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{\displaystyle C_{\mathrm {m} }{\frac {dV(t)}{dt}}=-\sum _{i}I_{i}(t,V).} The above equation is the time derivative of the law of capacitance, Q = CV where the change of the total charge must be explained as the sum over the currents. Each current is given by I ( t , V ) = g ( t , V ) ⋅ ( V − V e q ) {\displaystyle I(t... | Wikipedia - Biological neuron model - Electrical input–output membrane voltage models > Hodgkin–Huxley | 202 | 618 | null |
Each current is given by I ( t , V ) = g ( t , V ) ⋅ ( V − V e q ) {\displaystyle I(t,V)=g(t,V)\cdot (V-V_{\mathrm {eq} })} where g(t,V) is the conductance, or inverse resistance, which can be expanded in terms of its maximal conductance ḡ and the activation and inactivation fractions m and h, respectively, that determ... | Wikipedia - Biological neuron model - Electrical input–output membrane voltage models > Hodgkin–Huxley | 382 | 937 | null |
This expansion is given by g ( t , V ) = g ¯ ⋅ m ( t , V ) p ⋅ h ( t , V ) q {\displaystyle g(t,V)={\bar {g}}\cdot m(t,V)^{p}\cdot h(t,V)^{q}} and our fractions follow the first-order kinetics d m ( t , V ) d t = m ∞ ( V ) − m ( t , V ) τ m ( V ) = α m ( V ) ⋅ ( 1 − m ) − β m ( V ) ⋅ m {\displaystyle {\frac {dm(t,V)}{d... | Wikipedia - Biological neuron model - Electrical input–output membrane voltage models > Hodgkin–Huxley | 337 | 884 | null |
Section: Electrical input–output membrane voltage models > Perfect Integrate-and-fire. One of the earliest models of a neuron is the perfect integrate-and-fire model (also called non-leaky integrate-and-fire), first investigated in 1907 by Louis Lapicque. A neuron is represented by its membrane voltage V which evolves ... | Wikipedia - Biological neuron model - Electrical input–output membrane voltage models > Perfect Integrate-and-fire | 321 | 1,381 | null |
The firing frequency is the inverse of the total inter-spike interval (including dead time). The firing frequency as a function of a constant input current, is therefore f ( I ) = I C V t h + t r e f I . {\displaystyle \,\!f(I)={\frac {I}{C_{\mathrm {} }V_{\mathrm {th} }+t_{\mathrm {ref} }I}}.} A shortcoming of this mo... | Wikipedia - Biological neuron model - Electrical input–output membrane voltage models > Perfect Integrate-and-fire | 186 | 710 | null |
Section: Electrical input–output membrane voltage models > Leaky integrate-and-fire. The leaky integrate-and-fire model, which can be traced back to Louis Lapicque, contains a "leak" term in the membrane potential equation that reflects the diffusion of ions through the membrane, unlike the non-leaky integrate-and-fire... | Wikipedia - Biological neuron model - Electrical input–output membrane voltage models > Leaky integrate-and-fire | 276 | 956 | null |
For constant input, the minimum input to reach the threshold is Ith = Vth / Rm. Assuming a reset to zero, the firing frequency thus looks like f ( I ) = { 0 , I ≤ I t h [ t r e f − R m C m log ( 1 − V t h I R m ) ] − 1 , I > I t h {\displaystyle f(I)={\begin{cases}0,&I\leq I_{\mathrm {th} }\\\left[t_{\mathrm {ref} }-... | Wikipedia - Biological neuron model - Electrical input–output membrane voltage models > Leaky integrate-and-fire | 323 | 1,053 | null |
in the textbook Neuronal Dynamics) τ m d V m ( t ) d t = R I ( t ) − [ V m ( t ) − E m ] − R ∑ k w k {\displaystyle \tau _{\mathrm {m} }{\frac {dV_{\mathrm {m} }(t)}{dt}}=RI(t)-[V_{\mathrm {m} }(t)-E_{\mathrm {m} }]-R\sum _{k}w_{k}} τ k d w k ( t ) d t = − a k [ V m ( t ) − E m ] − w k + b k τ k ∑ f δ ( t − t f ) {\dis... | Wikipedia - Biological neuron model - Electrical input–output membrane voltage models > Adaptive integrate-and-fire | 347 | 771 | null |
in the textbook Neuronal Dynamics) τ m d V m ( t ) d t = R I ( t ) − [ V m ( t ) − E m ] − R ∑ k w k {\displaystyle \tau _{\mathrm {m} }{\frac {dV_{\mathrm {m} }(t)}{dt}}=RI(t)-[V_{\mathrm {m} }(t)-E_{\mathrm {m} }]-R\sum _{k}w_{k}} τ k d w k ( t ) d t = − a k [ V m ( t ) − E m ] − w k + b k τ k ∑ f δ ( t − t f ) {\dis... | Wikipedia - Biological neuron model - Electrical input–output membrane voltage models > Adaptive integrate-and-fire | 367 | 884 | null |
Section: Electrical input–output membrane voltage models > Fractional-order leaky integrate-and-fire. Recent advances in computational and theoretical fractional calculus lead to a new form of model called Fractional-order leaky integrate-and-fire. An advantage of this model is that it can capture adaptation effects wi... | Wikipedia - Biological neuron model - Electrical input–output membrane voltage models > Fractional-order leaky integrate-and-fire | 214 | 707 | null |
Section: Electrical input–output membrane voltage models > 'Exponential integrate-and-fire' and 'adaptive exponential integrate-and-fire'. In the exponential integrate-and-fire model, spike generation is exponential, following the equation: d V d t − R τ m I ( t ) = 1 τ m [ E m − V + Δ T exp ( V − V T Δ T ) ] . {\dis... | Wikipedia - Biological neuron model - Electrical input–output membrane voltage models > 'Exponential integrate-and-fire' and 'adaptive exponential integrate-and-fire' | 321 | 958 | null |
In this sense the exponential nonlinearity is strongly supported by experimental evidence. In the adaptive exponential integrate-and-fire neuron the above exponential nonlinearity of the voltage equation is combined with an adaptation variable w τ m d V d t = R I ( t ) + [ E m − V + Δ T exp ( V − V T Δ T ) ] − R w {\... | Wikipedia - Biological neuron model - Electrical input–output membrane voltage models > 'Exponential integrate-and-fire' and 'adaptive exponential integrate-and-fire' | 340 | 935 | null |
Important model parameters are the voltage reset value Vr, the intrinsic threshold V T {\displaystyle V_{T}} , the time constants τ {\displaystyle \tau } and τ m {\displaystyle \tau _{m}} as well as the coupling parameters a and b. The adaptive exponential integrate-and-fire model inherits the experimentally derived vo... | Wikipedia - Biological neuron model - Electrical input–output membrane voltage models > 'Exponential integrate-and-fire' and 'adaptive exponential integrate-and-fire' | 159 | 722 | null |
The expression for the adaptive threshold is given by: v t h ( t ) = v t h 0 + ∑ θ ( t − t f ) f = v t h 0 + ∑ θ 0 exp [ − ( t − t f ) τ θ ] f {\displaystyle v_{th}(t)=v_{th0}+{\frac {\sum \theta (t-t_{f})}{f}}=v_{th0}+{\frac {\sum \theta _{0}\exp \left[-{\frac {(t-t_{f})}{\tau _{\theta }}}\right]}{f}}} where θ ( t )... | Wikipedia - Biological neuron model - Electrical input–output membrane voltage models > Adaptive Threshold Neuron Model | 350 | 794 | null |
The membrane potential dynamics are described through equations and the threshold adaptation rule is: v t h ( t ) = b 0 + β 1 b 1 ( t ) + β 2 b 2 ( t ) {\displaystyle v_{th}(t)=b_{0}+\beta _{1}b_{1}(t)+\beta _{2}b_{2}(t)} The dynamics of b 1 ( t ) {\displaystyle b_{1}(t)} and b 2 ( t ) {\displaystyle b_{2}(t)} are give... | Wikipedia - Biological neuron model - Electrical input–output membrane voltage models > Double Exponential Adaptive Threshold (DEXAT) | 349 | 701 | null |
Section: Stochastic models of membrane voltage and spike timing. The models in this category are generalized integrate-and-fire models that include a certain level of stochasticity. Cortical neurons in experiments are found to respond reliably to time-dependent input, albeit with a small degree of variations between on... | Wikipedia - Biological neuron model - Stochastic models of membrane voltage and spike timing | 300 | 1,478 | null |
Section: Stochastic models of membrane voltage and spike timing > Noisy input model (diffusive noise). A neuron embedded in a network receives spike input from other neurons. Since the spike arrival times are not controlled by an experimentalist they can be considered as stochastic. Thus a (potentially nonlinear) integ... | Wikipedia - Biological neuron model - Stochastic models of membrane voltage and spike timing > Noisy input model (diffusive noise) | 282 | 924 | null |
τ m d V d t = f ( V ) + R I ( t ) + R I noise ( t ) {\displaystyle \tau _{m}{\frac {dV}{dt}}=f(V)+RI(t)+RI^{\text{noise}}(t)} Stein's model is the special case of a leaky integrate-and-fire neuron and a stationary white noise current I n o i s e ( t ) = ξ ( t ) {\displaystyle I^{\rm {noise}}(t)=\xi (t)} with mean zero ... | Wikipedia - Biological neuron model - Stochastic models of membrane voltage and spike timing > Noisy input model (diffusive noise) | 317 | 997 | null |
Stein's neuron model and variants thereof have been used to fit interspike interval distributions of spike trains from real neurons under constant input current. In the mathematical literature, the above equation of the Ornstein–Uhlenbeck process is written in the form d V = [ E m − V + R I ( t ) ] d t τ m + σ d W {\di... | Wikipedia - Biological neuron model - Stochastic models of membrane voltage and spike timing > Noisy input model (diffusive noise) | 289 | 936 | null |
The noisy input model can also be used in generalized integrate-and-fire models. For example, the exponential integrate-and-fire model with noisy input reads τ m d V d t = E m − V + Δ T exp ( V − V T Δ T ) + R I ( t ) + R ξ ( t ) {\displaystyle \tau _{m}{\frac {dV}{dt}}=E_{m}-V+\Delta _{T}\exp \left({\frac {V-V_{T}}{... | Wikipedia - Biological neuron model - Stochastic models of membrane voltage and spike timing > Noisy input model (diffusive noise) | 319 | 1,039 | null |
Section: Stochastic models of membrane voltage and spike timing > Noisy output model (escape noise). In deterministic integrate-and-fire models, a spike is generated if the membrane potential V(t) hits the threshold V t h {\displaystyle V_{th}} . In noisy output models, the strict threshold is replaced by a noisy one a... | Wikipedia - Biological neuron model - Stochastic models of membrane voltage and spike timing > Noisy output model (escape noise) | 322 | 1,075 | null |
A common choice for the 'escape rate' f {\displaystyle f} (that is consistent with biological data) is f ( V − V t h ) = 1 τ 0 exp [ β ( V − V t h ) ] {\displaystyle f(V-V_{th})={\frac {1}{\tau _{0}}}\exp[\beta (V-V_{th})]} where τ 0 {\displaystyle \tau _{0}} is a time constant that describes how quickly a spike is f... | Wikipedia - Biological neuron model - Stochastic models of membrane voltage and spike timing > Noisy output model (escape noise) | 266 | 952 | null |
The escape rate process via a soft threshold is reviewed in Chapter 9 of the textbook Neuronal Dynamics. For models in discrete time, a spike is generated with probability P F ( t n ) = F [ V ( t n ) − V t h ] {\displaystyle P_{F}(t_{n})=F[V(t_{n})-V_{th}]} that depends on the momentary difference between the membrane ... | Wikipedia - Biological neuron model - Stochastic models of membrane voltage and spike timing > Noisy output model (escape noise) | 326 | 983 | null |
But the functional form of F can also be derived from the stochastic intensity f {\displaystyle f} in continuous time introduced above as F ( y n ) ≈ 1 − exp [ y n Δ t ] {\displaystyle F(y_{n})\approx 1-\exp[y_{n}\Delta t]} where y n = V ( t n ) − V t h {\displaystyle y_{n}=V(t_{n})-V_{th}} is the threshold distance.... | Wikipedia - Biological neuron model - Stochastic models of membrane voltage and spike timing > Noisy output model (escape noise) | 180 | 628 | null |
Section: Stochastic models of membrane voltage and spike timing > Spike response model (SRM). main article: Spike response model The spike response model (SRM) is a generalized linear model for the subthreshold membrane voltage combined with a nonlinear output noise process for spike generation. The membrane voltage V(... | Wikipedia - Biological neuron model - Stochastic models of membrane voltage and spike timing > Spike response model (SRM) | 317 | 1,021 | null |
The contributions to the voltage caused by a spike at time t f {\displaystyle t^{f}} are described by the refractory kernel η ( t − t f ) {\displaystyle \eta (t-t^{f})} . In particular, η ( t − t f ) {\displaystyle \eta (t-t^{f})} describes the reset after the spike and the time course of the spike-afterpotential follo... | Wikipedia - Biological neuron model - Stochastic models of membrane voltage and spike timing > Spike response model (SRM) | 156 | 612 | null |
The voltage V(t) can be interpreted as the result of an integration of the differential equation of a leaky integrate-and-fire model coupled to an arbitrary number of spike-triggered adaptation variables. Spike firing is stochastic and happens with a time-dependent stochastic intensity (instantaneous rate) f ( V − ϑ ( ... | Wikipedia - Biological neuron model - Stochastic models of membrane voltage and spike timing > Spike response model (SRM) | 326 | 938 | null |
Spike firing is stochastic and happens with a time-dependent stochastic intensity (instantaneous rate) f ( V − ϑ ( t ) ) = 1 τ 0 exp [ β ( V − ϑ ( t ) ) ] {\displaystyle f(V-\vartheta (t))={\frac {1}{\tau _{0}}}\exp[\beta (V-\vartheta (t))]} with parameters τ 0 {\displaystyle \tau _{0}} and β {\displaystyle \beta } a... | Wikipedia - Biological neuron model - Stochastic models of membrane voltage and spike timing > Spike response model (SRM) | 327 | 833 | null |
In case of a fixed threshold, one sets θ 1 ( t − t f ) = 0 {\displaystyle \theta _{1}(t-t^{f})=0} . For β → ∞ {\displaystyle \beta \to \infty } the threshold process is deterministic. The time course of the filters η , κ , θ 1 {\displaystyle \eta ,\kappa ,\theta _{1}} that characterize the spike response model can be d... | Wikipedia - Biological neuron model - Stochastic models of membrane voltage and spike timing > Spike response model (SRM) | 219 | 883 | null |
The name spike response model arises because, in a network, the input current for neuron i is generated by the spikes of other neurons so that in the case of a network the voltage equation becomes V i ( t ) = ∑ f η i ( t − t i f ) + ∑ j = 1 N w i j ∑ f ′ ε i j ( t − t j f ′ ) + V r e s t {\displaystyle V_{i}(t)=\sum _{... | Wikipedia - Biological neuron model - Stochastic models of membrane voltage and spike timing > Spike response model (SRM) | 349 | 866 | null |
Section: Stochastic models of membrane voltage and spike timing > SRM0. The SRM0 is a stochastic neuron model related to time-dependent nonlinear renewal theory and a simplification of the Spike Response Model (SRM). The main difference to the voltage equation of the SRM introduced above is that in the term containing ... | Wikipedia - Biological neuron model - Stochastic models of membrane voltage and spike timing > SRM0 | 150 | 628 | null |
Another difference is that the threshold is constant. The model SRM0 can be formulated in discrete or continuous time. For example, in continuous time, the single-neuron equation is V ( t ) = η ( t − t ^ ) + ∫ 0 ∞ κ ( s ) I ( t − s ) d s + V r e s t {\displaystyle V(t)=\eta (t-{\hat {t}})+\int _{0}^{\infty }\kappa (s)I... | Wikipedia - Biological neuron model - Stochastic models of membrane voltage and spike timing > SRM0 | 331 | 725 | null |
For example, in continuous time, the single-neuron equation is V ( t ) = η ( t − t ^ ) + ∫ 0 ∞ κ ( s ) I ( t − s ) d s + V r e s t {\displaystyle V(t)=\eta (t-{\hat {t}})+\int _{0}^{\infty }\kappa (s)I(t-s)\,ds+V_{\mathrm {rest} }} and the network equations of the SRM0 are V i ( t ∣ t ^ i ) = η i ( t − t ^ i ) + ∑ j w ... | Wikipedia - Biological neuron model - Stochastic models of membrane voltage and spike timing > SRM0 | 367 | 841 | null |
Note that the time course of the postsynaptic potential ε i j {\displaystyle \varepsilon _{ij}} is also allowed to depend on the time since the last spike of neuron i to describe a change in membrane conductance during refractoriness. The instantaneous firing rate (stochastic intensity) is f ( V − ϑ ) = 1 τ 0 exp [ β... | Wikipedia - Biological neuron model - Stochastic models of membrane voltage and spike timing > SRM0 | 305 | 1,125 | null |
Given the model specifications, the probability that a given neuron i {\displaystyle i} spikes in a period t {\displaystyle t} may be described by P r o b ( X t ( i ) = 1 ∣ F t − 1 ) = φ i ( ∑ j ∈ I W j → i ∑ s = L t i t − 1 g j ( t − s ) X s ( j ) , t − L t i ) , {\displaystyle \mathop {\mathrm {Prob} } (X_{t}(i)=1\... | Wikipedia - Biological neuron model - Stochastic models of membrane voltage and spike timing > Galves–Löcherbach model | 349 | 819 | null |
Section: Didactic toy models of membrane voltage > FitzHugh–Nagumo. Sweeping simplifications to Hodgkin–Huxley were introduced by FitzHugh and Nagumo in 1961 and 1962. Seeking to describe "regenerative self-excitation" by a nonlinear positive-feedback membrane voltage and recovery by a linear negative-feedback gate vol... | Wikipedia - Biological neuron model - Didactic toy models of membrane voltage > FitzHugh–Nagumo | 314 | 1,085 | null |
In 1981, Morris and Lecar combined the Hodgkin–Huxley and FitzHugh–Nagumo models into a voltage-gated calcium channel model with a delayed-rectifier potassium channel represented by C d V d t = − I i o n ( V , w ) + I d w d t = φ ⋅ w ∞ − w τ w {\displaystyle {\begin{aligned}C{\frac {dV}{dt}}&=-I_{\mathrm {ion} }(V,w)+I... | Wikipedia - Biological neuron model - Didactic toy models of membrane voltage > Morris–Lecar | 350 | 709 | null |
Section: Didactic toy models of membrane voltage > Hindmarsh–Rose. Building upon the FitzHugh–Nagumo model, Hindmarsh and Rose proposed in 1984 a model of neuronal activity described by three coupled first-order differential equations: d x d t = y + 3 x 2 − x 3 − z + I d y d t = 1 − 5 x 2 − y d z d t = r ⋅ ( 4 ( x + 8 ... | Wikipedia - Biological neuron model - Didactic toy models of membrane voltage > Hindmarsh–Rose | 349 | 1,140 | null |
The standard formulation of the theta model is d θ ( t ) d t = ( I − I 0 ) [ 1 + cos ( θ ) ] + [ 1 − cos ( θ ) ] {\displaystyle {\frac {d\theta (t)}{dt}}=(I-I_{0})[1+\cos(\theta )]+[1-\cos(\theta )]} The equation for the quadratic integrate-and-fire model is (see Chapter 5.3 in the textbook Neuronal Dynamics ) τ m ... | Wikipedia - Biological neuron model - Didactic toy models of membrane voltage > Theta model and quadratic integrate-and-fire | 299 | 685 | null |
The standard formulation of the theta model is d θ ( t ) d t = ( I − I 0 ) [ 1 + cos ( θ ) ] + [ 1 − cos ( θ ) ] {\displaystyle {\frac {d\theta (t)}{dt}}=(I-I_{0})[1+\cos(\theta )]+[1-\cos(\theta )]} The equation for the quadratic integrate-and-fire model is (see Chapter 5.3 in the textbook Neuronal Dynamics ) τ m ... | Wikipedia - Biological neuron model - Didactic toy models of membrane voltage > Theta model and quadratic integrate-and-fire | 379 | 1,022 | null |
Section: Sensory input-stimulus encoding neuron models > The non-homogeneous Poisson process model (Siebert). Siebert modeled the neuron spike firing pattern using a non-homogeneous Poisson process model, following experiments involving the auditory system. According to Siebert, the probability of a spiking event at th... | Wikipedia - Biological neuron model - Sensory input-stimulus encoding neuron models > The non-homogeneous Poisson process model (Siebert) | 347 | 1,127 | null |
Section: Sensory input-stimulus encoding neuron models > Refractoriness and age-dependent point process model. Berry and Meister studied neuronal refractoriness using a stochastic model that predicts spikes as a product of two terms, a function f(s(t)) that depends on the time-dependent stimulus s(t) and one a recovery... | Wikipedia - Biological neuron model - Sensory input-stimulus encoding neuron models > Refractoriness and age-dependent point process model | 272 | 1,026 | null |
Section: Sensory input-stimulus encoding neuron models > Linear-nonlinear Poisson cascade model and GLM. The linear-nonlinear-Poisson cascade model is a cascade of a linear filtering process followed by a nonlinear spike generation step. In the case that output spikes feed back, via a linear filtering process, we arriv... | Wikipedia - Biological neuron model - Sensory input-stimulus encoding neuron models > Linear-nonlinear Poisson cascade model and GLM | 156 | 777 | null |
Section: Sensory input-stimulus encoding neuron models > The two-state Markov model (Nossenson & Messer). The spiking neuron model by Nossenson & Messer produces the probability of the neuron firing a spike as a function of either an external or pharmacological stimulus. The model consists of a cascade of a receptor la... | Wikipedia - Biological neuron model - Sensory input-stimulus encoding neuron models > The two-state Markov model (Nossenson & Messer) | 262 | 1,201 | null |
The firing rate is identified both as a normalized probability for neural spike firing and as a quantity proportional to the current of neurotransmitters released by the cell. The expression for the firing rate takes the following form: R fire ( t ) = P spike ( t ; Δ t ) Δ t = [ y ( t ) + R 0 ] ⋅ P 0 ( t ) {\displaysty... | Wikipedia - Biological neuron model - Sensory input-stimulus encoding neuron models > The two-state Markov model (Nossenson & Messer) | 332 | 966 | null |
y(t) is the input of the model and is interpreted as the neurotransmitter concentration on the cell surrounding (in most cases glutamate). For an external stimulus it can be estimated through the receptor layer model: y ( t ) ≃ g gain ⋅ ⟨ s 2 ( t ) ⟩ , {\displaystyle y(t)\simeq g_{\text{gain}}\cdot \langle s^{2}(t)\ran... | Wikipedia - Biological neuron model - Sensory input-stimulus encoding neuron models > The two-state Markov model (Nossenson & Messer) | 273 | 1,047 | null |
This range of mediation produces the following current dynamics: I A M P A ( t , V ) = g ¯ A M P A ⋅ [ O ] ⋅ ( V ( t ) − E A M P A ) {\displaystyle I_{\mathrm {AMPA} }(t,V)={\bar {g}}_{\mathrm {AMPA} }\cdot [O]\cdot (V(t)-E_{\mathrm {AMPA} })} I N M D A ( t , V ) = g ¯ N M D A ⋅ B ( V ) ⋅ [ O ] ⋅ ( V ( t ) − E N M D A ... | Wikipedia - Biological neuron model - Pharmacological input stimulus neuron models > Synaptic transmission (Koch & Segev) | 348 | 653 | null |
})} I G A B A B ( t , V ) = g ¯ G A B A B ⋅ [ G ] n [ G ] n + K d ⋅ ( V ( t ) − E K ) {\displaystyle I_{\mathrm {GABA_{B}} }(t,V)={\bar {g}}_{\mathrm {GABA_{B}} }\cdot {\tfrac {[G]^{n}}{[G]^{n}+K_{\mathrm {d} }}}\cdot (V(t)-E_{\mathrm {K} })} where ḡ is the maximal conductance (around 1S) and E is the equilibrium poten... | Wikipedia - Biological neuron model - Pharmacological input stimulus neuron models > Synaptic transmission (Koch & Segev) | 342 | 1,085 | null |
Section: Relation between artificial and biological neuron models. The most basic model of a neuron consists of an input with some synaptic weight vector and an activation function or transfer function inside the neuron determining output. This is the basic structure used for artificial neurons, which in a neural netwo... | Wikipedia - Biological neuron model - Relation between artificial and biological neuron models | 329 | 1,458 | null |
Time-dependent input is transformed by complex linear and nonlinear filters into a spike train in the output. Again, the spike response model or the adaptive integrate-and-fire model enables to prediction of the spike train in the output for arbitrary time-dependent input, whereas an artificial neuron or a simple leaky... | Wikipedia - Biological neuron model - Relation between artificial and biological neuron models | 334 | 1,582 | null |
Section: Cable theory and compartmental models. All of the above deterministic models are point-neuron models because they do not consider the spatial structure of a neuron. However, the dendrite contributes to transforming input into output. Point neuron models are valid description in three cases. (i) If input curren... | Wikipedia - Biological neuron model - Cable theory and compartmental models | 345 | 1,421 | null |
If everything is linear, the voltage changes as a function of timeWe introduce a length scale λ 2 = r m / r l {\displaystyle \lambda ^{2}={r_{m}}/{r_{l}}} on the left side and time constant τ = c m r m {\displaystyle \tau =c_{m}r_{m}} on the right side. The cable equation can now be written in its perhaps best-known fo... | Wikipedia - Biological neuron model - Cable theory and compartmental models | 324 | 1,104 | null |
A simple recursive algorithm scales linearly with the number of branches and can be used to calculate the effective conductance of the tree. This is given by G D = G m A D tanh ( L D ) / L D {\displaystyle \,\!G_{D}=G_{m}A_{D}\tanh(L_{D})/L_{D}} where AD = πld is the total surface area of the tree of total length l, ... | Wikipedia - Biological neuron model - Cable theory and compartmental models | 348 | 1,215 | null |
We obtain a series of equations for conductance ratios in and out of a compartment by making corrections to the normal dynamic Bout,i = Bin,i+1, as B o u t , i = B i n , i + 1 ( d i + 1 / d i ) 3 / 2 R m , i + 1 / R m , i {\displaystyle B_{\mathrm {out} ,i}={\frac {B_{\mathrm {in} ,i+1}(d_{i+1}/d_{i})^{3/2}}{\sqrt {R_{... | Wikipedia - Biological neuron model - Cable theory and compartmental models | 350 | 710 | null |
{\displaystyle B_{\mathrm {out,par} }={\frac {B_{\mathrm {in,dau1} }(d_{\mathrm {dau1} }/d_{\mathrm {par} })^{3/2}}{\sqrt {R_{\mathrm {m,dau1} }/R_{\mathrm {m,par} }}}}+{\frac {B_{\mathrm {in,dau2} }(d_{\mathrm {dau2} }/d_{\mathrm {par} })^{3/2}}{\sqrt {R_{\mathrm {m,dau2} }/R_{\mathrm {m,par} }}}}+\ldots } where the l... | Wikipedia - Biological neuron model - Cable theory and compartmental models | 314 | 648 | null |
We can iterate these equations through the tree until we get the point where the dendrites connect to the cell body (soma), where the conductance ratio is Bin,stem. Then our total neuron conductance for static input is given by G N = A s o m a R m , s o m a + ∑ j B i n , s t e m , j G ∞ , j . {\displaystyle G_{N}={\fra... | Wikipedia - Biological neuron model - Cable theory and compartmental models | 240 | 845 | null |
Section: Conjectures regarding the role of the neuron in the wider context of the brain principle of operation > The neurotransmitter-based energy detection scheme. The neurotransmitter-based energy detection scheme suggests that the neural tissue chemically executes a Radar-like detection procedure. As shown in Fig. 6... | Wikipedia - Biological neuron model - Conjectures regarding the role of the neuron in the wider context of the brain principle of operation > The neurotransmitter-based energy detection scheme | 349 | 1,785 | null |
Short-term neurotransmitter accumulation is likely to occur also in some types of neurons. Logical switching is executed by glial cells, and it results from exceeding a threshold level of neurotransmitter concentration. This threshold crossing is also accompanied by a change in neurotransmitter leak rate. Physical all-... | Wikipedia - Biological neuron model - Conjectures regarding the role of the neuron in the wider context of the brain principle of operation > The neurotransmitter-based energy detection scheme | 198 | 992 | null |
Section: General comments regarding the modern perspective of scientific and engineering models. The models above are still idealizations. Corrections must be made for the increased membrane surface area given by numerous dendritic spines, temperatures significantly hotter than room-temperature experimental data, and n... | Wikipedia - Biological neuron model - General comments regarding the modern perspective of scientific and engineering models | 325 | 1,699 | null |
Section: Tissue engineering. Biomimetic materials in tissue engineering are materials that have been designed such that they elicit specified cellular responses mediated by interactions with scaffold-tethered peptides from extracellular matrix (ECM) proteins; essentially, the incorporation of cell-binding peptides into... | Wikipedia - Biomimetic material - Tissue engineering | 316 | 1,612 | null |
In the beginning, long chains of ECM proteins including fibronectin (FN), vitronectin (VN), and laminin (LN) were used, but more recently the advantages of using short peptides have been discovered. Short peptides are more advantageous because, unlike the long chains that fold randomly upon adsorption causing the activ... | Wikipedia - Biomimetic material - Tissue engineering | 287 | 1,353 | null |
Section: Biomimetic mineralization. Proteins of the developing enamel extracellular matrix (such as amelogenin) control initial mineral deposition (nucleation) and subsequent crystal growth, ultimately determining the physico-mechanical properties of the mature mineralized tissue. Nucleators bring together mineral ions... | Wikipedia - Biomimetic material - Biomimetic mineralization | 350 | 1,643 | null |
Section: Extracellular matrix proteins. Many studies utilize laminin-1 when designing a biomimetic material. Laminin is a component of the extracellular matrix that is able to promote neuron attachment and differentiation, in addition to axon growth guidance. Its primary functional site for bioactivity is its core prot... | Wikipedia - Biomimetic material - Extracellular matrix proteins | 347 | 1,542 | null |
Laminin is known to stimulate neurite outgrowth and it plays a role in the developing nervous system. It is known that gradients are critical for the guidance of growth cones to their target tissues in the developing nervous system. There has been much research done on soluble gradients; however, little emphasis has be... | Wikipedia - Biomimetic material - Extracellular matrix proteins | 191 | 836 | null |
Section: Biomimetic photonic structures. The production of structural colours concerns a large array of organisms. From bacteria (Flavobacterium strain IR1) to multicellular organisms, (Hibiscus trionum, Doryteuthis pealeii (squid), or Chrysochroa fulgidissima (beetle)), manipulation of light is not limited to rare and... | Wikipedia - Biomimetic material - Biomimetic photonic structures | 237 | 1,110 | null |
Section: Type classification. The majority of studies on blindsight are conducted on patients who are hemianopic, i.e. blind in one-half of their visual field. Following the destruction of the left or right striate cortex, patients are asked to detect, localize, and discriminate amongst visual stimuli that are presente... | Wikipedia - Blindsight - Type classification | 347 | 1,681 | null |
It is for this reason that the phenomenon has more recently also been called the Riddoch syndrome. Since then it has become apparent that such subjects can also become aware of visual stimuli belonging to other visual domains, such as color and luminance, when presented to their blind fields. The ability of such hemian... | Wikipedia - Blindsight - Type classification | 216 | 1,107 | null |
Section: History. Much of our current understanding of blindsight can be attributed to early experiments on monkeys. One monkey, named Helen, could be considered the "star monkey in visual research" because she was the original blindsight subject. Helen was a macaque monkey that had been decorticated; specifically, her... | Wikipedia - Blindsight - History | 292 | 1,559 | null |
Section: Describing blindsight. Patients with blindsight have damage to the system that produces visual perception (the visual cortex of the brain and some of the nerve fibers that bring information to it from the eyes) rather than to the underlying brain system controlling eye movements. The phenomenon was originally ... | Wikipedia - Blindsight - Describing blindsight | 328 | 1,777 | null |
Section: Cause. There are multiple theories about what causes blindsight. The first states that after damage to area V1, other branches of the optic nerve deliver visual information to the superior colliculus, pulvinar and several other areas, including parts of the cerebral cortex. In turn, these areas might then cont... | Wikipedia - Blindsight - Cause | 344 | 1,806 | null |
This one proposes that the delivery of these signals is sufficient to arouse a conscious experience of fast visual motion, without implying that it is V5 alone that is responsible, since once signals reach V5, they may be propagated to other areas of the brain. The latter account would seem to exclude the possibility t... | Wikipedia - Blindsight - Cause | 179 | 841 | null |
Section: Research. Lawrence Weiskrantz and colleagues showed in the early 1970s that if forced to guess about whether a stimulus is present in their blind field, some observers do better than chance. This ability to detect stimuli that the observer is not conscious of can extend to discrimination of the type of stimulu... | Wikipedia - Blindsight - Research | 349 | 1,748 | null |
Section: Research > Evidence in animals. In a 1995 experiment, researchers attempted to show that monkeys with lesions in or even wholly removed striate cortexes also experienced blindsight. To study this, they had the monkeys complete tasks similar to those commonly used for human subjects. The monkeys were placed in ... | Wikipedia - Blindsight - Research > Evidence in animals | 315 | 1,721 | null |
Section: Research > Case studies > "DB". Researchers applied the same type of tests that were used to study blindsight in animals to a patient referred to as "DB". The normal techniques used to assess visual acuity in humans involved asking them to verbally describe some visually recognizable aspect of an object or obj... | Wikipedia - Blindsight - Research > Case studies > "DB" | 307 | 1,687 | null |
Section: Research > Case studies > Alexander and Cowey. Alexander and Cowey investigated how contrasting stimuli brightness affects blindsight patients' ability to discern movement. Prior studies have already shown that blindsight patients are able to detect motion even though they claim they do not see any visual perc... | Wikipedia - Blindsight - Research > Case studies > Alexander and Cowey | 341 | 1,833 | null |
Section: Research > Case studies > Kentridge, Heywood, and Weiskrantz. Kentridge, Heywood, and Weiskrantz used the phenomenon of blindsight to investigate the connection between visual attention and visual awareness. They wanted to see if their subject—who exhibited blindsight in other studies—could react more quickly ... | Wikipedia - Blindsight - Research > Case studies > Kentridge, Heywood, and Weiskrantz | 330 | 1,701 | null |
Section: Research > Case studies > "CB" and "SJ". Two separate studies involving the blindsighted patients “CB” and “SJ” both showed that visually guided action can occur in the absence of conscious perception. CB, a 75-year-old man blind on his left side, was asked to reach with his hand towards a target while avoidin... | Wikipedia - Blindsight - Research > Case studies > "CB" and "SJ" | 321 | 1,565 | null |
Section: Research > Case studies > "TN". A potential weak point of case studies like the ones above is that the participants were not completely blind, and therefore it is not out of the question that their existing vision could have assisted them in some way. So a particularly noteworthy patient is a man known as “TN”... | Wikipedia - Blindsight - Research > Case studies > "TN" | 325 | 1,668 | null |
Section: Brain regions involved. Visual processing in the brain goes through a series of stages. Destruction of the primary visual cortex leads to blindness in the part of the visual field that corresponds to the damaged cortical representation. The area of blindness – known as a scotoma – is in the visual field opposi... | Wikipedia - Blindsight - Brain regions involved | 324 | 1,674 | null |
Section: Brain regions involved > Lateral geniculate nucleus. Mosby's Dictionary of Medicine, Nursing & Health Professions defines the LGN as "one of two elevations of the lateral posterior thalamus receiving visual impulses from the retina via the optic nerves and tracts and relaying the impulses to the calcarine (vis... | Wikipedia - Blindsight - Brain regions involved > Lateral geniculate nucleus | 344 | 1,594 | null |
These researchers concluded that the magnocellular system of the LGN is less affected by the removal of V1, which suggests that it is because of this system in the LGN that blindsight occurs. Furthermore, once the LGN was inactivated, virtually all of the extrastriate areas of the brain no longer showed a response on t... | Wikipedia - Blindsight - Brain regions involved > Lateral geniculate nucleus | 342 | 1,606 | null |
Article: Body image (neuroscience). Body image is a complex construct, often used in the clinical context of describing a patient's cognitive perception of their own body. The medical concept began with the work of the Austrian neuropsychiatrist and psychoanalyst Paul Schilder, described in his book The Image and Appea... | Wikipedia - Body image (neuroscience) - Summary | 342 | 1,742 | null |
Section: Clinical significance > Measurements. Attempts by researchers to measure variances in body image include the FAI index, developed in a 2014 study (Zaccagni 2014). The FAI (feel-status minus actual-status inconsistency) index is used to assess someone's weight perception. FAI scores range from -3 to +3: Negativ... | Wikipedia - Body image (neuroscience) - Clinical significance > Measurements | 228 | 1,047 | null |
Section: Nervous system divisions > Peripheral nervous system. The PNS can be divided into the autonomic and somatic nervous system. The autonomic nervous system can be divided into the parasympathetic, sympathetic, and enteric nervous system. The sympathetic nervous system regulates the "fight or flight" responses. Th... | Wikipedia - Body reactivity - Nervous system divisions > Peripheral nervous system | 160 | 804 | null |
Section: Broad scope > The neuron doctrine. Neuron doctrine – A set of carefully constructed elementary set of observations regarding neurons. For more granularity, more current, and more advanced topics, see the cellular level section Asserts that neurons fall under the broader cell theory, which postulates: All livin... | Wikipedia - Outline of brain mapping - Broad scope > The neuron doctrine | 342 | 1,633 | null |
Neurons do not communicate via direct cytoplasm to cytoplasm contact.) Law of dynamic polarization. Although the axon can conduct in both directions, in tissue there is a preferred direction of transmission from cell to cell. Elements added later to the initial Neuron doctrine A barrier to transmission exists at the si... | Wikipedia - Outline of brain mapping - Broad scope > The neuron doctrine | 167 | 801 | null |
Section: Broad scope > Map, atlas, and database projects. Brain Activity Map Project – 2013 NIH $3 billion project to map every neuron in the human brain in ten years, based upon the Human Genome Project. NIH Brain Research through Advancing Innovative Neurotechnologies (BRAIN) Initiative [1] Community outreach site fo... | Wikipedia - Outline of brain mapping - Broad scope > Map, atlas, and database projects | 334 | 1,551 | null |
Coverage includes the brain and spinal cord of the four species most frequently studied by neuroscientists: human, macaque (monkey), rat and mouse. The controlled, standardized vocabulary for each structure is located in an unambiguous, strict physical hierarchy, and these terms are selected based on ease of pronunciat... | Wikipedia - Outline of brain mapping - Broad scope > Map, atlas, and database projects | 266 | 1,402 | null |
Section: Imaging and recording systems > Specific systems. Cortical stimulation mapping Diffusion MRI (dMRI) – includes diffusion tensor imaging (DTI) and diffusion functional MRI (DfMRI). dMRI is a recent breakthrough in brain mapping allowing the visualization of cross connections between different anatomical parts o... | Wikipedia - Outline of brain mapping - Imaging and recording systems > Specific systems | 332 | 1,715 | null |
Section: Imaging and recording systems > Imaging and recording componentry > Electrical. Event-related potential – positive and negative 10μ to 100μ Volts (μ is millionths) responses, measured via noninvasive electrodes attached to the scalp, that are the reliable and repeatable results of a certain specific sensory, c... | Wikipedia - Outline of brain mapping - Imaging and recording systems > Imaging and recording componentry > Electrical | 279 | 1,279 | null |
Section: Imaging and recording systems > Imaging and recording componentry > Electromagnetic. Magnetoencephalography – a technique for mapping brain activity by recording magnetic fields produced by electrical currents occurring naturally in the brain, using very sensitive magnetometers In research, MEG's primary use i... | Wikipedia - Outline of brain mapping - Imaging and recording systems > Imaging and recording componentry > Electromagnetic | 207 | 1,024 | null |
Section: Imaging and recording systems > Imaging and recording componentry > Visual processing and image enhancement. Scientific visualization – an interdisciplinary branch of science primarily concerned with the visualization of three-dimensional phenomena (including medical, biological, and others), where the emphasi... | Wikipedia - Outline of brain mapping - Imaging and recording systems > Imaging and recording componentry > Visual processing and image enhancement | 181 | 938 | null |
Section: Imaging and recording systems > Imaging and recording componentry > Information technology. Determining the number of clusters in a data set – a typical application is in data reduction: as the increase in temporal resolution of fMRI experiments routinely yields fMRI sequences containing several hundreds of im... | Wikipedia - Outline of brain mapping - Imaging and recording systems > Imaging and recording componentry > Information technology | 298 | 1,491 | null |
Section: Imaging and recording systems > Imaging and recording componentry > Software packages. Analysis of Functional NeuroImages – an open-source environment for processing and displaying functional MRI data Cambridge Brain Analysis – a software repository developed at University of Cambridge for functional magnetic ... | Wikipedia - Outline of brain mapping - Imaging and recording systems > Imaging and recording componentry > Software packages | 249 | 1,413 | null |
Section: Scientists, academics and researchers. Mark S. Cohen neuroscientist Professor at the UCLA. Early pioneer of functional brain imaging using magnetic resonance imaging (MRI). Anders Dale neuroscientist and Professor University of California, San Diego. He developed FreeSurfer brain imaging analysis software that... | Wikipedia - Outline of brain mapping - Scientists, academics and researchers | 307 | 1,489 | null |
Gitte Moos Knudsen Gitte Moos Knudsen neurobiologist and clinical neurologist professor at Copenhagen University Hospital. Kenneth Kwong Scientist at Harvard University known for his work in fMRI Robert Livingston (scientist) (October 9, 1918 – April 26, 2002) neuroscientist in 1964 Livingston founded the neuroscience ... | Wikipedia - Outline of brain mapping - Scientists, academics and researchers | 330 | 1,609 | null |
Article: Bridge locus. In neuroscience the bridge locus for a particular sensory percept is a hypothetical set of neurons whose activity is the basis of that sensory percept. The term was introduced by D.N. Teller and E.Y. Pugh Jr. in 1983, and has been sparingly used. Activity in the bridge locus neurons is postulated... | Wikipedia - Bridge locus - Summary | 333 | 1,648 | null |
Section: Background. Budapest Reference Connectome is a consensus graph of the brain graphs of 96 subjects in Version 2 and 418 subjects in Version 3. Only those edges are returned which are present in a given percentage of the subjects. Each of the selected edges has a certain weight in each of the graphs containing t... | Wikipedia - Budapest Reference Connectome - Background | 167 | 834 | null |
Article: Bursting. Bursting, or burst firing, is an extremely diverse general phenomenon of the activation patterns of neurons in the central nervous system where periods of rapid action potential spiking are followed by quiescent periods much longer than typical inter-spike intervals. Bursting is thought to be importa... | Wikipedia - Bursting - Summary | 208 | 1,055 | null |
Section: Physiological context > Overview. Neurons typically operate by firing single action potential spikes in relative isolation as discrete input postsynaptic potentials combine and drive the membrane potential across the threshold. Bursting can instead occur for many reasons, but neurons can be generally grouped a... | Wikipedia - Bursting - Physiological context > Overview | 220 | 1,201 | null |
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