A synchronous control method of a biopotential signal acquisition system with different interface timing and an acquisition circuit

Abstract

The present invention provides a synchronous control method for a biopotential signal acquisition system with different interface timings and an acquisition circuit, and belongs to the technical field of biopotential signal acquisition. The acquisition system includes a controller, first and second timing control logics, and first and second biopotential signal acquisition circuits. The control method first generates a sampling trigger pulse signal sequence with equal intervals by the controller. When the trigger pulse signal arrives, the controller sends a set of control command sequences required by each biopotential signal acquisition circuit in parallel to control it to complete the actions of all channels in the circuit, and then waits for the next sampling trigger pulse signal to arrive and repeat the above workflow. The present invention can control a synchronous control method for sampling according to the required sampling frequency for multiple biopotential signal acquisition circuits with different interfaces, number of acquisition channels, sampling time and additional functions; it is also suitable for multi-channel biopotential signal acquisition circuits that use only one analog-to-digital converter for time-division multiplexing sampling.

Description

Technical Field

[0001] The present invention belongs to the technical field of biopotential signal acquisition, and relates to a different-interface-sequential biopotential signal acquisition system and a different-interface-sequential biopotential signal acquisition circuit synchronization control method. Background Art

[0002] The electrophysiological signals generated by human cells or tissues are the main way for the nervous system to communicate. They contain a wealth of information about physiology, disease, and mental state. The recording of bioelectric signals can be used to effectively monitor the state of the human body and is also the basis for building a human-computer interaction highway. Common recordings of biopotential signals include direct recording of neuronal action potentials in the cerebral cortex; local field potential signals (LFP) recorded from the brain or cerebral blood vessels; electroencephalograms (ECoG) measured from the surface of the cerebral cortex; electroencephalograms (EEG) measured from the scalp; electromyographic signals (EMG) measured from within or near the muscles, and electrocardiograms (ECG) measured from the heart or near the heart.

[0003] The biopotential signal acquisition system usually includes a biopotential signal collector and special software running on a computer. The biopotential signal collector generally includes electrodes, electrode interfaces, signal amplifiers, analog-to-digital converters (ADCs), microcontrollers, data communication interfaces, etc. In brain science related research, it is often necessary to apply electrical stimulation to the cerebral cortex to obtain induced EEG signals, so an EEG signal acquisition system with electrical stimulation function has emerged. In order to obtain EEG signals from multiple brain regions more comprehensively, or to more finely distinguish the areas of cerebral cortical activity, it is necessary to increase the number of electrode channels of the EEG acquisition system, and the number of channels can be as high as 1000 or more. Increasing the number of channels will multiply the number of EEG signal amplifiers and analog-to-digital converters, and proportionally increase the system volume. With the advancement of integrated circuit technology, it is possible to integrate multi-channel EEG signal amplifiers, analog-to-digital converters and other parts into a dedicated EEG acquisition circuit, or to integrate multi-channel EEG signal amplifiers, analog-to-digital converters, and electrical stimulation circuits into a dedicated EEG acquisition circuit with electrical stimulation function. The application of multi-channel EEG acquisition circuits has greatly improved the integration of multi-channel EEG acquisition systems.

[0004] Biopotential signal acquisition circuits with different interface timings generally use different interface clock frequencies, different communication timings, different numbers of acquisition channels, different single-channel sampling times, and different additional functions, while existing biopotential signal collectors are only suitable for the same type of EEG acquisition circuits, such as a biopotential signal collector composed of multiple biopotential signal acquisition circuits with only acquisition functions and a microcontroller. The number of channels of this biopotential signal collector can be as many as more than 1,000, but it cannot perform electrical stimulation. In addition, there are also biopotential signal collectors with electrical stimulation functions that are composed of multiple biopotential signal acquisition circuits with electrical stimulation functions and circuits such as microcontrollers. However, this biopotential signal collector has a small number of channels, generally only more than 100. In order to meet the application requirements of both being able to perform electrical stimulation and having enough acquisition channels, the biopotential signal acquisition circuit with electrical stimulation function and the biopotential signal acquisition circuit with only acquisition function can be integrated into one biopotential signal collector. However, the biopotential signal acquisition circuits with different interface timings have different interfaces, different commands, and different external clock frequencies. How to make the biopotential signal acquisition circuits with different interface timings perform synchronous sampling at the same sampling frequency while taking into account the electrical stimulation function has become a technical problem that needs to be solved urgently. Summary of the invention

[0005] In order to solve the above technical problems, the present invention provides a synchronous control method involving a different interface timing biopotential signal acquisition system and a different interface timing biopotential signal acquisition circuit, and the synchronous control method includes two schemes.

[0006] The technical solution adopted by the present invention is:

[0007] A different-interface sequential biopotential signal acquisition system, the acquisition system comprising a controller, a first sequential control logic, a second sequential control logic, a first biopotential signal acquisition circuit, and a second biopotential signal acquisition circuit.

[0008] The first biopotential signal acquisition circuit and the second biopotential signal acquisition circuit have different interface timings;

[0009] The controller is used to generate a sampling trigger pulse signal, and the first timing control logic is used to control the first biopotential signal acquisition circuit to perform a first action according to a first control command sequence during the period of the sampling trigger pulse signal, and the first action includes an acquisition action and an electrical stimulation action; the second timing control logic is used to control the second biopotential signal acquisition circuit to perform a second action according to a second control command sequence during the period of the sampling trigger pulse signal, and the second action includes an acquisition action.

[0010] Further, the command in the first control command sequence for controlling the first biopotential signal acquisition circuit to perform an acquisition action is executed first; and / or, the command in the second control command sequence for controlling the second biopotential signal acquisition circuit to perform an acquisition action is executed first.

[0011] Furthermore, the first biopotential signal acquisition circuit includes multiple first interfaces, and the first biopotential signal acquisition circuit performs acquisition actions and electrical stimulation actions on the first interfaces in sequence according to a first control command sequence; and / or the second biopotential signal acquisition circuit includes multiple second interfaces, and the second biopotential signal acquisition circuit performs acquisition actions on the second interfaces in sequence according to a second control command sequence.

[0012] Furthermore, the time interval of the sampling trigger pulse signal is T s The time required for each of the m first biopotential signal acquisition circuits and the nm second biopotential signal acquisition circuits to complete all channels is T i (i is 1 to n, n, m are natural numbers, and n>m), where T g For T1, T2, T3, …, T i The maximum value, and T s Greater than T g .

[0013] A synchronous control method for different interface timing biopotential signal acquisition circuits is implemented based on the above acquisition system and includes the following two schemes:

[0014] The specific steps of Solution 1 are as follows:

[0015] (1) The controller generates a continuous sequence of sampling trigger pulse signals with the same time interval.

[0016] (2) When the sampling trigger pulse signal is valid (i.e., during the sampling trigger pulse signal), the controller immediately sends a set of control command sequences that are compatible with the timing and functions of the respective interfaces of the biopotential signal acquisition circuits to all biopotential signal acquisition circuits in parallel. After each biopotential signal acquisition circuit receives the set of control command sequences for itself, it will control itself to complete one-time sampling of all channels on the circuit and other additional functions. In this step, the sampling command is triggered by the controller to trigger the timing logic, and the timing logic automatically sends sampling commands to each channel in sequence. The electrical stimulation command is dynamically generated by the controller based on the electrical stimulation waveform sequence data, and the timing logic is responsible for reading and sending it in the additional function time slot. (3) After each biopotential signal acquisition circuit completes one-time sampling of all channels on the circuit and other additional functions, it enters a waiting state until the next sampling trigger pulse signal arrives, and then repeats step (2).

[0017] The specific steps of Option 2 are as follows:

[0018] (1) The controller generates a sampling trigger pulse signal.

[0019] (2) The sampling trigger pulse signal triggers the timing control logic to simultaneously send a corresponding control command sequence to the corresponding n biopotential signal acquisition circuits.

[0020] (3) Each biopotential signal acquisition circuit controls all channels thereon to complete actions according to the received control command sequence, wherein the actions include acquisition actions.

[0021] (4) Each biopotential signal acquisition circuit enters a waiting state after all channels on it complete the action, and the interval of the sampling trigger pulse signal is greater than the time required to complete step (2) and step (3). Furthermore, the frequency of the sampling trigger pulse signal is the required sampling frequency, and the sampling frequency of each channel of all biopotential signal acquisition circuits in the biopotential signal collector is the same as the sampling trigger pulse signal frequency. The sampling frequency is configured by a computer according to the requirements of different application scenarios. The sampling of the present invention is a time-division multiplexing method. After each trigger pulse, each ch is sampled only once. Therefore, if any ch is taken out separately, its nominal sampling frequency is the same as the trigger frequency, that is, the required sampling frequency.

[0022] Furthermore, the additional functions in both schemes include electrical stimulation function.

[0023] Furthermore, the controller ensures that the biopotential signal acquisition circuits of the same interface timing receive the set of control command sequences at the same time, and the biopotential signal sampling data is outputted while receiving the set of control command sequences. In the present invention: the sampling result of the first sampling command is outputted while the third command enters, and so on. Because there are more than two additional commands at the end, the sampling results of the last two sampling commands can also be obtained within this trigger cycle. In short, a set of control command sequences sent by each sampling trigger can obtain the sampling data of all required channels.

[0024] Furthermore, the time interval (i.e., sampling period) of the sampling trigger pulse signal is Ts; the time required for each biopotential signal acquisition circuit to complete one sampling of all channels and additional functions is Ti (i is 1 to n, corresponding to the serial number of each biopotential signal acquisition circuit, where n is the number of biopotential signal acquisition circuits), and the largest one in Ti is recorded as Tg. In order not to miss any sampling trigger pulse, it is necessary to ensure that Ts is always greater than Tg.

[0025] The beneficial effects of the technical solution provided by the present invention are:

[0026] The present invention realizes synchronous control of biopotential signal acquisition circuits with different interface clock frequencies, different interface formats, different acquisition channel numbers, different single-channel sampling times, and different additional functions that require external clocks; one sampling trigger pulse signal triggers all channels to sample once, and changing the channel sampling frequency only requires changing the frequency of the sampling trigger pulse signal (that is, the time interval of the sampling trigger pulse signal sequence), and a single channel on the controlled biopotential signal acquisition circuit always completes sampling with its shortest sampling time (the same as the transmission time of the set of control command sequences), and the sampling time slots of multiple channels on a single biopotential signal acquisition circuit start from when the sampling trigger pulse signal is valid, and are arranged continuously and closely. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 A schematic diagram of a biopotential signal collector system for synchronous sampling control using different interface timing biopotential signal acquisition circuits provided by an embodiment of the present invention (not including all functional modules).

[0028] Figure 2 A timing diagram of a sampling trigger pulse signal and a control command sequence provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0029] The technical solution of the present invention will be clearly and completely described below in conjunction with the accompanying drawings and embodiments. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0030] The embodiment of the present invention provides a synchronous control method of biopotential signal acquisition circuits with different interface timings and a biopotential signal acquisition system.

[0031] Figure 1 Schematic diagram of a biopotential signal collector system for synchronous sampling control using two different interface timing biopotential signal acquisition circuits provided in an embodiment of the present invention. The biopotential signal collector system includes a controller, a first subsystem 1 and a second subsystem 2. Among them, the first subsystem 1 includes m first biopotential signal acquisition circuits, and m is a natural number. That is, the first subsystem 1 includes first biopotential signal acquisition circuits 1 to first biopotential signal acquisition circuits m. Further, each first biopotential signal acquisition circuit includes multiple first electrode interfaces. In addition to the acquisition function, each first electrode interface also has a first additional function. In this embodiment, the first additional function of the first electrode interface is an electrical stimulation function. Therefore, the first subsystem 1 has electrical stimulation and acquisition functions, and the first subsystem 1 is therefore also called an electrical stimulation and acquisition subsystem. In addition, the first subsystem 1 also includes a first timing control logic. The first timing control logic is used to simultaneously issue a first control command sequence to all first biopotential signal acquisition circuits after being triggered by the controller. The first control command sequence includes a first sampling command and a first additional command. In this embodiment, see Figure 2 , the first control command sequence is interface timing 1. The first sampling command includes all first electrode interface sampling commands arranged in sequence, namely the first first electrode interface sampling command (ch0 sampling command), the second first electrode interface sampling command (ch1 sampling command) until the last first electrode interface sampling command. The first additional command includes an electrical stimulation command. The specific parameters of the electrical stimulation can be dynamically generated by the controller according to the electrical stimulation waveform sequence data, and the first timing control logic reads the electrical stimulation parameters before issuing the electrical stimulation command, and sends them to each first biopotential signal acquisition circuit together with the electrical stimulation command. In addition to the electrical stimulation command, the first additional command may also include other additional commands, such as a clear limit state command, an output sampling data command, an output execution result command, and the like.

[0032] Similarly, the second subsystem 2 includes nm second biopotential signal acquisition circuits, where n is a natural number greater than m. That is, the second subsystem 2 includes second biopotential signal acquisition circuits 1 to second biopotential signal acquisition circuits nm. Further, each second biopotential signal acquisition circuit includes multiple second electrode interfaces, and each second electrode interface has a collection function. In addition, each second electrode interface may also have a second additional function, and the first additional function and the second additional function are not completely the same. In this embodiment, the second electrode interface only has an acquisition function. Therefore, the second subsystem 2 only has an acquisition function, and the second subsystem 2 is therefore also called a single acquisition subsystem. In addition, the second subsystem 2 also includes a second timing control logic. The second timing control logic is used to simultaneously issue a second control command sequence to all second biopotential signal acquisition circuits after being triggered by the controller. The second control command sequence includes a sampling command, and a second additional command, and the second additional command is not completely the same as the first additional command. In this embodiment, see Figure 2 , the second control command sequence is interface timing 2. The second sampling command includes all the second electrode interface sampling commands arranged in sequence, that is, the first second electrode interface sampling command (ch0 sampling command), the second second electrode interface sampling command (ch1 sampling command) until the last second electrode interface sampling command. In this embodiment, since only the second electrode interface is required to perform the sampling action, the second additional command includes the output sampling data command, the dummy command that does not affect the working state, such as the register read action, etc.

[0033] The number of electrode interfaces in the biopotential signal acquisition circuit contained in each subsystem is not limited. For example, in this embodiment, each first biopotential signal acquisition circuit in the electrical stimulation and acquisition subsystem includes 16 electrode interfaces, and each second biopotential signal acquisition circuit in the single acquisition subsystem includes 64 electrode interfaces. Therefore, the first biopotential signal acquisition circuit and the second biopotential signal acquisition circuit have different numbers of electrode interfaces and different execution actions of the electrode interfaces, resulting in different times required for the first biopotential signal acquisition circuit and the second biopotential signal acquisition circuit to complete the action.

[0034] The present invention has no particular restrictions on the types of the controller, the first timing control logic, and the second timing control logic. The controller, the first timing control logic, and the second timing control logic can be hardware that performs logical operations in physical form, such as a single-chip microcomputer, a microprocessor, a programmable logic controller (PLC) or a field-programmable gate array (FPGA), or a software program, functional module, function, object library (Object Libraries) or dynamic link library (Dynamic-Link Libraries) that implements the above functions based on hardware. In this embodiment, the controller is a single-chip microcomputer, and the first timing control logic is a software program.

[0035] Each biopotential signal acquisition circuit in the biopotential signal acquisition system works synchronously in parallel under the control of the controller and the timing control logic of each subsystem. All biopotential signal acquisition circuits receive control commands under the control of their own timing control logic, perform sampling actions on each electrode interface or perform additional actions (for example, a biopotential signal acquisition circuit with an electrical stimulation function controls some electrode interfaces to perform electrical stimulation actions). All biopotential signal acquisition circuits in each subsystem always receive control commands from the controller at the same time, and the control commands in different subsystems do not have to be the same.

[0036] Figure 2 A schematic diagram of the control timing of a biopotential signal acquisition system provided by an embodiment of the present invention. The controller is used to generate a frequency of a specified sampling frequency f s When the controller generates a sampling trigger pulse signal, it triggers the timing control logic of all subsystems to issue their own control command sequences, thereby driving all corresponding biopotential signal acquisition circuits to synchronously execute actions according to the control command sequence, completing one-time sampling of all electrode interfaces on the biopotential signal acquisition circuit and other additional functions (if there are additional functions). For example, Figure 1 After the first timing control logic in the first subsystem 1 is triggered, the first control command sequence is simultaneously sent to all the first biopotential signal acquisition circuits in the first subsystem 1. When all command sequences are sent, the sampling data or command execution results are also obtained, and then the waiting state is entered until the controller generates the next sampling trigger pulse signal. Obviously, the higher the sampling frequency, the shorter the sampling trigger pulse interval, and the shorter the above waiting state time.

[0037] Specifically, for the electrical stimulation and acquisition subsystem, the first control command sequence in a sampling trigger pulse signal cycle includes a sampling control command for controlling each electrode interface in the first biopotential signal acquisition circuit to perform a sampling action, an electrical stimulation command for controlling the electrode interface that generates electrical stimulation to perform an electrical stimulation action, and other additional commands. In the above-mentioned sampling trigger pulse signal cycle, the first timing control logic first sends the sampling control commands of each electrode interface to each first biopotential signal acquisition circuit in sequence. If the electrode interface is required to perform an electrical stimulation action, the first timing control logic continues to send the electrical stimulation command after the sampling control command. If the electrode interface is not required to perform an electrical stimulation action, the first timing control logic can send other additional function commands after the sampling control command. Of course, other additional commands are not limited to being sent after the sampling control command, but can also be inserted before the sampling control command or between the sampling control commands. However, based on the principle of completing the important task (biopotential signal sampling) first, it is most appropriate to arrange the additional command after the sampling command.

[0038] For a single acquisition subsystem, the second control command sequence in one sampling trigger pulse signal cycle includes sampling control commands for controlling each electrode interface in the second biopotential signal acquisition circuit to perform sampling actions and other additional commands. In the above sampling trigger pulse signal cycle, the second timing control logic first sends the sampling control commands of each electrode interface to each second biopotential signal acquisition circuit in sequence, and then sends the additional function commands. Similarly, based on the principle of completing the important task (biopotential signal sampling) first, it is most appropriate to arrange the additional commands after the sampling commands.

[0039] For all biopotential signal acquisition circuits in the biopotential signal acquisition system, their internal sampling actions or electrical stimulation actions, as well as command result outputs, are all synchronously driven by the interface clock, and the corresponding timing control logic always sends the control command sequence at the maximum rate allowed by the biopotential signal acquisition circuit communication interface of each interface timing, and controls the biopotential signal acquisition circuit to execute each command in the shortest, same-width time slot, without waiting between commands, so that the execution time of the entire command sequence is the shortest, closely arranged, and the time used for the command sequence executed by a sampling trigger is fixed. Different sampling frequencies only have different waiting times after the command sequence. This method maximizes the highest sampling frequency.

[0040] like Figure 2 As shown, the time interval (i.e., sampling period) of the sampling trigger pulse signal generated by the controller is T sThe biopotential signal acquisition circuits in the same subsystem that use the same interface timing are guaranteed by the timing control logic to take exactly the same time to complete the same command timing (for example, controlling all electrode interfaces to perform a sampling action and additional functions). Two subsystems that use biopotential signal acquisition circuits with different interface timings may have different communication timings, so the time required to complete different control command sequences may also be different. The subsystem that takes longer is recorded as T g As long as T s Greater than T g The biopotential signal acquisition system can achieve a sampling period of T s (The sampling frequency of each channel f s =1 / T s ) without losing any channel's sampling.

[0041] The present invention can control a plurality of biopotential signal acquisition circuits with different interfaces, number of acquisition channels, sampling time and additional functions to sample at a required sampling frequency; it is also applicable to a multi-channel biopotential signal acquisition circuit that uses only one analog-to-digital converter for time-division multiplexing sampling. A controller generates a sampling trigger pulse signal sequence with equal intervals; when the trigger pulse signal arrives, the controller sends a set of control command sequences required by each biopotential signal acquisition circuit in parallel to control it to complete the actions of all channels in the circuit, and then waits for the next sampling trigger pulse signal to arrive and repeat the above workflow. The interfaces and functions of each biopotential signal acquisition circuit can be different, and the time to execute the set of command sequences does not have to be the same. When the total time to execute a set of control command sequences is less than the required sampling period, changing the channel sampling frequency only requires changing the frequency of the sampling trigger pulse signal.

[0042] The above-described embodiments merely express the implementation methods of the present invention, but they cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A different interface sequential biopotential signal acquisition system, characterized by: The acquisition system includes a controller, a first timing control logic, a second timing control logic, a first biopotential signal acquisition circuit, and a second biopotential signal acquisition circuit; The first biopotential signal acquisition circuit and the second biopotential signal acquisition circuit have different interface timings; The controller is used to generate a sampling trigger pulse signal, and the first timing control logic is used to control the first biopotential signal acquisition circuit to perform a first action according to a first control command sequence during the period of the sampling trigger pulse signal; The second timing control logic is used to control the second biopotential signal acquisition circuit to perform a second action according to a second control command sequence during the period of the sampling trigger pulse signal; The command in the first control command sequence for controlling the first biopotential signal acquisition circuit to perform an acquisition action is executed first, and / or, The command in the second control command sequence for controlling the second biopotential signal acquisition circuit to perform an acquisition action is executed first; The first biopotential signal acquisition circuit includes a plurality of first interfaces, and the first biopotential signal acquisition circuit sequentially performs acquisition actions and electrical stimulation actions on the first interfaces according to a first control command sequence; and / or, The second biopotential signal acquisition circuit includes a plurality of second interfaces, and the second biopotential signal acquisition circuit sequentially performs acquisition actions on the second interfaces according to a second control command sequence.

2. A different interface sequential biopotential signal acquisition system according to claim 1, characterized in that: The first action includes a collection action and an electrical stimulation action; the second action includes a collection action.

3. A synchronous control method for different interface timing biopotential signal acquisition circuits implemented based on the acquisition system according to claim 1 or 2, characterized in that: The following steps are involved: Step (1), the controller generates a continuous sampling trigger pulse signal with equal time intervals; the frequency of the sampling trigger pulse signal in step (1) is the required sampling frequency, and the sampling frequencies of all channels of all controlled biopotential signal acquisition circuits are the same as the sampling trigger pulse signal frequency, and the sampling frequency can be configured according to the requirements of different application scenarios; Step (2), during the period of the sampling trigger pulse signal, the controller continuously sends a set of control command sequences compatible with the interface timing and functions of the respective biopotential signal acquisition circuits to all biopotential signal acquisition circuits in parallel, and after each biopotential signal acquisition circuit receives the corresponding set of control command sequences, it controls all channels thereon to complete the action; Step (3), each biopotential signal acquisition circuit enters a waiting state after all channels thereon complete the action, until the next sampling trigger pulse signal arrives, and then repeats step (2).

4. A synchronous control method for different interface timing biopotential signal acquisition circuits implemented based on the acquisition system according to claim 1 or 2, characterized in that: The following steps are involved: Step (1), the controller generates a sampling trigger pulse signal; the frequency of the sampling trigger pulse signal in step (1) is the required sampling frequency, and the sampling frequencies of all channels of all controlled biopotential signal acquisition circuits are the same as the sampling trigger pulse signal frequency, and the sampling frequency can be configured according to the requirements of different application scenarios; Step (2), the sampling trigger pulse signal triggers the timing control logic to simultaneously send a corresponding control command sequence to the corresponding n biopotential signal acquisition circuits; Step (3), each biopotential signal acquisition circuit controls all channels thereon to complete the action according to the received control command sequence; Step (4), each biopotential signal acquisition circuit enters a waiting state after all channels on it complete the action, and the interval of the sampling trigger pulse signal is greater than the time required to complete steps (2) and (3).

5. A synchronous control method for different interface timing biopotential signal acquisition circuits according to claim 3 or 4, characterized in that: The controller ensures that the biopotential signal acquisition circuits with the same interface timing simultaneously receive the corresponding set of control command sequences, and the biopotential signal sampling data is outputted while receiving the set of control command sequences.

6. A synchronous control method for different interface timing biopotential signal acquisition circuits according to claim 3 or 4, characterized in that: The time interval of the sampling trigger pulse signal is T s ; The time required for each of the n biopotential signal acquisition circuits to complete all the channels is T i , i is 1 to n, n is a natural number, where T g For T1, T2, T3, …, T i The maximum value, and T s Greater than T g .

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