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Edited by: Anke Meyer-Baese, Florida State University, United States

Reviewed by: Li Su, University of Cambridge, United Kingdom; Alle Meije Wink, VU University Medical Center, Netherlands

†Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database (

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Neurodegenerative diseases (NDD) gain increasing socioeconomic relevance due to an aging society (WHO,

The candidate biological mechanism under investigation in the present study is related to amyloid beta (Abeta), a protein that is an oligomeric cleavage product of the physiological amyloid precursor protein (APP) (Bloom,

Biology-infered cause-and-effect model: alteration of the molecular Abeta pathway in AD cause hyperexcitation in the neural mass model. An altered pathway from soluble Abeta monomers to oligomers to insoluble plaques leads to potentially neurotoxic Abeta accumulation (Hardy and Selkoe,

Near Abeta plaques, a shift in neural activity has been observed (Busche et al., _{A} receptor endocytosis after Abeta application. In a recent study by Ren et al. (

One already established drug that assesses the pathology of hyperexcitation is memantine, an N-methyl-D-aspartate (NMDA) antagonist. Memantine is recommended for the symptomatic treatment of severe AD as a mono- and combination therapy with cholinesterase inhibitors and should be also considered as possible treatment in moderate AD in the current version of the UK National Institute for Health and Care Excellence (NICE) guidelines of dementia management (Pink et al.,

Changes in electroencephalography (EEG) are described in AD as a general and progressive slowing of brain oscillations. In AD, cognitive decline and ^{18}F-fluorodeoxyglucose (FDG) PET signal decreases are linked with increased left temporal power in the delta and the theta frequency bands, whereas temporo-parieto-occipital alpha band coherence decreases and delta coherence increases (Loewenstein et al.,

As a consequence of these findings, we will focus in our modeling approach on three main aspects of AD:

Spatial heterogeneous Abeta distribution in the brain

Hyperexcitation caused by impaired inhibitory function

Slowing of neural frequencies.

For Abeta, we propose a change in local neuronal excitability. Therefore, we construct a model of a healthy “standard brain” with an averaged structural connectivity (SC) with inferred micro-scale characteristics of excitation in those areas where a deposition of Abeta is found. We will infer this information about the local distribution of Abeta from individual AV-45 (florbetapir) positron emission tomography (PET) images. AV-45 is a PET tracer which binds to Abeta (Clark et al.,

We investigate three clinical diagnostic groups of age- and gender-matched healthy controls (HC), individuals with mild cognitive impairment (MCI) and AD patients [see method section Alzheimer's Disease Neuroimaging Initiative (ADNI) Database and

Basic epidemiological information of the study population.

AD | 10 (5) | 72.0 | 9.6 | 55.9 | 86.1 | 21.3 | 6.8 | 9 | 30 |

HC | 15 (9) | 70.6 | 4.7 | 63.1 | 78.0 | 29.3 | 0.8 | 28 | 30 |

MCI | 8 (3) | 68.2 | 6.4 | 57.8 | 76.6 | 27.1 | 1.6 | 25 | 30 |

We will in the following provide an overview of the fundamentals of the here employed brain simulation technique. The particular strength of computational connectomics (Ritter et al.,

In this study we used TVB, an open source neuroinformatics platform (Ritter et al.,

TVB provides several types of NMMs. In the present study, we selected a NMM that can simulate EEG and enables us to implement disinhibition. The wiring pattern of cortical circuitry is characterized by recurrent excitatory and inhibitory loops, and by bidirectional sparse excitatory connections at the large-scale (Schüz and Braitenberg,

Postulated Abeta effect and its implementation to the Jansen-Rit model. _{3}) and excitatory interneurons (υ_{1}) are (exemplarily) located in layer V (internal pyramidal layer), while the inhibitory stellate (inter-neurons (υ_{2}) are located in layer IV (internal granular layer). In layer I (molecular layer) we see the dendrites of the pyramidal cells, where the input from the interneurons happens. The effect to the other neuron populations is represented by m_{1−3} [background is a modified version of figure 13 from Schmolesky (_{i} (see main text for more detailed explanation). This is intended to lead to an increased activity and higher output of the pyramidal cell population. The excitatory impulse response function (IRF) is specified as _{e}(_{e} exp(–t/τ_{e})/τ_{e}, the inhibitory IRF is specified as _{i}(_{i} exp(–t/τ_{i}(β))/τ_{i}(β) (Equations 1, 2). These IRFs can be translated into second-order ordinary differential equations, see Equations 3–5. For explanation of the used variables, see

Used parameters for each Jansen-Rit element in the large-scale brain network (Jansen and Rit,

_{e} |
Coefficient of the maximum amplitude of EPSP. Also called average synaptic gain (Equations 1, 3). | 3.25 | 1 mV |

_{i} |
Coefficient of the maximum amplitude of IPSP. Also called average synaptic gain (Equations 2, 4). | 22.0 | 1 mV |

_{e}( |
Amplitude of EPSP as a function of time (Equation 1). | Variable | 1 mV |

_{i}(_{a} |
Amplitude of IPSP as a function of time and local Abeta burden (Equation 2). | Variable | 1 mV |

τ_{e} |
Excitatory dendritic time constant (Equations 1, 3, 5). | 10.0 | 1 ms |

τ_{i}(_{a} |
Inhibitory dendritic time constant as a function of Abeta load (Equations 2, 4, 13, 14). | 14.29 ≤ τ_{i} <50 |
1 ms |

υ_{0} |
Is the mean PSP threshold for 50% of maximum firing rate (Equation 11). | 6.0 | 1 mV |

υ_{1} |
PSP of excitatory population (Equations 3, 10). | Variable | 1 mV |

υ_{2} |
PSP of inhibitory population (Equations 4, 10). | Variable | 1 mV |

υ_{3} |
PSP of pyramidal population (Equation 5). | Variable | 1 mV |

υ_{30} |
Outgoing projection of pyramidal population (Equation 10). | Variable | 1 mV |

_{0} |
The firing rate at the inflection point _{0} = S(_{0}). The maximum firing rate is 2_{0} (Equation 11). |
2.5 | 1 s^{−1} |

_{v} |
Steepness of the sigmoid PSP-to-firing-rate transfer function (Equation 11). | 0.56 | (mV)^{−1} |

_{31} |
Average number of synaptic contacts from excitatory to pyramidal cells (Equation 3). | 108.0 | 1 |

_{13} |
Average number of synaptic contacts from pyramidal to excitatory cells (Equation 3). | 135.0 | 1 |

_{32} |
Average number of synaptic contacts from inhibitory to pyramidal cells (Equation 4). | 33.75 | 1 |

_{23} |
Average number of synaptic contacts from pyramidal to inhibitory cells (Equation 4). | 33.75 | 1 |

_{3T, 0} |
Input firing rate at the pyramidal cells (Equation 12). | 0.1085 | (ms)^{−1} |

Global structural connectivity scaling factor. | 0 ≤ |
1 | |

_{max, τ} |
Maximum value of the inhibitory rate/reciprocal of inhibitory time constant (Equation 14). | 0.07 | (ms)^{−1} |

_{0, τ} |
Minimum value of the inhibitory rate/reciprocal of inhibitory time constant (Equation 14). | 0.02 | (ms)^{−1} |

β_{max} |
95th percentile value for the Abeta burden Aβ as the PET SUVR for all regions and all participants (Equations 13, 14). | 2.65 | 1 |

β_{off} |
Cut-off-value for the Abeta burden Aβ as the PET SUVR, from which one a pathological meaning is suspected (Equations 13, 14). | 1.4 | 1 |

Specifically we chose the Jansen-Rit model for the present study due to the following considerations:

The Jansen-Rit model comprises three interacting neural masses (representing different cellular populations) in each local circuitry: pyramidal cells, inhibitory, and excitatory interneurons (

The ratio of excitatory and inhibitory time constants τ_{e}/τ_{i} in the Jansen-Rit model is suitable to model the effect of Abeta on the inhibitory interneurons (by affecting the transmission from inhibitory interneurons to pyramidal cells, _{e} and τ_{i} are scaled simultaneously and uniformly, the local equilibrium of interaction between the neural masses remains the same but the time signature such as frequency changes [see Figure 9 in Spiegler et al. (_{i} does not necessarily lead to slower rhythms and vice versa.

Jansen-Rit can simulate physiological rhythms observable in local field potentials (intracranially), stereo-EEG (sEEG), scalp EEG, and MEG (Jansen and Rit,

Our hypothesized effect of local Abeta deposition as inferred from subject-specific AV-45 PET is a decrease of local inhibition (Busche et al.,

Graphs of the sigmoid transfer function of Abeta. The abscissa represents the Abeta burden β_{a}, the ordinate represents the reciprocal _{τ}(β_{a}) of the inhibitory time constant τ _{i}. See Equation 14.

Empirical data were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database (adni.loni.usc.edu). The ADNI was launched in 2003 as a public-private partnership, led by Principal Investigator Michael W. Weiner. The primary goal of ADNI has been to test whether serial MRI, PET, other biological markers, and clinical and neuropsychological assessment can be combined to measure the progression of MCI and early AD. For up-to-date information, see

In the presently ongoing trial, ADNI-3, the measurements contain T1, T2, DTI, fMRI, Tau PET, Abeta PET, and FDG PET for the participants. The total population of ADNI-3 will contain data of about 2,000 participants (comprising AD, MCI, and HC, see

All images used in this study were taken from ADNI-3. To reach comparable datasets, we used only data from Siemens scanners with a magnetic field strength of 3T (models: TrioTim, Prisma, Skyra, Verio). However, some acquisition parameters differed slightly. See Supplementary Material with

We calculated an individual brain parcellation for each included participant of ADNI-3. We followed the minimal preprocessing pipeline (Glasser et al., ^{3}, and all recon-all and intermediate steps were performed with the original image resolution. We then registered the subject cortical surfaces (32 000 vertices) to the cortical parcellation of Glasser et al. (

We used the preprocessed version of AV-45 PET. These images had following preprocessing already performed by ADNI: Images acquired 30–50 min post tracer injections: four 5-min frames (i.e., 30–35 min, 35–40 min…). These frames are co-registered to the first and then averaged. The averaged image was linearly aligned such that the anterior-posterior axis of the subject is parallel to the AC-PC line. This standard image has a resolution of 1.5 mm cubic voxels and matrix size of 160 · 160 · 96. Voxel intensities were normalized so that the average voxel intensity was 1. Finally, the images were smoothed using a scanner-specific filter function. The filter functions were determined in the certification process of ADNI from a PET phantom. We used the resulting image and applied the following steps: Rigid aligning the PET image to participants T1 image (after being processed in the HCP structural pipeline). The linear registration was done with FLIRT (FSL). The PET image was than masked with the subject specific brainmask derived from the structural preprocessing pipeline (HCP). To obtain the local burden of Abeta, we calculated the relative intensity to the cerebellum as a common method in the interpretation of AV-45-PET, because it is known that the cerebellum does not show relevant AV-45 PET signals and can therefore act as a reference region for inter-individual comparability between patients (Clark et al., _{a} for the Abeta burden in each brain region

We calculated individual tractography only for included HC participants of ADNI-3 to average them to a standard brain template (see section Virtual Human Standard Brain Template Out of Averaged Healthy Brains below). Preprocessing of the diffusion weighted images was mainly done with the programs and scripts provided by the MRtrix3 software package (

The following steps were performed:

After structural preprocessing with the HCP pipeline we used the individual cortical surfaces and T1 images to compute the person specific Boundary Element Models in Brainstorm (Tadel et al.,

We use the SCs of all ADNI-3 participants of the group HC, derived from the diffusion-weighted and structural MRI, to average them to one connectome matrix. Two of the HC participants included in the average template were excluded for simulations because it was impossible to compute their leadfield matrices for EEG calculation. Therefore, we use an arithmetic mean _{μ} = (_{= 1} _{i})/n = (C_{1} + C_{2} + … + C_{n})/n, wherein _{μ} is the averaged SC matrix, _{i} is the individual SC matrix. The SC matrix and the organization of the corresponding graph can be found in

Underlying average HC structural connectome.

The dynamics of the Jansen-Rit model show a rich parameter dependent behavior (Spiegler et al.,

The information about the local Abeta burden is derived from the individual AV-45 PET. As there exists no established clinical standard for SUVR cut-off thresholds differentiating normal form pathological Abeta loads. To scale the possible neurotoxic effect in a realistic way, we need to approximate at what point Abeta toxicity occurs. Following the literature, a 96% correlation to autopsy after Abeta PET was achieved via visual assessment of PET images. The corresponding SUVR cut-off was 1.2 (Clark et al.,

The inhibitory time constant τ_{i} in each point is a function of β_{a}. The higher Abeta SUVR, the higher τ_{i} and therefore the filter action for the synaptic transmission is slower. We decided for this implementation via a synaptic filter slowing because of several reasons:

We are focusing on disease linked alterations of EEG frequencies. Hence, we intended to assess a model feature that is already known to be frequency-effective, i.e., it can vary resulting simulated EEG frequencies. From former explorations of the Jansen-Rit-model we know that the neural frequencies are influenced by the ratio of excitatory and inhibitory time constants (Spiegler et al.,

Cellular studies are supporting the hypothesis of altered inhibition as a cause for hyperexcitation (Hazra et al.,

By using a time-effective feature, we intended to differentiate the micro-scale neurotoxic effect of Abeta on synaptic level (Ripoli et al.,

A detailed exploration of the effects that we introduce by this model can be found in the discussion section.

We develop a transform function to implement the PET SUVR in parameters of the brain network model. Specifically, we postulate a sigmoidal decrease function that modifies the default value for inhibitory time constant τ_{i} (Equation 14 and _{off}–differentiating normal form pathological Abeta burden—was chosen according to the literature, stating that only after a certain level of tracer uptake a region is considered pathological (β_{off} = 1.4, see above). The maximum possible Abeta burden value β_{max} was chosen to be the 95% percentile of the Abeta regional SUVR distribution across all participants. The midpoint of the sigmoid was chosen such that it was half the way between β_{off} and β_{max}. The steepness was chosen such that the function converges to a linear function between β_{off} and β_{max}.

For the reasons stated in the above introduction, for our simulation approach we selected the Jansen-Rit model (Zetterberg et al.,

As a general approach, the impulse response function (IRF) of a neural mass allows to transform an incoming action potential into a PSP by using a linear time-invariant system. The IRF is the transfer function of the system, which is convoluted with the incoming input (action potentials) to calculate the output (PSPs). The general form of the IRF is the systems output to a (infinitesimal short and high) Dirac impulse and can be estimated experimentally by using short impulses or step functions (Lopes da Silva et al.,

The excitatory IRF _{e}(

where τ_{e} is the excitatory time constant (the time until the PSP reaches its maximum), _{e} is a coefficient of the PSP amplitude and t is time.

Similarly, the inhibitory IRF _{i}(

with the same variables as above. As we will describe below in detail, the inhibitory IR is a function of the spatially distributed Abeta burden β, which affects the time characteristics τ_{i}(β) and therefore _{i}(

These IRFs can be translated into second-order ordinary differential equations by interpreting them as Green's functions. See Spiegler et al. (

The differential equations that describe the network of three neural masses are now presented in Equations 3–5. The variables used for the simulations are listed in

Excitatory projections υ_{1} onto pyramidal cells at location

Inhibitory projections υ_{2} onto pyramidal cells at location

Projections υ_{3} of pyramidal cells

wherein _{31}, _{13}, _{23} are the local connectivity weights between the three neural masses. Equation (4) shows the spatial dependency of the activity of inhibitory interneurons projected onto the pyramidal cells by τ_{i}(β_{a}).

Taking into account the biologically plausible configuration of the Jansen-Rit model shown in

and, thanks to linearity, translates the summation of excitatory postsynaptic potentials

into a sum of incoming firing rate, that is, _{3T, a}(_{31} _{13} υ_{3, a}(_{1}. This simplification is without restrictions, simply exploits the linearity of the operators and reduces the dimensionality by 2. Furthermore, to adjust notation, the postsynaptic potentials caused by the inhibitory neural mass at pyramidal cells are denoted as

and its kernel is as

The projecting variable of one brain region at location

transferred into a firing rate using a sigmoid. The general form of this transfer function is

with, λ = υ, _{υ}, _{max} = 2e_{0} and _{υ}, _{min} = 0 for the potential-to-firing-rate transfer.

Incoming mean firing rates _{3T, a}(

where _{3T, 0} is baseline input _{3T, 0} = const. for _{a}_{, b} incoming at location

In all populations, the state variable [υ_{1}, υ_{2}, υ_{3}]_{a}(_{4}, υ_{5}, υ_{6}]_{a}(

To model how the local Abeta load β_{a}, measured by the Abeta PET SUVR is affecting the inhibitory time constant we introduce a transfer function (_{i} and τ_{i} as well as _{32}. The coefficient _{i} is not a suitable candidate because it has no direct physiological correlate. The coupling coefficient _{32} corresponds best to synaptic transmission from inhibitory to pyramidal cells and therefore can be mainly seen as a receptor surrogate. The time constant τ_{i} acts as a filter for IPSPs and correlates best with the evidence of decreased IPSP firing rate (Busche et al., _{a}_{, off} = 1.4 and the upper border at the 95th percentile in our data at β_{a}_{, max} = 2.65. By exploring the effects of τ_{i} in a single region model, we determined the effective range 14.29 ms ≤ τ_{i} <50 ms. Based on this range we defined the following three-conditional linear function

wherein τ_{i,min} and τ_{i,max} are the maximum and minimum values for τ_{i},

_{i,max}-τ_{i,min})/(β_{a}_{,max}-β_{a}_{,off}) = 28.6 and

_{a}_{,off}-τ_{i,min} = 25.7.

Since this function is not differentiable in β_{a}_{,off} and β_{a}_{,max}, we used the sigmoid function Equation (12) instead, which is continuous and differentiable. Moreover, a sigmoid can be interpreted as the cumulative (of a logistic distributed) activity acquired by the PET of a small brain volume (voxel) with a low spatial resolution of about 2.5 mm and above (Moses,

Therefore, the Abeta transfer function is defined as

wherein _{βa} is the slope of the sigmoid, β_{0} is the midpoint of the sigmoid and the coefficients are chosen to fit the conditions explained before. In this function, τ_{i} appears as its reciprocal value τ_{i}^{−1} as it is implemented in the code of TVB. Because τ_{i} is a time in ms, the inverse of τ_{i} is a rate of potential change, and does not directly correspond to a firing rate. The Abeta load affects the inhibitory rate following a sigmoid curve. The rate ranges between _{min} and _{max} and the time constant ranges consequently between 1/_{max} and 1/_{min}.

To simulate the model using TVB, physical space and time are discretized. The system of difference equations is then solved using deterministic Heun's method with a time step of 5 ms. We used a deterministic method to avoid stochastic influences since the simulation was performed in the absence of noise.

The system was integrated for 2 min and the last minute was analyzed in order to diminish transient components in the time series due to the initialization and settle the system into a steady state.

We explore a range of 0 ≤

In TVB, we simulate EEG as a projection of the oscillating membrane potentials inside the brain via its electromagnetic fields to the skin surface of the head (Sanz-Leon et al.,

We analyzed the dominant frequency in the simulated EEG and regional neural signal (referred to as local field potential (LFP) (

Spectral behavior in individuals of the different groups.

We observed a physiologically looking irregular behavior with two frequency clusters in the alpha and in the theta spectrum (

In order to locate the individual simulations in the spectrum of possible dynamics, meaning in the range of possible Abeta load, we examined extreme values of Abeta distribution. The virtual brains with a mean Abeta load of zero (

To give a mathematical explanation of those phenomena, we related each participants Abeta-burden to the corresponding inhibitory time constant τ_{i} and used former analyses of the uncoupled local Jansen-Rit model (Spiegler et al., _{i} by local Abeta burden fundamentally influences the systems bifurcations by shifting the bifurcation point along the range of external input to the pyramidal cells. As a consequence, different values of Abeta lead to a variable occurrence of two limit cycles and a stable focus. Therefore, for a single region with constant external input on pyramidal cells, depending on Abeta the region might be in an alpha limit cycle, in a theta limit cycle, in a bistable condition where both cycles are possible or in a stable focus.

Exemplary bifurcation diagrams of the Jansen-Rit model for three different inhibitory time constants linked to three different local Abeta burdens. The modulation of the inhibitory time constant τ_{i} by Abeta induces shifts in the corresponding bifurcation diagrams. All bifurcation diagrams _{30} of pyramidal cells (y) depending on the pyramidal input (x) for uncoupled simulations modified from Spiegler et al. (_{i} to keep the product of synaptic gains and dendritic time constants constant. The default input _{3T,0} on pyramidal cells starts at a firing rate of 108.5/s. Because of the potential-to-firing-rate transfer function (Equation 11), global scaling factor G is affecting both the input currents and the firing rates. For higher values of G, the input on pyramidal cells is expected to increase. First Columns, panels

AD-specific slowing in EEG and LFP and influence of the heterogeneous pattern of Abeta distribution to the spectral behavior.

We next examined how LFP/EEG slowing is related to the underlying Abeta burden (^{2} = 0.625), i.e., an Abeta-dependent EEG slowing. In contrast, for non-AD participants the relation was revers, i.e., higher values of Abeta caused EEG acceleration.

Abeta-dependent slowing of LFPs is specific for AD participants. Meanwhile there is a significant linear dependency between Abeta and LFP frequency for all groups, only for AD a higher burden of Abeta leads to a decrease of frequency. HC and MCI show inverse correlations. Plotted are density plots showing the dependency between the local Abeta loads and LFPs.

To test if specific regions are more important for the observed phenomena, we had to overcome the bias that only specific regions were strongly affected by Abeta. I.e., for the empirical Abeta distribution we cannot say e.g., for a region with high Abeta if it shows EEG/LFP slowing only because of its high Abeta value or because of its specific spatial and graph theoretical position in the network. Therefore, we next performed simulation with 10 random spatial distributions of the individual Abeta PET SUVRs for the 10 AD participants. In these simulations, the neural slowing appeared similarly to the empirical spatial distributions of Abeta (

The results of random spatial distribution of Abeta PET SUVRs were also used for a parameter space exploration (_{i} < 30 ms, but for the full spectrum of G, more probable for lower G values; (2) relevant amounts of bistable rhythms are only apparent for 17 ms < τ_{i} < 39 ms and G > 120; (3) theta rhythms are present across almost the full spectra of G and τ_{i}, with an equal appearance across G, but with a local minimum at τ_{i} ≈ 18 ms, where the system is dominated by alpha and bistable rhythms. This exploration demonstrates two major insights. First, it confirms the crucial role of τ_{i} for the appearance of alpha or theta rhythms as we expect it out of the (non-coupled) bifurcation diagrams of _{i}), but play a minor role here. Second, the value of G does not significantly affect the probability of theta rhythm, except of an alpha-theta shift for low τ_{i} < 20 ms and higher G > 160. This is caused by the coexistence of stable focus in alpha regime and theta limit cycle in theta regime for high pyramidal input

Alpha and bistable rhythms only appear in a specific part of the parameter space between G and τ_{i}. This parameter space exploration was done by coupled simulations and therefore includes network effects. Frequency (by color) is presented dependent on global coupling G (x) and inhibitory time constant τ_{i} (y). Projections to G and τ_{i} are shown beside the matrix plot, here the frequencies are classified into alpha rhythm (_{i}, the full spectrum of τ_{i} could be explored. Single empty columns are filled with neighbor columns for better readability. In principle wee the an “isle” of alpha for low coupling and low time constant, while the rest of the dynamics is dominated by theta and delta. A full frequency spectrum (also green and yellow colors) is only apparent near the borders of the alpha isle in higher coupling.

In the analysis of spatial distribution in relation to the organization of the underlying SC network (

Theta rhythms affect central parts of the network independently of the spatial distribution of Abeta. ^{2} = 0.183, in contrast to the distribution of Abeta ^{2} = 0.29) between structural degree and theta rhythm

The former analyses have shown that Abeta-mediated simulated hyperexcitation can lead to realistic changes of simulated brain imaging signals in AD such as EEG slowing (

The idea in our model is now that in theory memantine acts anti-excitotoxic via its NMDA antagonism and should therefore be able to weaken the hyperexcitation we introduced to the system by Abeta _{31} represents the main part of the glutamatergic transmission and can therefore also be seen as a surrogate of NMDAergic transmission _{31} stepwise to observe the effects on the system. The analysis of the Jansen-Rit equilibria supports the concept of lower excitation introduced by lower c_{31} _{31} and the input on pyramidal cells _{3T, 0}. The manifold is the object onto which the system is moving or collapsing dependent on the parameters—in a way the equilibrium that underlies the dynamics of the system. The virtual memantine leads to a partial reversibility of the altered dominant frequencies in AD compared to HC/MCI _{i}) has led to a local hyperexcitation. It is to mention, that in an uncoupled network both the decrease of c_{31} (memantine) and the increase of τ_{i} (by Abeta) would have the same effect (

Modeling NMDA antagonism by virtual memantine. We modified the local dynamics for the AD group by homogeneously decreasing the coefficient _{31}, which represents the coupling from excitatory population to the pyramidal cell and therefore is a potential surrogate for NMDA receptor activity _{31} was decreased by 25% to model the effect of memantine and was applied homogenously to all regions for the 10 AD participants. _{30} is a function of the model input _{3T, 0} and c_{31} for the median Abeta load of AD participants β = 2.1447. Note the decrease of PSP at pyramidal cells υ_{30} with increasing c_{31} for a constant input level—this can also be seen in the top view of the same three-dimensional plot in panel _{31}. Blue areas indicate the lower branch of the equilibrium manifold and red areas the upper branch (white areas are unstable). This demonstrates, as we suggested, that when maintaining the same input level, a lower c_{31} leads to a lower PSP at the pyramidal cells. ^{2} = 0.783) between the effect of memantine and the relative hyperactivity of regions. The homogenously applied virtual memantine therefore acts selectively in those regions, where hyperexcitation is already there. These regions in central network parts are also those, where slowing effects appears

Local hyperexcitation is introduced by Abeta and spatially linked to LFP slowing. _{i} = 14 ms, the firing rate shows low heterogeneity. There are neither hypoactive, nor hyperactive regions—the whole systems activity is near the “baseline of the brain” (mean firing rate of all regions). ^{2} = 0.594) between the relative PSP and the natural logarithm of the structural degree

Evaluation of the used cause-and-effect model. _{i}(t) as a function of Abeta. The kernel is flattened with increasing Abeta and the area under the curve increases as follows: AUC = H_{i} • τ_{i}(β). Therefore, longer τ_{i} by higher Abeta leads to a slowed down filter action (because of the delayed maximum of the IPSP). As a side effect, because of the higher AUC in the inhibitory transmission, the overall inhibition in the system increases—this can also be seen in _{30} is a function of the model input _{3T, 0} and β. The reaction of the system to input is changed by Abeta. Note the decrease of PSP at pyramidal cells υ_{30} with increasing β for a constant input level—this can also be seen in

Local Abeta-mediated disinhibition and hyperexcitation are considered candidate mechanisms of AD pathogenesis. In TVB simulations, the molecular candidate mechanism has led to macro-scale slowing in EEG and neural signal with a particular shift form alpha to theta previously observed in AD patients (Loewenstein et al.,

We showed that the slowing in simulated EEG and LFP is specific for the AD group (

We demonstrate the computational principles underlying this Abeta dependent slowing of EEG/LFP (

The simulated LFP/EEG slowing in AD patients crucially depends on the spatially heterogenous Abeta distribution as measured by PET—the slowing disappears when using a homogenously distributed mean Abeta burden instead for simulation (

Independently of the location of high Abeta burdens in the simulated brain, slowing emerges at the core, i.e., hubs of the structural connectome (

Abeta leads by the disturbance of E/I balance to more local hyperexcitation (

We also showed that the drug memantine that is known for improving brain function in severe AD can be modeled by a decreased transmission between the excitatory interneurons and the pyramidal cells and is able to achieve a “normalized” brain function

One major limitation of this study is the lack of direct validation of the simulated electrophysiological phenomena. Neither EEG nor LFP data was available in the ADNI-3 cohort. Although EEG slowing in AD is an established concept (Loewenstein et al.,

The second important limitation is the implementation of disturbed E/I balance by the inhibitory time constant. Although the longer time constants lead to slowed filter action (_{3T, 0} with higher mean Abeta burdens or by increasing a coefficient inside the IRF (Equation 2) to keep the AUC and therefore the transmitted energy at inhibitory transmission constant. This should be examined in future studies to evaluate the effect of such a correction. However, this would only be necessary if the global activity level would be a target of interest for another research question. Because of the feedback loops in a coupled brain network, each introduction of over- or dis-inhibition will lead both to hypo- and hyper-active regions. An analysis of hyperactivity needs therefore always a control activity—because hyperactivity can be meant spatially, temporally, or dependent on other factors. In our model, we could introduce spatially distributed hyperactivity (

The differential equations that describeThe differential equations that describeOf course the pathophysiological model presented in this study can only cover a small subspace of possible AD mechanisms. Even Abeta itself is probably only one player in the multifactorial pathogenesis (Selkoe and Hardy,

Another limitation is the small sample size of 33 participants. Future studies will have to consider much more participants, which will then help to formulate even more general conclusions. However, because of emergent effects in the brain simulation, differences between the groups were often very relevant and significant. An overview of all used statistical test in this study can be found in

However, we present a first proof of concept for linking molecular changes as detected by PET to large-scale brain modeling using the simulation framework TVB. This study therefore can work as a blueprint for future approaches in computational brain modeling bridging scales of neural function. For the research on AD pathogenesis, this study provides a possible mechanistic explanation that links Abeta-related synaptic disinhibition at the micro-scale to AD-specific EEG slowing. In general, our study can be seen as proof of concept that TVB enables research on disease mechanisms at a multi-scale level and has potential to lead to improved diagnostics and to the discovery of new treatments.

The raw data for this study is available in ADNI. The codes used in this study are available on request to the corresponding author.

This study has been approved from the Ethics Board of the Charité - Universitätsmedizin Berlin under the approval number EA2/100/19.

All authors have made substantial intellectual contributions to this work and approved it for publication. LS and PR had the idea to this study. LS, PT, ASp, and PR developed the concept and study design. LS wrote the manuscript, conducted the analysis and interpretation of results, and developed the figures. PT performed the MRI and PET image processing and supercomputer simulations. PT, ASp, M-AD-C, ASo, VJ, AM, and PR contributed to the interpretation of the results, figure development, and writing of the manuscript.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The Supplementary Material for this article can be found online at:

PR acknowledges the following funding sources: H2020 Research and Innovation Action grants 826421 and 650003, 720270 and 785907, and ERC 683049; German Research Foundation CRC 1315 and 936, and RI 2073/6-1; Berlin Institute of Health and Foundation Charité, Johanna Quandt Excellence Initiative.

We acknowledge support from the German Research Foundation (DFG) and the Open Access Publication Fund of Charité—Universitätsmedizin Berlin.

Further we acknowledge Lea Doppelbauer and Jan Roediger for their helpful discussions.