how long th estimulus is off (in msec) +## to try new image samples, change the image_sample and re-run the subsequent code lines +@named stim = ImageStimulus(image_set[[image_sample],:]; namespace=global_namespace, t_stimulus=1000, t_pause=0) + +# assemble the blox into a graph and set connections + +circuit = [stim,VAC,AC,ASC1] +d = Dict(b => i for (i,b) in enumerate(circuit)) ## can refer to nodes through their names instead of their indices + +g = MetaDiGraph() +add_blox!.(Ref(g), circuit) ## add all the blox into the graph + +## set connections and their keword arguments like connection weight and connection density +add_edge!(g, d[stim], d[VAC], :weight, 14) +add_edge!(g, d[ASC1], d[VAC], Dict(:weight => 44)) +add_edge!(g, d[ASC1], d[AC], Dict(:weight => 44)) +add_edge!(g, d[VAC], d[AC], Dict(:weight => 3, :density => 0.08)) + +## define odesyste, simplify and solve +sys = system_from_graph(g, name=global_namespace) +sys = structural_simplify(sys) +prob = ODEProblem(sys, [], (0.0, 1000), []) ## tspan = (0,1000) +sol = solve(prob, Vern7(), saveat=0.1) + +##plot voltage stacks, mean fields and powerspectrums + +## VAC +voltage_stack(VAC,sol) +mnv = meanfield_timeseries(VAC,sol) +Plots.plot(sol.t,mnv) +powerspectrumplot(VAC,sol) + +## AC +voltage_stack(AC,sol) +mnv = meanfield_timeseries(AC,sol) +Plots.plot(sol.t,mnv) +powerspectrumplot(AC,sol) \ No newline at end of file diff --git a/docs/src/tutorials/neural_assembly.md b/docs/src/tutorials/neural_assembly.md new file mode 100644 index 0000000..17b661d --- /dev/null +++ b/docs/src/tutorials/neural_assembly.md @@ -0,0 +1,46 @@ +# [Tutorial on building a neural assembly from bottom-up](@id neural_assembly_tutorial) + +## Single spiking neuron from Hodgkin-Huxley model + +Hodgkin-Huxley (HH) formalism to describe membrane potential of a single neuron + +```math + \begin{align} + C_m\frac{dV}{dt} &= -g_L(V-V_L) - {g}_{Na}m^3h(V-V_{Na}) -{g}_Kn^4(V-V_K) + I_{in} - I_{syn} \\ + \frac{dm}{dt} &= \alpha_{m}(V)(1-m) + \beta_{m}(V)m \\ + \frac{dh}{dt} &= \alpha_{h}(V)(1-h) + \beta_{h}(V)h \\ + \frac{dn}{dt} &= \alpha_{n}(V)(1-n) + \beta_{n}(V)n + \end{align} +``` + +A single HH neuron can be simulated as follows + +```@example neural_assembly +using Neuroblox +using MetaGraphs +using DifferentialEquations +using Random +using Plots +using Statistics + +#create a single excitatory neuron with steady input current I_in = 0.5 microA/cm2 +nn1 = HHNeuronExciBlox(name=Symbol("nrn1"), I_bg=0.5) + +#add a single neuron blox as a single node in a graph +g = MetaDiGraph() +add_blox!.(Ref(g), [nn1]) +``` + +```@example neural_assembly +@named sys = system_from_graph(g) +sys = structural_simplify(sys) +length(unknowns(sys)) +``` + +To solve the system, we first create an Ordinary Differential Equation Problem and then solve it over the tspan of (0,1e) using a Vern7() solver. The solution is saved every 0.1ms. The unit of time in Neuroblox is 1ms. + +```@example neural_assembly +prob = ODEProblem(sys, [], (0.0, 1000), []) +sol = solve(prob, Vern7(), saveat=0.1) +plot(sol.t,sol[1,:],xlims=(0,1000),xlabel="time (ms)",ylabel="mV") +``` \ No newline at end of file diff --git a/docs/src/tutorials/resting_state_wb.md b/docs/src/tutorials/resting_state_wb.md index 67194df..1edae59 100644 --- a/docs/src/tutorials/resting_state_wb.md +++ b/docs/src/tutorials/resting_state_wb.md @@ -50,12 +50,12 @@ sys = structural_simplify(sys) length(unknowns(sys)) ``` -To solve the system, we first create an Stochastic Differential Equation Problem and then solve it over the tspan of (0,6e) using a EulerHeun solver. The solution is saved every 0.5ms. The unit of time in Neuroblox is 1ms. +To solve the system, we first create an Stochastic Differential Equation Problem and then solve it over the tspan of (0,60000) using a EulerHeun solver. The solution is saved every 0.5ms. The unit of time in Neuroblox is 1ms. ```@example resting-state-circuit prob = SDEProblem(sys,rand(-2:0.1:4,76*2), (0.0, 6e5), []) sol = solve(prob, EulerHeun(), dt=0.5, saveat=5) -plot(sol.t,sol[5,:],xlims=(0,10000)) +plot(sol.t,sol[5,:],xlims=(1000,10000)) ``` To evaluate the connectivity of our simulated resting state network, we calculate the statistically significant correlations