Han Yan

Cédric Gueguen

Bernard Cousin

Jean Paul Vuichard

Gil Mardon

Green Home Network based on an Overlay Energy Control Network

Keywords: Energy saving, Green networking, Home network, Overlay control network, ZigBee

Today, reducing global greenhouse gas emissions has become a crucial issue for protecting the earth's environment. This requires the reduction of energy consumption in as many sectors as possible, including home networks. Indeed, in the home environment, networked devices consume a large proportion of household energy.

There are three reasons that can explain the high energy consumption of home network devices. Firstly, devices are in idle state for hours when they are not in operation. Secondly, they cannot go to an ultra-low power consumption state when they are not needed. And last but not least, there is an increasing number of home network devices with soaring power consumption in our homes.

These home network devices have a long switching time from idle state to sleeping state. Moreover, explicit user commands are required to switch the device from idle state to soft-off state. We can certainly gain energy if the device stays in sleeping state or soft-off state instead of idle state. We propose an Overlay Energy Control Network (OECN) which can switch devices from idle state to sleeping state much more quickly and from idle state to soft-off state automatically.

The Overlay Energy Control Network (OECN) is formed by at least one overlay energy control node connected to each home network device. The OECN power management coordinates the power states of all home network devices. The overlay energy control nodes can exchange energy control messages. The devices can be turned on or turned off, or can return to their power states when they receive the OECN messages.

So that the OECN can be adaptive to our home network devices, the OECN is developed in two ways: (i) all overlay energy control nodes in the home network are ZigBee nodes. This is a ZigBee Mandatory OECN Solution (ZMS); (ii) one or more devices become the overlay energy control nodes where there are no ZigBee modules on that device. This is a ZigBee Optional OECN Solution (ZOS).

In our simulation, we will evaluate our overlay energy-saving solutions with a selfcontrolled energy solution in three metrics: energy consumption, delay and cost. In the selfcontrolled solution, the device controls its own power state.

The proposed Overlay Energy Control Network provides an efficient energy-saving solution for home network devices. In our use case, the ZigBee Mandatory Solution can gain 21.79% energy on average compared to the self-controlled solution. It is an efficient energy-saving solution, but it has a relatively high delay compared to the ZigBee Optional Solution and the self-controlled solution.

Introduction

In the last decade, there has been a proliferation of connected devices in the home environment. The number of connected devices has led to a sharp increase in energy consumption in the home [START_REF] Rose | Home networks: a standards perspective[END_REF]. A home network is a complex environment which contains several different types of devices: Set-Top Box (STB), Home Gateway (HGW), PC, laptop, power line communication plugs and so on, with different kinds of connections: Wi-Fi, Ethernet and power line communication.

Energy saving in this complex home network is crucial for the following two reasons:  Firstly, each electricity generation system has a "carbon footprint" [START_REF] Wiedmann | A Definition of 'Carbon Footprint[END_REF]. This means that all electricity generation systems generate carbon emissions, which are a major cause of global warming. Thus, for future generations, it is necessary to find an efficient energy-saving solution which will reduce carbon emissions.

 Secondly, the cost of electricity is not an insignificant part of the family's household budget. Especially for low income families, it is always difficult to meet energy costs. According to report [START_REF]Energy cost impacts on American families, 2001-2012[END_REF], electricity costs may rise to more than one fifth of a family's income. In order to improve quality of life, it is essential to reduce electricity bills by reducing energy consumption.

As seen, it is essential to provide an effective way of reducing power consumption for both environmental and economic reasons. The Overlay Energy Control Network (OECN) is proposed as a way of meeting the requirement to reduce energy consumption. This solution is based on a dedicated control network, in overlay with a typical home network. By sending overlay energy control messages, the OECN can turn off the devices or switch the devices to an ultra low power consumption mode when they are not in operation.

Several studies have contributed to the topic of energy saving. In terms of the device system, dynamic power management is proposed [START_REF] Benini | A survey of design techniques for systemlevel dynamic power management[END_REF], [START_REF] Qiu | Dynamic power management based on continuous-time markov decision processes[END_REF], and [START_REF] Chung | Dynamic power management for non-stationary service requests[END_REF]. Devices can be switched to a lower power mode when there is reduced demand for service. In addition, several algorithms have been proposed to minimise the energy consumption of device components, for instance, Ethernet links [START_REF] Gupta | Dynamic Ethernet Link Shutdown for Energy Conservation on Ethernet Links[END_REF], and memory [START_REF] Khargharia | An adaptive interleaving technique for memory performance-per-watt management[END_REF], [START_REF] Fan | Memory controller policies for dram power management[END_REF]. Since home network devices usually work together to offer multifunction, it is not sufficient to save energy at the level of each individual device. Consequently, the OECN provides a collaborative method by exchanging energy control messages to control the power states of home network devices.

On the network layer, Youn-Kware Jeong et al. have proposed a power management algorithm. This reduces power consumption by reconfiguring the power control elements of each device [START_REF] Jeong | A network level power management for home network devices[END_REF]. Nevertheless, this study does not take into account the consumption associated with network connections, necessarily active in the proposed model. The authors also lack the consideration of the delay necessary for state changes. This delay can strongly influences the user perceived experience. In this chapter we propose a model based on an overlay network with very low energy consumption and evaluate the efficiency of our solution by analysing not only the energy gain and cost gain, but also the delay generated by the energy-saving solution. The evaluation is based on a home network which simulates real family life with variant day types.

With a home network, users want to be able to use the internet at any time on any device when they need the network service. Moreover, home network devices work together to provide some collaborative services. For instance, a laptop user may want to watch a video saved on the set-top box hard drive, and these home network devices work together to offer the video playing service [START_REF]Use Case Scenarios White Paper[END_REF]. The OECN offers a collaborative way to immediately turn off/switch-to-sleep the devices when they are not interacting or in operation. With the help of the OECN, devices can be switched to an ultra low power state (soft-off state or sleeping state), instead of away state where the power consumption is much higher than the former two states.

We defined power states according to the Advanced Configuration and Power Interface (ACPI) standard [START_REF]Advance Configuration and Power Interface Specification[END_REF]:

 G0 (Working State): The device is on and applications are executed.  G0-1 (Away State or Idle State): This is a subset of the working state. The device is on but idle, and no applications are executed. We distinguish this state from the working state because this state consumes a lot of energy that is not required by the user.  G1 (Sleeping State): The device is sleeping.  G2 (Soft-off State): The device is turned off, but the power supply is still plugged in to the power source.  G3 (Mechanical-off State): The power supply to the device has been completely removed.

Initially, the device needs a long waiting time, typically half an hour to one hour, to switch from G0-1 (away/idle state) to G1 (sleeping state). Moreover, users need to regulate the device manually to switch from G0-1 to G2 (soft-off state). We can gain energy if the device stays in G1 (sleeping state) or G2 (soft-off state) instead of G0-1 (away/idle state). In this chapter, we propose an always-on Overlay Energy Control Network (OECN) which can switch devices from G0-1 to G1 much more quickly and from G0-1 to G2 automatically. This always-on overlay architecture consumes little energy since it is partly constructed on the ultra-low power consumption ZigBee modules. Each ZigBee module consumes about 18 to 120 milliwatt hours per day [START_REF]A true system-on-chip solution for 2.4-ghz IEEE[END_REF], and it can turn on/turn off one device through the USB port. ZigBee is used to satisfy the need for a standard-based wireless network that has low power consumption, low data rates and robust security. The other part of the overlay architecture is based on the Ethernet. Our system could wake the devices up by implementing the method of Wake-On-Lan, turn the devices off and request the power state of the devices by the UPnP Low Power protocol [START_REF]UPnP Low Power Architecture Version 1.0[END_REF]. UPnP low power protocol is defined to satisfy the demand of reporting and tracking the power states of the UPnP nodes. If possible, the UPnP low power protocol could also request the device to enter the sleeping state.

In this chapter, section 2 sets out the architecture of our OECN. Section 3 describes the methodology used to evaluate our solutions and the simulations, and then presents the analysis of the results.

The proposed Overlay Energy Control Network

In a home network, there are many kinds of devices such as a home gateway (HGW), set-top box (STB), power line communication (PLC) plugs, PC, laptop, and so on. In order to reduce the overall energy consumption of the integral home network devices, a low power consumption control layer over this home network is proposed: this is an Overlay Energy Control Network. In this section, we present firstly the global architecture and the protocol stack of the OECN system, two solutions based on this system will be proposed.

Global architecture

The Overlay Energy Control Network (OECN) is formed by at least one overlay energy control node connected to each home network device. The OECN power management coordinates the power states of all the home network devices. The overlay energy control nodes can exchange energy control messages. The devices can be turned on or turned off, or they can return to their power states when they receive the OECN messages.

We chose to implement the OECN power management in the Home Gateway because we assumed that this device is always present and in active state in the home network to support VOIP phone calls. At the home network level, all devices are interacting components which work together. By exchanging OECN messages, the devices centralise their information on the OECN management node. The OECN management collects the power information and controls the network devices (shown in Figure 1 below). In the home network, all devices interact together to provide collaborative services. The network topology dependence, network traffic and power state information of the devices is required by the OECN manager node. Meanwhile, the OECN manager node controls the integral home network based on this information.

When one device receives the power turn-on/turn-off message from ZigBee, it will be shut down by a command sent by ZigBee or woken up by WAKE-ON-USB. Since home network devices are generally equipped with a USB port, we assume that we can apply our solution to those USB-equipped devices.

The devices can be turned on or turned off, or they can return to their power states when they receive the OECN messages. These OECN messages can be sent in two ways. Therefore, the OECN can be implemented in two ways. This depends on the type of energy control node and the way overlay energy control messages are exchanged: if all OECN nodes are ZigBee nodes in the home network, this is a ZigBee Mandatory OECN Solution; if, however, one or more OECN nodes are devices that do not have Zigbee modules, this is a ZigBee Optional OECN Solution.

Protocol stack

In the overlay energy control network, the user device and the home gateway (or any two user devices) can communicate through ZigBee network or any LAN (like Ethernet or WiFi). User devices which is capable to support a ZigBee module should have the function of powering the ZigBee module, exchanging the messages with the ZigBee USB/UART interface, being powered on/off by the module. Between two user devices without ZigBee modules, the communication is realized by the UPnP low power messages over the HTTP protocol. Figure 2 shows the protocol stack of the proposed OECN.

ZigBee Mandatory energy-saving Solution (ZMS)

ZigBee Mandatory energy-saving Solution (ZMS): When all the energy control nodes are ZigBee modules, this is called a ZigBee Mandatory energy-saving Solution, as shown in Figure 2

(below).

There are several advantages to having ZigBee modules as control nodes. A device can be turned off and can also be started up by the ZigBee module connected to it, which is always on. Therefore, this device can go into an ultra-low power consumption state (softoff state).

Although there are some significant advantages to using ZigBee modules as overlay energy control nodes, it is not possible to use this solution everywhere. As it might not be possible to connect a ZigBee module to the device or if the ZigBee transmission diameter is limited, we propose another alternative solution, namely the ZigBee Optional energysaving Solution.

ZigBee Optional energy-saving Solution (ZOS)

ZigBee Optional energy-saving Solution (ZOS): Compared to the ZMS, the ZigBee Optional energy-saving Solution (ZOS) does not need each device to be fitted with a ZigBee module. When there is no ZigBee module on a device, the device itself becomes the energy control node and the energy control messages are sent via the data home network.

In Figure 3, the OECN is formed by ZigBee OECN nodes, one PLC plug and the STB.

The reasons why the devices (PLC plug and STB) become overlay energy control nodes are because:

 The set-top box is not equipped with a ZigBee module;  The distance between the two PLC plugs is too great for the ZigBee transmission diameter. On these non-ZigBee devices, the overlay energy control messages are sent through the data home network instead of a ZigBee network. Non-ZigBee devices can immediately go into a low power state (sleeping state) when there is no executing application. However, we cannot switch the device to a soft-off state since the OECN cannot turn on a soft-off device without the help of ZigBee module. Although not all devices can be switched to an ultralow power consumption state (soft-off state), we can still save energy using the ZOS by only leaving active those elements required for wake up (network interfaces, etc.).

Simulation and analysis of results

In order to demonstrate the efficiency of the two OECN solutions (ZMS and ZOS), we will compare the performance of these two proposed solutions with a traditional energysaving solution called a self-controlled solution. 1) Self-controlled energy-saving solution: The device controls its own power state.

This means that the device goes into the low power consumption state (sleeping state) by a user-defined condition (a one hour timer, for example). 2) ZigBee Mandatory energy-saving Solution: The OECN manager controls all home network devices with a ZigBee module connected to each device. All overlay energy control messages will be transmitted by the ZigBee modules. 3) ZigBee Optional energy-saving Solution: The OECN manager controls devices in a hybrid way. The overlay energy control messages will be sent by the ZigBee overlay network or the data home network.

Simulation methodology

In this section, we firstly build our device modelling which is in context of four different day types. Then we are going to apply three solutions on one or several devices.

Device Utilisation Modelling

We first generated the device modelling, and on top of that we applied the energy efficient solutions. Each device in the home network may be used at random time. Thus, the device modelling is expected to characterise its stochastic behaviour. Here, we use a simple Markov process to describe each device. From the user's perspective, a home network device is either in operation (active) or not in operation (inactive). Figure 4 shows that the probability of one active device becoming inactive is v and the probability from inactive to active is r. As the utilisation rate of one device may vary during the day, the device will be represented by different r and v values over the 24 hour period. The device active utilisation ratio is defined as:

(1)

This device active utilisation ratio gives the normalised probability of being in active state. When the device is active, this corresponds to "working state". When the device is inactive, it can be in "away state", "sleeping state" or "soft-off state". The last two power states are low and ultra-low power consumption states. The different power states of an inactive device depend on the power-saving solution that we applied to this device. These different states have different power consumptions (Watt-hour), as shown in Using the PC as an example, we can see that it consumes 205 Watt-hours when it is in "working state". This is the average power consumption when a user uses the PC to download or play multimedia files. The PC consumes 123.5 Watt-hours (away state) and 3.2 Watt-hours (soft-off state). The difference in power consumption in these two states is significant. It proves that changing the power state when the device is inactive can effectively save energy.

Four day types

In order to make the device modelling realistic and adaptive to the family home network devices, the probabilities r and v are categorised into four different day types. We need to define a set of r and v values for one device in one day type. This is an example of four day types for a family of four. As a telecom operator, we have chosen these four day types according to our knowledge of our customers and how they use the devices. We also assumed that the home network devices are those shown in Figure 1.

1) Day type 1 (Working day): Parents go to work and children go to school. We will take the laptop as an example. The laptop has a high utilisation ratio between 8am and 9am because one family member needs to check his/her email. In the evening from 8pm to 12pm, one family member wants to surf the internet. Thus, the laptop has also a significant utilisation ratio. Each home network device has its own utilisation ratio at each time.

2) Day type 2 (Wednesday*): On this day type, the children stay at home and parents are at work. On this day type, the set-top box has a relatively high utilisation ratio during the daytime. The laptop and PC are used at various times throughout the whole day.

3) Day type 3 (Weekend): All family members are at home. The laptop, PC and settop box are needed at different times over the weekend.

4) Day type 4 (Holiday day):

The whole family is on holiday. Apart from the PC that is equipped with a home security camera, which is on, the other devices in the home network are turned off completely. We use the set-top box on day type 1 as an example. As shown in Figure 5, all family members are at work or at school. The set-top box and television are turned on to watch the news when they get up. That is why we have high device utilisation at 7am. When the family members leave to go to school or work, the device utilisation goes down. At 12 noon, we have peak device utilisation, since the children return home to eat and watch television at the same time. In the evening, we also have high device utilisation of the settop box when every family member is at home. The device utilisation of one device is relatively stable for each day type. Therefore, we can fix a set of device utilisation values for each day type.

Application of the three solutions

As mentioned earlier, device utilisation could be represented by a Markov process. Comparing this Markov process with the device power states, active corresponds to "working state", while inactive corresponds to "away state", "sleeping state" or "soft-off state". The selected state depends on which energy efficient solution we apply.

Each energy efficient solution can therefore be defined by a finite-state machine. In the finite-state machine representation, we use the four power states which are cited in Section 1. From one power state to another, there is always a power and performance cost. A low power state has low power consumption and a long transition time. Conversely, a high power state has high power consumption and a short transition latency.

In our modelling, the abbreviations are defined in The transition time between two states. For instance, is the transition time from "sleeping state" to "working state".

The time spent in one state. For example, is the time spent in sleeping state.

The power consumption in one state. The power consumption of each transition. For instance, is the transition power consumption from "sleeping state" to "working state". Based on the device utilisation modelling, we can apply the three solutions to the device. Figure 6 shows the application of the self-controlled energy-saving solution. If a device is not being operated, the device will go into "away mode". Then, after the timer has timed out (For instance, = one hour), the device will go into sleeping state. After staying in sleeping state for , the device will be woken up by a user. So we can define the total energy for the self-controlled solution as:

(2)

Figure 7 shows that in the ZMS, if the device is not in operation, the device will put into soft-off state immediately after utilisation. In this case, the device does not need to go into "away state". The energy consumption for ZMS can be defined as:

(3)
Here, in ZMS is equal to in the self-controlled solution. The ZOS is shown in Figure 8. If the device is not in operation, the device immediately goes into sleeping state. The energy consumption for ZOS is:

(4)
Here, in ZOS is equal to in the self-controlled solution. Since the transition power consumption is lower than the power consumption in each state, we ignore the power consumption on each transition. In these three solutions, the energy consumed during the working state is the same. The greatest difference between the self-controlled solution and the OECN solutions is that the device does not need to remain in away state for the time defined by the timer. With the OECN solutions, we assume that the manager knows when a device will not be useful (could be switched off). For instance, the home network manager knows when the video broadcast is ending or when the internet connection is closed. Thus, devices could go to low power consumption states immediately if they are not in operation. Since is always bigger than or , energy is saved by putting devices into sleeping state and soft-off state instead of away state.

Simulation of one device & analysis of results

As presented above, we simulated the device utilisation to evaluate these energy-saving solutions: self-controlled energy-saving solution, ZMS and ZOS. To simulate the three solutions applied to one device, we used the following parameters:

Power consumption of each device in different power states: , as presented in Table 1.

Device utilisation probabilities over 24 hours: A defined timer for the self-controlled solution. In our simulations, we used a one hour timer.

Number of simulation runs: 1,000. We compared the results obtained by 10,000 runs and 1,000 runs. The difference in results for laptop consumption on a day type 1 was lower than 1%. We can therefore assume that 1,000 times is sufficient to obtain good accuracy.

Simulation of one laptop on a "Weekend" day type

This is an example of one simulation based on one device in the home network. We firstly simulated laptop utilisation on the weekend. Since all family members are at home on the weekend, they play video games and surf the internet nearly all day.

The laptop utilisation ratio is defined in Figure 9 (below). At 9.30am, there is a high probability that one family member at home is on the laptop until 11:30am. After lunch, it is also quite probable that one family member turns on the laptop. We can see an utilisation peak at 8.30pm, since the father checks his personal email after dinner. We simulated the device usage 1,000 times based on the given probabilities. After each simulation of the device usage, we applied the three different energy-saving solutions to the device utilisation. Figure 10 shows how the three power-saving solutions worked on this device for 1,000 simulation runs. The three coloured lines plot average power consumption. The red line is the power consumption of the device using the self-controlled energy solution. After operation, the device goes into away state for one hour, and then goes into sleeping state.

The blue line represents the power consumption of the device using the ZMS. The device goes into soft-off state immediately after operation.

The green line represents the power consumption of the device using the ZOS. This line sometimes overlaps with the ZMS line, because the power consumption in sleeping state and soft-off state are approximate. The device goes into sleeping state immediately after operation.

From Figure 10 we can clearly see that the power consumption in the sleeping state and soft-off state is less than in the idle state, for instance, from 11.30am to 12.30. Thus, the energy gain comes from the times when device utilisation changes from active to inactive.

Simulation for one laptop on a "Wednesday" day type

Energy is mostly gained when a device switches from active to inactive. In the first simulation example, there were fewer power state transitions. In this example, we simulated the same device another day type where the power state transitions are more frequent.

On the Wednesday day type, the laptop is used at different times during the day. The stay time in active or inactive is more random and irregular than on the weekend day type. This is shown in Figure 11, where we have simulated laptop power consumption for a weekend day type. The power consumption obviously decreases when the laptop utilisation ratio decreases in Figure 12. From 9.30am to 10.30am, there is an energy gain between the self-controlled solution and the OECN solutions. This is because the device is quickly turned off (ZMS) or switched to sleeping state (ZOS), instead of staying in away state (self-controlled solution). At 10.30am, the self-controlled solution consumes almost the same energy as the ZOS since the device is in sleeping state in these two solutions. The ZMS can gain more energy than the other two solutions because the device is in soft-off state which consumes less than in sleeping state. Our OECN solutions gain energy when there is a transition from active to inactive and while the device is in inactive state. There is a greater number of state transitions of power; more energy is gained.

Simulation of one home network & analysis of results

Based on the home network shown in Figure 1, we will simulate the home network devices for one year (365 days).

Simulation setup

In order to evaluate energy efficient solutions in a home network environment, simulations are carried out for different day types. In one year, we will have 191 type 1 days, 96 type 2 days, 48 type 3 days and 30 type 4 days. All these different days make up one year (365 days). This choice is representative on the basis of our own knowledge of our customers and how they use the devices.

The three energy-saving solutions are analysed in 3 metrics:  Annual energy consumption: Energy consumption is the energy used in the whole home network in one year. The power consumption of the devices is presented in Table 1 (above). We take the energy consumption of the ZigBee modules into account for the OECN solutions.

 Daily delay: Daily delay is the cumulative waiting time every day. The waiting time is calculated from the moment that the device is requested to the moment that the device is in operation. It is the total duration of all transitions from inactive to active. For these energy-saving solutions, the delay for one day is calculated as:

(

The "a+b" is the number of times that the device changes state from inactive to active in one day. "a" is the number of times that the device changes state and does not stay in the inactive state for more than one hour. "b" is the number of times that the device changes state and stays in the inactive state for more than one hour. The transition time is shown in Table 3. The home network delay is the sum of the delays for each home network device.  Cost: The total monetary cost of the three solutions. We calculate the cost of electricity based on the European electricity tariff (for the year 2012) in Table 4. This tariff is cheaper during the night than during the daytime. For the selfcontrolled energy solution, we calculated the cost of electricity. For the ZMS, we calculated the cost of the electricity and the ZigBee modules. For the ZOS, we calculated the electricity cost of the electricity and the ZigBee module if the device has one. Otherwise, we just calculated the electricity cost of the device.

Analysis of results

The results of the three energy-saving solutions simulated on one home network is analysed in three dimensions: energy consumption, delay and cost.

Energy consumption

From Figure 13 (below) we can see the energy consumption of one home network with different energy solutions applied. Compared with the self-controlled solution, we can gain 21.79% energy with the ZMS and 16.96% energy consumption with the ZOS in one year. By applying the ZMS, the devices are in the soft off power state which consumes the least energy when they are not in operation. Without the help of the ZigBee modules in the ZOS system, the device could immediately goes to the sleeping power state after the operations and we note the sleeping power state is also a low energy cost state comparing with the idle power state.

Of these four day types, an OECN solution is less effective at the weekend. We gain 10.58% with the ZMS and 7.28% with the ZOS. For day type 3, however, OECN solutions are quite effective for energy saving: 28% (ZMS) and 21% (ZOS). On day type 3, the devices change their power states more often than on day type 2. This is why OECN solutions are more effective on one day type than on another.

As we explained in the part 3.2.2, the more frequently the device changes its state from active to inactive, the more energy is saved. That is why on day type 3 we might have a large energy gain by using OECN solutions. Meanwhile, delay performance increases when the energy gain increases. The more frequently the device changes state, the more delays are accumulated from inactive to active state.

Home network delay

The OECN solutions are effective for energy saving. However, the energy gain is not free, and the OECN solutions pay by the delay to have the energy gain. As explained in the simulation setup, the daily delay is the sum of the delays for each home network device. This cumulative delay per day of the home network is 4.8 minutes when using the ZigBee Mandatory Solution. This is acceptable for many users. For other users, the ZOS could be an opportune trade-off, where the daily home network delay is only 0.48 minutes. Note that by applying ZMS, devices are capable to enter the lowest power state which needs longer time to return back to the working power state. That is why ZMS has a higher delay comparing to the other two solutions. ZOS and self-controlled solutions have similar delay for the different day types. However, using the self-controlled solution the user needs to turn on/ turn off the user device manually which is not favourable for the quality of the user's experience. From this point of view, the additional delay of ZOS and ZMS is favourably compensated by the automatic OECN management.

The greater the amount of energy gained, the more delay there is. As shown in Figure 14 for day type 2, the daily delay of all home network devices is 1.447 minutes (ZMS) and 0.146 minutes (ZOS). For day type 3, the OECN solutions are effective for energy saving but we also have an additional delay with the OECN solutions. Every time energy is gained from transitions, the OECN solutions put devices in a low or ultra-low power consumption state, which requires a longer time to wake up.

Cost

Reducing electricity bills can be a powerful motivation for home network users. At first, extra money must be spent on ZigBee modules. In Figure 15, this family uses six ZigBee modules for ZMS and four ZigBee modules for ZOS. However, after one year, the total cost for the OECN solutions are less than the cost for the self-controlled solution.

Comparing the two OECN solutions, the ZMS with six ZigBee modules consumes less energy than the ZOS after 1.5 years in our use case. For users who want to have a short term benefit in one year, they should choose the ZOS solution which is the most profitable solution from the 11th month to the 20th month. Users who want to have a long term profit should choose the ZMS solution which is the most profitable energy saving solution after the 20th month.

Conclusion

In this chapter, we have proposed energy-saving solutions based on an Overlay Energy Control Network. This proposition aims to reduce the energy consumption of the home network devices, and thus reduce the environmental impacts caused by the carbon footprint from electricity generation. The proposed Overlay Energy Control Network provides two efficient energy-saving solutions for home network devices. Compared to the two OECN solutions, the device self-controlled energy solution is the solution that saves the least energy. The ZMS, which is based on a complete OECN, is more efficient in terms of energy saving, but it has a relatively high delay compared to the two other solutions. The ZOS, which is based on a partial OECN, is the second most efficient energy-saving solution. This solution also has a delay that is slightly greater than the device self-controlled energy solution but less than the ZMS.

Our ZMS is proven to be an effective energy-saving solution. In addition, the ZOS is proven to be a good trade-off of energy saving and delay. This trade-off depends first and foremost on the selection of non-ZigBee devices and on the time each device takes to change state.

The future challenge will lie in combining ZMS and ZOS solutions for a certain amount of time, depending on our knowledge of usage or user behaviour. In the second phase, we plan to achieve better energy gain with minimum delay to assure better quality of user experience.

Figure 1 :

 1 Figure 1: OECN management

Figure 2

 2 Figure 2 OECN protocol stack

Figure 3 :Figure 4 :

 34 Figure 3: OECN Architecture: ZigBee Mandatory energy-saving Solution (ZMS)

Figure 5 :

 5 Figure 5: Device modelling from the user's perspective

Figure 6 :

 6 Figure 6: Set-top box utilisation ratio on day type 1

Figure 7 :

 7 Figure 7: Self-controlled energy-saving Solution

Figure 10 :

 10 Figure 10: Device utilisation ratio on the weekend Figure 11: Device power consumption on the weekend

Figure 12 :Figure 13 :

 1213 Figure 12: Device Utilisation on day type 3 Figure 13: Device power consumption on day type 3

Figure 14 :

 14 Figure 14: Home network energy consumption results

Figure 15 :

 15 Figure 15: Home network delay results

Figure 16 :

 16 Figure 16: Home network cost results

Table 1 :

 1

	Device /Watt-hour	Working	Away	Sleeping	Soft-off
	STB	21	19.2	13.5	2.5
	PC	205	123.5	4.9	3.2
	Laptop	79	54	5	2.5
	PLC	6	3	2.6	0.15

Table 1 :

 1 Power consumption

Table 2 (

 2 below):

	Abbreviations	Meaning
	w; s; a and o	Power state: working state, sleeping state, away state and soft-off state.

Table 2 :

 2 Modelling abbreviations

Table 3 :

 3 Transition delay

	Device / Delay (seconds)
	HGW	0.01	1	40
	STB	0.01	7	80
	PLC	0.01	1	3
	PC	0.01	4	30
	Laptop	0.01	2	25

Table 4 :

 4 Electricity and ZigBee module tariff

	Cost		Tariff
	Electricity (€/Kilowatt-hour)	Day Rate:	Night
		0.1312	Rate: 0.0895
	ZigBee Module (€/unit)		6.05

* This study was conducted in France where pupils do not currently attend school on Wednesdays.


Yiming Xiao
email: yiming.xiao@mail.mcgill.ca

Pierre Jannin

D ' Albis

Nicolas Guizard

Claire Haegelen

Lalys Florent

Marc Verin

D Louis Collins

Keywords: Atlas, Parkinson's disease, deep brain stimulation, principal component analysis, label fusion, morphometric variability, subthalamic nucleus

Subthalamic nucleus (STN) deep brain stimulation (DBS) is an effective surgical therapy to treat Parkinson's disease (PD). Conventional methods employ standard atlas coordinates to target the STN, which, along with the adjacent red nucleus (RN) and substantia nigra (SN), is not well visible on conventional T1w MRIs. However, the positions and sizes of the nuclei may be more variable than the standard atlas, thus making the pre-surgical plans inaccurate. We investigated the morphometric variability of the STN, RN and SN by using label-fusion segmentation results from 3T high resolution T2w MRIs of 33 advanced PD patients. In addition to comparing the size and position measurements of the cohort to the Talairach atlas, principal component analysis (PCA) was performed to acquire more intuitive and detailed perspectives of the measured variability. Lastly, the potential correlation between the variability shown by PCA results and the clinical scores was explored.

Introduction

Chronic deep brain stimulation (DBS) of the subthalamic nucleus (STN) is an effective alternative treatment for Parkinson's disease (PD) patients that have adverse responses or resistance to the pharmaceutical treatment [START_REF] Kleiner-Fisman | Longterm follow up of bilateral deep brain stimulation of the subthalamic nucleus in patients with advanced Parkinson disease[END_REF][START_REF] Vingerhoets | Subthalamic DBS replaces levodopa in Parkinson's disease: two-year follow-up[END_REF]. Often the therapeutic benefits of DBS in reducing motor-function-related symptoms are closely related to the precise placement of the DBS electrode to the motor sub-region of the STN, while avoiding adjacent nuclei (e.g. substantia nigra) and white matter tracts as their simulation can cause undesired side effects (Montgometry, 2010). Classical pre-surgical targeting for STN DBS relies on indirect inference of the nucleus location, based on the locations of other neuroanatomical landmarks, such as the anterior commissures (AC) and posterior commissures (PC) seen in the patient's T1w MRI or ventriculography. For better targeting quality, many groups [START_REF] Acar | Safety of anterior commissureposterior commissure-based target calculation of the subthalamic nucleus in functional stereotactic procedures[END_REF][START_REF] Guehl | Statistical determination of the optimal subthalamic nucleus stimulation site in patients with Parkinson disease[END_REF][START_REF] Lanotte | Deep brain stimulation of the subthalamic nucleus: anatomical, neurophysiological, and outcome correlations with the effects of stimulation[END_REF][START_REF] Mcclelland | Subthalamic stimulation for Parkinson disease: determination of electrode location necessary for clinical efficacy[END_REF] promoted using the mid-point of the AC-PC line, or the middle commissure (MC) point as the reference landmark instead of the AC and PC points. The relative spatial relationship between the STN and the landmarks is often derived from brain atlases such as the Talairach [START_REF] Talairach | Co-planar stereotaxic atlas of the human brain : 3-dimensional proportional system : an approach to cerebral imaging[END_REF] or Schaltenbrand [START_REF] Schaltenbrand | Atlas for stereotaxy of the human brain[END_REF] atlases.

Since both of these atlases have shorter AC-PC lines, some groups infer the location of the STN by scaling the atlas to align the AC and PC points [START_REF] Guehl | Statistical determination of the optimal subthalamic nucleus stimulation site in patients with Parkinson disease[END_REF][START_REF] Nowinski | A probabilistic functional atlas of the human subthalamic nucleus[END_REF].

During surgery, the precise stimulation site is refined with physiological micro-electrode recording (MER), which may require creating multiple parallel electrode insertion trajectories.

Evidently, an accurate pre-surgical plan is instrumental to reduce the number of re-insertions, and thus reduce the surgical time and risks. Although such indirect inference can be helpful in identifying the STN, which, together with substantia nigra (SN) and red nucleus (RN), are not readily visible on standard clinical T1w MRIs, the assumption that their sizes and locations with respect to brain landmarks stay fairly fixed may not hold across different individuals. This can be particularly true for patients with advanced PD, which may introduce further global and local morphological changes to the brain [START_REF] Camicioli | Parkinson's disease is associated with hippocampal atrophy[END_REF][START_REF] Hutchinson | Structural changes of the substantia nigra in Parkinson's disease as revealed by MR imaging[END_REF][START_REF] Nagano-Saito | Cerebral atrophy and its relation to cognitive impairment in Parkinson disease[END_REF] in addition to normal aging [START_REF] Den Dunnen | Anatomical alterations of the subthalamic nucleus in relation to age: a postmortem study[END_REF][START_REF] Keuken | Ultra-high 7T MRI of structural age-related changes of the subthalamic nucleus[END_REF][START_REF] Kitajima | Human subthalamic nucleus: evaluation with high-resolution MR imaging at 3.0[END_REF][START_REF] Murphy | Age-Related Differences in Volumes of Subcortical Nuclei, Brain Matter, and Cerebrospinal-Fluid in Healthy-Men as Measured with Magnetic-Resonance-Imaging[END_REF][START_REF] Scahill | A longitudinal study of brain volume changes in normal aging using serial registered magnetic resonance imaging[END_REF]. An evaluation of the assumption for indirect localization, with an analysis of the size and location variability for these nuclei in comparison to the standard atlases [START_REF] Schaltenbrand | Atlas for stereotaxy of the human brain[END_REF][START_REF] Talairach | Co-planar stereotaxic atlas of the human brain : 3-dimensional proportional system : an approach to cerebral imaging[END_REF] will likely facilitate the surgical planning for STN DBS.

With the help of chemical stains, histology data have been the gold standard for neuroanatomy definition, and previously anatomical variability studies have been conducted using post-mortem brains (Den Dunne and Staal, 2005;[START_REF] Massey | High resolution MR anatomy of the subthalamic nucleus: imaging at 9.4 T with histological validation[END_REF]. It is true that with high resolution and visual aid of chemical stains, the anatomical knowledge obtained from histology data is undoubtedly valuable. However, three reasons still justify the need of anatomical variability studies based on MRI of in vivo brains. First, due to the availability of funds and brain donors, histology-based studies often cannot include a big number of subjects, and a larger sample size can potentially provide more reliable results. Second, the brain is susceptible to texture changes and deformation due to external force, tissue preservation methods, and environmental changes (i.e. temperature, humidity, pressure). Once the brain is extracted from the skull, the morphometric properties of the brain structures may alter, and the measurement will be different from the situation when the subject is alive. Third, often dissection of the brain can only be performed in one principle direction. This limits the accuracy of 3D analysis of the nuclei of the same subject, unlike the MR images. Therefore, as MRI is still the chief method for pre-surgical planning, morphometric variability analysis of the midbrain nuclei using MRI is still important for the clinical consideration.

To date, a few previous endeavors [START_REF] Ashkan | Variability of the subthalamic nucleus: the case for direct MRI guided targeting[END_REF][START_REF] Daniluk | Assessment of the variability in the anatomical position and size of the subthalamic nucleus among patients with advanced Parkinson's disease using magnetic resonance imaging[END_REF][START_REF] Patel | Comparison of atlas-and magnetic-resonance-imaging-based stereotactic targeting of the subthalamic nucleus in the surgical treatment of Parkinson's disease[END_REF][START_REF] Richter | Determining the position and size of the subthalamic nucleus based on magnetic resonance imaging results in patients with advanced Parkinson disease[END_REF][START_REF] Zhu | Magnetic resonance imaging-based morphometry and landmark correlation of basal ganglia nuclei[END_REF] have reported the size and location variability with respect to the standard atlases for the STN by using 1.5 T T2w MRI with a 2 or 3 mm axial-slice thickness and manual structural contour identification. However, for a small nucleus like the STN as well as for the commissure points, the partial volume effects associated with a 2 or 3 mm slice thickness may make accurate delineation of STN boundaries challenging. The later 3T or higher-field MRI scanners that allow better image contrast, signal-to-noise-ration (SNR) and resolution can be better suited for the task. Although some (Forstmann et al., 2012; Keuken et al., 2013; Kitajima et al., 2008; Massey et al., 2012) have attempted the variability analysis with highfield MRI, the selections of stereotactic space as well as landmarks often differ from the clinical practice, and furthermore, there is a lack of pathological patient data.

In this article, we investigate the morphometric variability of the STN and the neighboring SN and RN that are directly visualized by 3T T2w MR images (1 mm isotropic resolution), and compare the results within the Talairach AC-PC based coordinate system. Instead of 2D manual contour identification [START_REF] Ashkan | Variability of the subthalamic nucleus: the case for direct MRI guided targeting[END_REF][START_REF] Daniluk | Assessment of the variability in the anatomical position and size of the subthalamic nucleus among patients with advanced Parkinson's disease using magnetic resonance imaging[END_REF][START_REF] Richter | Determining the position and size of the subthalamic nucleus based on magnetic resonance imaging results in patients with advanced Parkinson disease[END_REF][START_REF] Zhu | Magnetic resonance imaging-based morphometry and landmark correlation of basal ganglia nuclei[END_REF], we employed an automatic majority-voting label-fusion segmentation technique [START_REF] Aljabar | Multi-atlas based segmentation of brain images: atlas selection and its effect on accuracy[END_REF][START_REF] Heckemann | Automatic anatomical brain MRI segmentation combining label propagation and decision fusion[END_REF][START_REF] Rohlfing | Evaluation of atlas selection strategies for atlas-based image segmentation with application to confocal microscopy images of bee brains[END_REF][START_REF] Rohlfing | Shape-based averaging[END_REF] to identify the nuclei in 3D. Besides measuring the nuclei's relative locations with respect to the commissure points as commonly practiced in DBS pre-surgical planning, we performed principal-component analysis (PCA) to obtain more in-depth and intuitive perspectives of their morphometric variability. Finally, the computed principal components were correlated with patients' clinical information to explore the possible link between the morphometric variability and disease progression.

Methods and Materials

Patients and MRI protocols

For the analysis, 33 PD patients (19 male & 14 female, age = 61±8 yo) that received DBS procedures at the CHU Rennes (France) were scanned before surgery with a Philips Achieva 3T MRI scanner for both T1w MRIs (TR = 8.4 ms, TE = 3.7 ms, flip angle = 8°, acquisition matrix = 240×240, 160 axial slices, 1 mm 3 isotropic resolution) and turbo spin echo T2w MRIs (TR = 3035 ms, TE = 80 ms, flip angle = 90°, acquisition matrix = 256×256, 36 coronal slices, 1 mm 3 isotropic resolution). While the T1w MRI covers the entire head, the T2w MRI only images a coronal slab of the brain that contains the relevant nuclei. In Fig. 1, coronal and sagittal slices of the T1w and T2w MR images, which cut through the RN and SN, are shown for a PD patient.

The pre-surgical unified Parkinson's disease scale (UPDRS) III scores were evaluated as 8.35±5.37 and 30.89±14.35 (information missing for six patients) for with and without medication (on-Dopa and off-Dopa), respectively. All patients gave informed consent and the project was approved by the local research ethics board.

Figure 1 goes here

Automatic segmentation

In earlier investigations [START_REF] Ashkan | Variability of the subthalamic nucleus: the case for direct MRI guided targeting[END_REF][START_REF] Daniluk | Assessment of the variability in the anatomical position and size of the subthalamic nucleus among patients with advanced Parkinson's disease using magnetic resonance imaging[END_REF][START_REF] Richter | Determining the position and size of the subthalamic nucleus based on magnetic resonance imaging results in patients with advanced Parkinson disease[END_REF], structure identification was conducted with manual contour drawing or landmark picking (e.g. selecting the most anterior point of a structure) in the axial slices, and no volumetric segmentation or evaluation was involved. Manual segmentation can be good to identify structures, but automatic segmentation can provide more consistent results against inter-and intra-rater segmentation quality incoherence while saving both labor and time. Previously, automatic segmentation techniques have contributed to morphometric studies relating to neurological diseases and brain development [START_REF] Hu | Volumetric analysis of medial temporal lobe structures in brain development from childhood to adolescence[END_REF][START_REF] Morra | Automated 3D mapping of hippocampal atrophy and its clinical correlates in 400 subjects with Alzheimer's disease, mild cognitive impairment, and elderly controls[END_REF]. Among the proposed methods, label-fusion techniques have gained the popularity with the robust performance in identifying structures that are typically difficult to segment solely by image intensity features. In this paper, we employed the majority-voting label-fusion method [START_REF] Aljabar | Multi-atlas based segmentation of brain images: atlas selection and its effect on accuracy[END_REF][START_REF] Heckemann | Automatic anatomical brain MRI segmentation combining label propagation and decision fusion[END_REF][START_REF] Rohlfing | Evaluation of atlas selection strategies for atlas-based image segmentation with application to confocal microscopy images of bee brains[END_REF][START_REF] Rohlfing | Shape-based averaging[END_REF] to segment the RN, SN and STN. Before segmentation, the T1w and T2w images were pre-processed for all patients. All images were first denoised by the non-local mean filter technique proposed by [START_REF] Coupe | An optimized blockwise nonlocal means denoising filter for 3-D magnetic resonance images[END_REF], and then corrected for field inhomogeneity [START_REF] Sled | A nonparametric method for automatic correction of intensity nonuniformity in MRI data[END_REF]. Each patient's T1w and T2w MRIs were rigidly co-registered using a normalized mutual information objective function [START_REF] Studholme | An overlap invariant entropy measure of 3D medical image alignment[END_REF]. The essence of label-fusion is to deform multiple atlases (segmented labels and MRI volumes) to the target subject's anatomy and determine the final segmentation based on the consensus of all customized atlases in order to mitigate imperfect registration and label interpolation in the single atlas deformation. In this project, 10 out of the total of 33 subjects were selected to form the label-fusion atlas library, where each subject's brain was brought to the MNI305 space by a 9parameter linear registration. Then, the SN, RN and STN were segmented manually in the stereotactic space for both hemispheres with ITK-SNAP (http://www.itksnap.org) by an experienced neurosurgeon (CH). To further enrich the library, left-right mirrored versions of these atlases were also included, effectively doubling the original library size.

For each subject to be segmented, the library atlases were first registered to the target patient's anatomy with a global affine registration using T1w MRI, and then deformed through local T2-T2 nonlinear registration with SyN [START_REF] Avants | Symmetric diffeomorphic image registration with cross-correlation: evaluating automated labeling of elderly and neurodegenerative brain[END_REF] in the central region of the brain. Here, instead of using the conventional nearest-neighborhood interpolation, we used trilinear interpolation to deform the labels. This adds certain level of fuzziness to the atlases. The procedure is repeated for all 20 atlases in the template library. A demonstration of the label fusion procedure is shown in Fig. 2.

To obtain the final segmentation at each voxel location in the patient's image, the structural label with the maximum counts determined voxel's label (i.e. a simple voting scheme). Some subjects from the cohort of 33 patients formed the atlas library. In these cases, the labelfusion was performed in a leave-one-out manner, where the effective library would exclude the subject to be segmented.

Figure 2 goes here

Validation of automatic segmentation

The label-fusion automatic segmentation method for delineating the RN, SN and STN is validated in a leave-one-out manner using the 10 patients' MRIs, which formed the atlas library.

To avoid resampling errors and ensure the quality of comparison, the RN, SN and STN were automatically segmented in the stereotactic space (MNI305), where manual segmentations were performed. The comparison between the automatic and manual segmentation was performed with three metrics: 1) Dice overlapping coefficient, or kappa=2*a/(b+c) where a is the intersection of two segmentations, and b and c are volumes of each segmentation; 2) 95% Hausdorff distance, and 3) the Euclidean distance between the centers of mass (COM) of the manual and automatic segmentations.

Coordinate spaces

Any variability estimated will depend on the choice of coordinate space. Hence, selecting a coordinate space is important for understanding the anatomical variability and its potential link to other factors, such as the clinical information. In stereotactic neurosurgeries, the commissure points were frequently employed as the landmarks to infer the location of the subcortical structures, and thus these landmarks are natural choices to define a coordinate space to evaluate variability. To verify the spatial relationship and size differences between the nuclei and the Talairach atlas, which is often employed in the conventional DBS planning, we analyzed the variability in two different AC-PC aligned spaces. For both spaces, AC and PC points were manually identified for each subject, and the brain was re-oriented in the same manner as specified in the Talairach atlas [START_REF] Talairach | Co-planar stereotaxic atlas of the human brain : 3-dimensional proportional system : an approach to cerebral imaging[END_REF]. That is to say that the superior edge of AC and the inferior edge of PC were aligned at the centerline of the same axial plane, perpendicular to the mid-sagittal plane of the subject's brain.

For the first space, the brain re-orientation employed a rigid transformation. For the second space, in addition to the rigid transformation, all brains were scaled uniformly in three dimensions so that all AC-PC distances were normalized to be 23 mm as measured in the Talairach atlas [START_REF] Talairach | Co-planar stereotaxic atlas of the human brain : 3-dimensional proportional system : an approach to cerebral imaging[END_REF], and the AC-PC lines were aligned at exactly the same location for all patients. To avoid confusion, here we refer to the first and second space as the "AC-PC native space" and "AC-PC normalized space", respectively. Automatic segmentations were performed for each patient in these two spaces separately. Although we mainly employed the "AC-PC normalized space" to analyze the position and size variability, it is still important to acquire the nuclei sizes in the "AC-PC native space" in the absence of the scaling factor for comparison. Therefore, both of them were necessary for this study.

Distance-based variability analysis

As used in many clinical papers [START_REF] Ashkan | Variability of the subthalamic nucleus: the case for direct MRI guided targeting[END_REF][START_REF] Daniluk | Assessment of the variability in the anatomical position and size of the subthalamic nucleus among patients with advanced Parkinson's disease using magnetic resonance imaging[END_REF][START_REF] Richter | Determining the position and size of the subthalamic nucleus based on magnetic resonance imaging results in patients with advanced Parkinson disease[END_REF], measuring Euclidean distances between points within the structure of interest and other anatomical landmarks is a straightforward approach to explore the anatomical variability in terms of both position and size. For both coordinate spaces, we measured nuclei sizes in term of volume (in mm 3 ) as well as the extents of their 3D dimensions defined by the smallest rectangular box that contains the nucleus. The position variability of the nuclei was explored only in the "AC-PC normalized space". Because in DBS planning, the position of the STN is often inferred from the MC point, we measured the relative position between the center of mass (COM) of the nuclei and the geometric center of the "bounding box" to the MC point. The measurements were compared against the Talairach atlas ( [START_REF] Talairach | Co-planar stereotaxic atlas of the human brain : 3-dimensional proportional system : an approach to cerebral imaging[END_REF], and the comparison was studied with one-sided paired t-tests.

PCA-based variability analysis

Although the distance measurements offer quantitative comparison between subjects and standard atlases, the interpretation is less intuitive for 3D volumes. Alternatively, more detailed and intuitive morphometric variability analysis for the nuclei can be achieved using PCA, which is able to isolate shape variations that are independent in a high-dimensional space and offers the possibility to rank them according to their level of contribution to the overall variability. To bridge the volumetric segmentation and PCA, we employed the concept of a level-set [START_REF] Osher | Fronts Propagating with Curvature-Dependent Speed -Algorithms Based on Hamilton-Jacobi Formulations[END_REF]. Thus, for each structure, a signed distance transformation function (negative inside, positive outside and zero at the boundary) is computed. An example of the distance transformation is demonstrated for the left red nucleus with a coronal view in Fig. 3.

Figure 3 goes here

Results

Automatic segmentation and validation

The automatic segmentations for the SN, RN and STN for one patient registered to the MNI305 space are demonstrated in Fig. 4, along with the manual segmentations in the corresponding views.

Figure 4 goes here

The segmentation validation results are shown in Fig. 5 for all three evaluation metrics as boxplots with the mean values and standard deviations in the same graphs.

Figure 5 goes here

Distance-based variability analysis

The AC-PC distance is an important measurement for the application of Talairach atlas. In the "AC-PC native space", the AC-PC distance (mean ± standard deviation) is measured at 24.18 ± 1.81 mm with a range of 21.52 to 28.32 mm. In the Talairach atlas, the AC-PC distance is 23 mm, which is at the 27% percentile of the cohort under study.

With a fairly large variability in the AC-PC distance, fitting of the atlas often employs the process of scaling the AC-PC line so that the commissures will overlap those of the patient. In this context, variability was examined in the "AC-PC normalized space". In general, two main factors are often investigated for the anatomical variability, size and position. With regard to the nucleus size, we first took the measurement in terms of the medio-lateral (M-L), antero-posterior (A-P), and supero-inferior (S-I) dimensions of a smallest rectangular bounding box that completely contains the nucleus. The 3D dimensions of the bounding boxes were measured in both "AC-PC native space" and "AC-PC normalized space". To take advantage of the volumetric segmentation, we also measured the volume of the nuclei in mm 3 . Unfortunately, it was not possible to compare this value to a corresponding metric from the Talairach atlas. Both of the size measurements are detailed in Table I, along with the corresponding available metrics obtained from the Talairach atlas.

Table I goes here

From Table I, it is shown that the mean nuclei sizes are smaller in the "AC-PC normalized space" than the "AC-PC native space" due to the AC-PC distance normalization.

However, except the supero-inferior and antero-posterior dimensions of the STN, the STN sizes measured from the Talairach atlas are on average larger than the cohort in both coordinate spaces. Through paired t-tests, except the A-P dimensions of the left and right RN in the "AC-PC normalized space", the M-L dimension of the left and right STN in the "AC-PC native space", and the A-P dimension of the right SN in the "AC-PC native space", the 3D extents of the nuclei are significantly different from the Talairach atlas.

The second main factor of anatomical variability is position. To study the position variability, the analysis was only conducted in "AC-PC normalized space". Since in DBS planning, the MC point is often used to infer the location of the STN, the distances between the nuclei's center of mass (COM) and the MC point in the M-L, A-P and S-I directions are reported in Table II. Here, we see that on average, the left STN is 10.08 mm lateral, 0.94 mm posterior, and 5.00 mm inferior to the MC point while the right STN is 10.18 mm lateral, 0.71 mm posterior, and 5.06 mm inferior to the MC point. However, the center of the STN is 12 mm lateral, 2 mm posterior, and 4 mm inferior to the MC point on the Talairach atlas [START_REF] Ashkan | Variability of the subthalamic nucleus: the case for direct MRI guided targeting[END_REF]. Our measurements do not correspond with those from the standard atlas, and the average STN position is more medial, more anterior, and more inferior to that in the Talairach atlas.

While the previous report [START_REF] Richter | Determining the position and size of the subthalamic nucleus based on magnetic resonance imaging results in patients with advanced Parkinson disease[END_REF]) also attempts to utilize the COM to measure the relative distances between the nuclei and the MC point, it is possible that this disagreement may be due to the fact that the COM of the nucleus is difficult to estimate on the 2D atlas. For the same reason, our measurements of the other nuclei locations in terms of the COM relative to the MC point were not compared with the atlas. Instead, we measured the location for geometric center of the "bounding box" of each nucleus relative to the MC point, which is more easily quantified objectively. From Table III, it is demonstrated that such definition for the position of the STN is again significantly different (p<0.05) between the cohort and the Talairach atlas.

Also, the positions of the right RN posterior and lateral to the MC, that of the left and right RN inferior to the MC, and that of the SN lateral and posterior to the MC are also significantly different from the Talairach atlas [START_REF] Talairach | Co-planar stereotaxic atlas of the human brain : 3-dimensional proportional system : an approach to cerebral imaging[END_REF].

Table II goes here Table III goes here

PCA-based variability analysis

The experiments above give an idea of the positions and extents of the STN, RN and SN, but don't give any insight into how the shapes of these structures vary in the PD population. To address this limitation, PCA analysis was performed in "AC-PC normalized space" for each structure with the left and right side analyzed separately. The PCA analysis decomposes the anatomical variability into ranked variation modes, and thus allows a more intuitive view on the nature of the variability. For all structures of interest, the first 5 and the first 10 components account for 95-98% and roughly 99% of the total variability, respectively. The eigenvalues of the first 10 components for all structures are illustrated as bar plots in Fig. 6.

Through investigating the ordered eigenvalues of the structures using paired t-tests, the eigenvalues of the RN are significantly lower (p<0.05) than those of the SN and STN on the respective side. This implies that in terms of variability, the RN is less variable than the SN and STN. To demonstrate the variation modes, the first 6 most prominent shape variations for all structures are shown from Fig. 7 to Fig. 9, with the degree of 3 folds of standard deviation (negative and positive) from the mean shape. Through the evolution between the two extreme shape variations (negative and positive deviations) for each mode, we can identify the specific type of shape variation that is represented by a mode. In the same figures, the mean shapes are overlaid on the average of all 33 AC-PC normalized T2w MRIs, and they, not surprisingly, fit the averaged T2w MRI after AC-PC normalization. However, owing to the structural variability remaining after the linear AC-PC scaling alignment, the nuclei in the averaged T2w MRI appear blurry.

In general, for each structure, the first 3 shape variations are mostly related to the spatial displacements while the later principal components account for relatively more subtle global and local shape variations. More specifically, for the RN, the A-P position displacement appears most significant, and the M-L and S-I displacements are secondary. It is interesting that for the RN, the second and third mode appears very similar in nature, but the direction of the displacement in space varies. For the SN and STN, a mix of A-P and S-I position difference is the most dominant. However, for the SN, the importance of S-I and M-L displacements come in the second and third while for the STN, after the first mode, the contribution of the M-L displacement is more than the S-I displacement. Overall, within the principal component representation of the position variability, the variability often involves displacements in three principal directions (medio-lateral, infero-superior, and antero-posterior), but a prevailing trend in one or two directions can still be easily identified.

An additional observation is that while on average the variation modes appear similar between the left and right side, the symmetry does not hold all the time. Example of this phenomenon can be seen when comparing bilaterally the third modes of the SN and STN, as well as in the later principal component representations. Despite the symmetry assumption in many atlases, it is not surprising to discover asymmetric anatomical variability in these nuclei as in many other structures in the human brain.

Table IV goes here

Discussion

Label fusion

For the purpose of nuclei segmentation, we employed the majority-voting label-fusion techniques despite that a number of more recent and sophisticated label-fusion techniques [START_REF] Artaechevarria | Combination strategies in multiatlas image segmentation: application to brain MR data[END_REF][START_REF] Chen | Evaluation of multiple-atlas-based strategies for segmentation of the thyroid gland in head and neck CT images for IMRT[END_REF][START_REF] Isgum | Multi-atlasbased segmentation with local decision fusion--application to cardiac and aortic segmentation in CT scans[END_REF][START_REF] Coupe | Patch-based segmentation using expert priors: application to hippocampus and ventricle segmentation[END_REF][START_REF] Wang | Optimal weights for multi-atlas label fusion[END_REF][START_REF] Wang | Multi-Atlas Segmentation with Joint Label Fusion[END_REF][START_REF] Warfield | Simultaneous truth and performance level estimation (STAPLE): an algorithm for the validation of image segmentation[END_REF] have demonstrated superior performance by exploring statistical behaviors of the images and atlases. Two reasons contribute to our selection of segmentation method. Firstly, the relatively simple majority-voting segmentation has shown robust performance [START_REF] Aljabar | Multi-atlas based segmentation of brain images: atlas selection and its effect on accuracy[END_REF][START_REF] Collins | Towards accurate, automatic segmentation of the hippocampus and amygdala from MRI by augmenting ANIMAL with a template library and label fusion[END_REF][START_REF] Heckemann | Automatic anatomical brain MRI segmentation combining label propagation and decision fusion[END_REF][START_REF] Rohlfing | Evaluation of atlas selection strategies for atlas-based image segmentation with application to confocal microscopy images of bee brains[END_REF][START_REF] Rohlfing | Shape-based averaging[END_REF]. Secondly, a complete comparison of these new methods is not available, and the performance of the more sophisticated segmentation techniques depends on the successful re-implementation. It is true that majority-voting labelfusion techniques have never been used in segmenting midbrain nuclei. However, a comparison of different algorithms is out of the scope of this paper, and thus we will not include it here. By visual inspection, the selected segmentation method demonstrates satisfactory results according to the manual segmentation protocols adopted by the neurosurgeon who labeled the relevant structures for the atlas library. From quantitative validation, we have achieved fairly satisfactory results for such small structures, compared with previous publications in terms of kappa [START_REF] Haegelen | Automated segmentation of basal ganglia and deep brain structures in MRI of Parkinson's disease[END_REF] and the Euclidean distance between COMs [START_REF] Brunenberg | Magnetic resonance imaging techniques for visualization of the subthalamic nucleus[END_REF]. In this study, to further ensure the segmentation accuracy, T2-T2 nonlinear registration was used instead of the more common T1-T1 registration seen in DBS applications.

Stereotactic spaces

The selection of coordinate space may determine the final results of the morphological study.

With different coordinate space and volume normalization strategy, the analysis results can vary.

While both are employed in DBS planning, the Schaltenbrand atlas [START_REF] Schaltenbrand | Atlas for stereotaxy of the human brain[END_REF] is more commonly seen in the previous studies of midbrain nuclei anatomical variability [START_REF] Ashkan | Variability of the subthalamic nucleus: the case for direct MRI guided targeting[END_REF][START_REF] Castro | A cross validation study of deep brain stimulation targeting: from experts to atlas-based, segmentation-based and automatic registration algorithms[END_REF][START_REF] Daniluk | Assessment of the variability in the anatomical position and size of the subthalamic nucleus among patients with advanced Parkinson's disease using magnetic resonance imaging[END_REF][START_REF] Richter | Determining the position and size of the subthalamic nucleus based on magnetic resonance imaging results in patients with advanced Parkinson disease[END_REF] than the Talairach atlas [START_REF] Talairach | Co-planar stereotaxic atlas of the human brain : 3-dimensional proportional system : an approach to cerebral imaging[END_REF]. However, we referred to the latter for our analysis. In contrast to the Talairach atlas, which only contains one healthy aged female subject without Parkinson's disease, the Schaltenbrand atlas was created with different subjects for different sections. To obtain more consistent dimension measurements, the Talairach atlas may be a better choice. Furthermore, the definitions of AC-PC line and thus the MC point in these two atlases differ [START_REF] Weiss | Clinical brain MR imaging prescriptions in Talairach space: technologist-and computer-driven methods[END_REF], making it difficult to simultaneously compare the two atlases to the measurements of the cohort in the same coordinate space. Besides the histologyderived stereotactic spaces, there also exist MRI-derived stereotactic spaces, such as the ICBM152 [START_REF] Fonov | Unbiased average age-appropriate atlases for pediatric studies[END_REF] and MNI305 spaces [START_REF] Collins | Automatic 3D intersubject registration of MR volumetric data in standardized Talairach space[END_REF]. These newer stereotactic spaces resemble the brain orientation of the Talairach space, and the stereotactic space re-alignment for any upcoming subject is achieved fully automatically. Variability analysis [START_REF] Forstmann | Cortico-subthalamic white matter tract strength predicts interindividual efficacy in stopping a motor response[END_REF] has also been previously conducted using such stereotactic space. Yet, often due to the availability of the software and the long history of successful applications in neurological studies, the histology-derived atlases [START_REF] Schaltenbrand | Atlas for stereotaxy of the human brain[END_REF][START_REF] Talairach | Co-planar stereotaxic atlas of the human brain : 3-dimensional proportional system : an approach to cerebral imaging[END_REF] are still more commonly employed.

Morphometric variability

While the T2w MRI is still the most common way to image the midbrain nuclei in the clinics, as the medical imaging technology advances, there have been a number of MRI methods [START_REF] Brunenberg | Magnetic resonance imaging techniques for visualization of the subthalamic nucleus[END_REF][START_REF] O'gorman | Optimal MRI methods for direct stereotactic targeting of the subthalamic nucleus and globus pallidus[END_REF][START_REF] Xiao | Multicontrast multiecho FLASH MRI for targeting the subthalamic nucleus[END_REF] designed to directly visualize the STN. Consequently, this raised the debate of whether direct targeting using these MRI methods is superior to the classical landmark-based indirect targeting method. On one hand, some studies [START_REF] Richter | Determining the position and size of the subthalamic nucleus based on magnetic resonance imaging results in patients with advanced Parkinson disease[END_REF][START_REF] Zhu | Magnetic resonance imaging-based morphometry and landmark correlation of basal ganglia nuclei[END_REF] support the use of direct visualization; on the other hand, a number of studies [START_REF] Acar | Safety of anterior commissureposterior commissure-based target calculation of the subthalamic nucleus in functional stereotactic procedures[END_REF][START_REF] Guehl | Statistical determination of the optimal subthalamic nucleus stimulation site in patients with Parkinson disease[END_REF][START_REF] Lanotte | Deep brain stimulation of the subthalamic nucleus: anatomical, neurophysiological, and outcome correlations with the effects of stimulation[END_REF][START_REF] Mcclelland | Subthalamic stimulation for Parkinson disease: determination of electrode location necessary for clinical efficacy[END_REF] have reported successful application of indirect targeting. As a result, an investigation is still necessary, especially with better imaging methods and high field scanners becoming increasingly available.

Similar to a previous study [START_REF] Richter | Determining the position and size of the subthalamic nucleus based on magnetic resonance imaging results in patients with advanced Parkinson disease[END_REF], the measured STN size is smaller than that of the Talairach atlas [START_REF] Talairach | Co-planar stereotaxic atlas of the human brain : 3-dimensional proportional system : an approach to cerebral imaging[END_REF] in the M-L dimension, but larger in the I-S and A-P dimensions. While [START_REF] Richter | Determining the position and size of the subthalamic nucleus based on magnetic resonance imaging results in patients with advanced Parkinson disease[END_REF] reported that the position of the STN is more posterior and lateral on the images than the Talairach atlas, our study shows that the STN is more anterior, lateral and inferior to the atlas. Unfortunately, most previous studies only focused on the analysis of the STN, and their AC-PC line alignment may differ from the method described in this article, especially when using the Schaltenbrand atlas [START_REF] Schaltenbrand | Atlas for stereotaxy of the human brain[END_REF] as the reference. It is difficult to compare our results, and especially those of the RN and SN, to previous publications. Nevertheless, the additional measurements of the RN and SN, and the comparison to the Talairach atlas with a larger population than in [START_REF] Richter | Determining the position and size of the subthalamic nucleus based on magnetic resonance imaging results in patients with advanced Parkinson disease[END_REF] provide valuable complementary knowledge to the application of atlases.

As far as the cohort is concerned, the Talairach atlas [START_REF] Talairach | Co-planar stereotaxic atlas of the human brain : 3-dimensional proportional system : an approach to cerebral imaging[END_REF] does not match our measurements. One possible reason for the disagreement is that the subject for atlasing lacks of sufficient representativeness of the population under study (i.e. PD). This is a universal issue for all single-subject derived atlases. In this sense, unbiased anatomical atlases [START_REF] Fonov | Unbiased average age-appropriate atlases for pediatric studies[END_REF][START_REF] Haegelen | Automated segmentation of basal ganglia and deep brain structures in MRI of Parkinson's disease[END_REF] that represent the averaged anatomical features of the population of interest (i.e. advanced PD patients) may be more desirable as both aging and disease progression may alter the anatomy due to global and local tissue degeneration and atrophy. Whether targeting the STN with such unbiased atlas is superior than direct visualization will require further evaluation beyond the scope of this paper. At the moment, the evidence presented here supports the use of direct targeting method over the landmark-based indirect targeting based on the Talairach atlas.

Another issue related to the analysis is image distortion. For the image protocols involved, a distortion study was conducted using a LEGO phantom, and the procedure is detailed in [START_REF] Caramanos | Gradient distortions in MRI: characterizing and correcting for their effects on SIENA-generated measures of brain volume change[END_REF]. Through the analysis, an average distortion below 0.5 mm was measured within the field of view for both T1w and T2w MRI protocols presented. For the central region, where our analysis was conducted, the distortion is close to 0.2 mm. Compared with the magnitude of our measurements, this will not likely influence our final conclusion that the metrics obtained from the cohort differ from the Talairach atlas.

In this study, PCA offers a new perspective on the issue of anatomical variability of the midbrain nuclei compared with the conventional coordinate analysis. When correlated with clinical information (UPDRS III scores), one can identify specific types of shape variation that are possibly related to the disease progression. In addition, the intuitive nature of the analysis results allows visual identification of the subtle morphometric changes possibly due to disease progression. With the help of PCA, we discovered the lateral displacement of the nuclei with disease progression on the right side likely due to the enlargement of the third ventricle [START_REF] Daniluk | Assessment of the variability in the anatomical position and size of the subthalamic nucleus among patients with advanced Parkinson's disease using magnetic resonance imaging[END_REF], but the asymmetry of this discovery requires further investigation. The off-Dopa UPDRS III scores were only shown to be related the STN with size reduction on the left side and position alteration on the right side. The difference between the on-and off-Dopa results is very likely due to the interplay between the structure changes and the influence of external dopamine supply. It should also be noted that the morphometric alterations of the nucleus for PD should be a result of shape changes of both the nucleus itself and the surrounding structures (i.e. ventricle enlargement and brain atrophy). The PCA analysis may offer a potential method for disease prediction of Parkinson's disease. However, to better understand and further confirm this correlation, a larger patient population is required. For this study, only the motor-function-related UPDRS III scores were used because among all the UPDRS assessment sub-scores, this metric is obtained most objectively by the neurologist while the rest were self-evaluated by the patients, and the motor function disability is more prominent than other cognitive and psychological symptoms for PD.

Conclusion

In conclusion, we analyzed the sizes and positions of the STN and the adjacent RN and SN by using label-fusion techniques to automatically segment structures from high resolution 3 Tesla FSE T2w MRI. From the analysis, significant differences were discovered between the studied cohort and the Talairach atlas, and the discovery supports the use of MRI-based direct targeting method for locating the SN, RN and STN. In addition to conventional coordinate measurement, we employed PCA analysis to obtain more intuitive and detailed information regarding the morphometric variability of the nuclei, and correlations between the PCA components and UPDRS III scores were found.

Table legends

Table I. Measurements of nuclei sizes as maximum extents in the medio-lateral, anteroposterior, supero-inferior dimensions, as well as the nuclei volumes measured in mm 3 . Note that each value is shown as mean ± standard deviation. Here, the measurements in "AC-PC native space" are shown in black fonts while those in "AC-PC normalized space" are shown in italic fonts with underlines. The measurements from the Talairach atlas are listed in the parentheses.

Table II. Measured distances (mean± standard deviation) between the COM of the nuclei and the middle commissure point in the left-right, anterior-posterior, and superior-inferior directions.

Table III. Measured distances (mean± standard deviation) between the geometry centers of the nuclei and the middle commissure point in the left-right, anterior-posterior, and superior-inferior directions. An asterisk ("*") indicates that the measurements disagree with those from the Talairach atlas with statistical significance (p<0.05).

Table IV. Table of variation

  Therefore, for a dataset of N patients, the distance transform function of patient i and structure L is denoted as , where i = {1,2, .., N} and L = {Left RN, Right RN, Left STN, Right STN, Left SN, Right SN}. Given the average level set function , eigenvalues and the corresponding orthonormal eigenvectors (or principal components) are found for the matrix , where and . This is achieved by decomposing K so that with being the diagonal matrix containing the eigenvalues and U being the orthonormal matrix that has the corresponding eigenvectors. Note that here, the eigenvectors are arranged in the descending order. Given a shape ψ L , it can be represented as a linear combination of PCA components, as where is the mean level-set function, is the principal components, and is the reconstruction coefficient of . By changing the principal components and their associated reconstruction coefficients, different variants of the structural shapes can be obtained. Two perspectives were explored with PCA in the "AC-PC normalized space". Firstly, the specific variation type with respect to each principal component (or variation mode in the context of shape analysis) was examined. This is achieved by acquiring the level set function , which represents the positive (and negative) 3-fold standard deviation for the shape variation of the jth variation mode . The specific type of shape variation is visually identified from comparing the binary shapes obtained by thresholding the level-set function and with the value of 0.8. Secondly, the relationship between the variation modes (in the form of level-set) and the disease progression was experimentally explored. Here, the Pearson correlation between the reconstruction coefficient of the jth variation mode and the UPDRS-III scores while controlling for sex and age was computed for each structure under study, and the results with statistical significance (p<0.05) were reported.

Figure

  Figure 6 goes here

Figure 1 .

 1 Figure 1. Example of T1w and T2w MRI images from one Parkinson's disease patient in the study. From left to right: A. a coronal slice of T1w MRI cutting through the region of the red nucleus and substantia nigra; B. a sagittal slice of T1w MRI cutting through the region of the red nucleus and substantia nigra; C. a coronal slice of T2w MRI corresponding to A; and D. a sagittal section of the T2w MRI corresponding to B. Note that the T2w acquisition does not cover the entire brain.

Figure 2 .

 2 Figure 2. Demonstration of majority-voting label-fusion procedure for a Parkinson's disease patient, whose brain MRIs are in the "AC-PC normalized space".

Figure 3 .

 3 Figure 3. Structural segmentation and distance transformation. A. segmentation of the left red nucleus overlaid on the coronal slice of the T2w MRI; B. distance transformation of the left red nucleus label with the color map shown on the right.

Figure 4 .

 4 Figure 4. Demonstration of automatic segmentation results with one PD subject in MNI305 space. First column (from top to bottom): T2w MRI slices of the subject in axial, sagittal and coronal views; Second column: automatic segmentation results in the corresponding view of the first column; Third column: manual segmentation results in the corresponding view of the first column; Fourth column: 3D volumetric rendering of manual and automatic segmentation. Here the label colors are shown as: green = left STN, yellow = right STN, red = left SN, white = right SN, purple = left RN, and blue = right RN.

Figure 5 .

 5 Figure 5. Results of automatic segmentation validation as boxplots. From top to bottom: kappa overlapping coefficient, Euclidean distance between center of mass (COM), and 95% Hausdorff distance. The value of mean ± standard deviation for each result is shown beside the corresponding boxplot.

Figure 6 .

 6 Figure 6. Bar plot showing the eigenvalues of the first 10 principal components from the PCA analysis of each nucleus.

Figure 7 .

 7 Figure 7. PCA analysis results for the left (top three rows) and right (bottom three rows) RNshowing effects of the first 6 variation modes and the mean shape overlaid on an average of AC-PC normalized T2w MRIs. For each variation mode shown, the cyan color label represents mean shape minus 3 folds of standard deviation while the red color label represents mean shape plus 3 folds of standard deviation. Note that in each group of figures demonstrating the left or right RN, the cross-hair cursor is placed at the same position, and the three rows show the axial, sagittal, and coronal views (from top to bottom) of the nucleus.

Figure 8 .

 8 Figure 8. PCA analysis results for the left (top three rows) and right (bottom three rows) SNshowing effects of the first 6 variation modes and the mean shape overlaid on an average of AC-PC normalized T2w MRIs. For each variation mode shown, the cyan color label represents mean shape minus 3 folds of standard deviation while the red color label represents mean shape plus 3 folds of standard deviation. Note that in each group of figures demonstrating the left or right SN, the cross-hair cursor is placed at the same position, and the three rows show the axial, sagittal, and coronal views (from top to bottom) of the nucleus.

Figure 9 .

 9 Figure 9. PCA analysis results for the left (top three rows) and right (bottom three rows) STNshowing effects of the first 6 variation modes and the mean shape overlaid on an average of AC-PC normalized T2w MRIs. For each variation mode shown, the cyan color label represents mean shape minus 3 folds of standard deviation while the red color label represents mean shape plus 3 folds of standard deviation. Note that in each group of figures demonstrating the left or right STN, the cross-hair cursor is placed at the same position, and the three rows show the axial, sagittal, and coronal views (from top to bottom) of the nucleus.

  modes that have statistically significant (p<0.05) correlations with on-and off-Dopa UPDRS III scores. Note that the value of correlation is shown inside the parenthesis after the respective variation mode number. Here only the first 10 variation modes are shown in the table.

Figure 1 Figure 2 Figure

 12 Figure 1

Table II

 II

	Nucleus		Lateral to MC (mm)	Posterior to MC (mm)	Inferior to MC (mm)
	Left RN		4.85 ± 0.51 (4.75)	7.30 ± 1.09 (7.5)	4.95 ± 0.78 (5.25)*
	Right RN	4.92 ± 0.55 (4.75)*	7.17 ± 0.92 (7.5)*	4.92 ± 0.77 (5.25)*
	Left STN	9.80 ± 1.01 (9.50)	2.14 ± 1.10 (1.25)*	4.97 ± 1.01 (3.75)*
	Right STN	9.83 ± 0.96 (9.50)*	1.96 ± 1.05 (1.25)*	4.97 ± 0.92 (3.75)*
	Left SN		9.16 ± 0.89 (9.00)	4.83 ± 1.36 (6.00)*	7.57 ± 0.88 (8.25)*
				± 0.79 (9.00)	4.70 ± 1.29 (6.00)*	7.67 ± 1.03 (8.25)*
				Table III -new
	Nucleus		On-Dopa UPDRS III On-Dopa UPDRS III	Off-Dopa UPDRS III Off-Dopa UPDRS III
	Left RN
	Right RN	Mode 3 (0.35)	Mode 4 (0.55)	Mode 1 (0.34) Mode 1 (0.34)
	Left STN				Mode 7 (0.45) Mode 7 (0.45)
	Right STN	Mode 2 (0.43)		Mode 1 (0.36) Mode 1 (0.36)
	Left SN
	Right SN	Mode 3 (0.38)
					-new

Table IV - new

 IVnew