Patent Publication Number: US-9839397-B2

Title: Motion compensation in photopletysmography-based heart rate monitoring

Description:
BACKGROUND 
     Technical Field 
     The present disclosure relates to photopletysmography (PPG)-based heart rate determination under motion conditions. In particular, the present disclosure relates to a device that compensates motion artifacts introduced in a PPG signal. 
     Description of the Related Art 
     PPG-based heart rate monitoring and determination is sensitive to noise artifacts. The noise artifacts can be introduced as a result of movement of a biological body or a heart rate measurement device used to perform the heart rate measurement. The noise corrupts a heart rate signal detected by the heart rate measurement device using PPG techniques. Further, the noise makes heart rate determination unreliable. 
     BRIEF SUMMARY 
     A device may be summarized as including: a first light source configured to emit light having a first wavelength at a biological body, the first wavelength being associated with a first absorption coefficient for blood components; a second light source configured to emit light having a second wavelength at the biological body, the second wavelength being associated with a second absorption coefficient for the blood components that is less than the first absorption coefficient; a photodetector configured to capture a first reflected signal as a result of the light having the first wavelength being reflected from the biological body and capture a second reflected signal as a result of the light having the second wavelength being reflected from the biological body; and a processor coupled to the photodetector and configured to receive the first reflected signal and the second reflected signal from the photodetector, obtain a heart rate signal as a difference between the first reflected signal and the second reflected signal and determine a heart rate of the biological body based on the heart rate signal. 
     The processor may be further configured to: obtain an amplitude adapting coefficient for the second reflected signal; and obtain the heart rate signal as a difference between the first reflected signal and a quotient of the second reflected signal and the amplitude adapting coefficient. The amplitude adapting coefficient may be a divisor of the second reflected signal that minimizes a difference in energy between the first reflected signal and the quotient of the second reflected signal and the amplitude adapting coefficient. The processor may be further configured to: cross-correlate the first reflected signal and the second reflected signal to produce a cross-correlation function between the first reflected signal and the second reflected signal; identify a maximum of the cross-correlation function; identify a time index corresponding to the maximum of the cross-correlation function; and shift the second reflected signal by the time index prior to obtaining the heart rate signal using the second reflected signal shifted by the time index. The processor may be further configured to: low-pass filter the first reflected signal and the second reflected signal; and de-trend the first reflected signal and the second reflected signal. A cutoff frequency of the low pass filter may be 4 Hertz or lower. The device may further include a motion detector coupled to the processor and configured to output a signal to the processor indicating whether the device was displaced, wherein: the processor is further configured to determine the heart rate based on the heart rate signal if the signal to the processor indicates that the device was displaced. The device may further include an output device coupled to the processor and configured to receive the heart rate from the processor and display the heart rate. 
     A method may be summarized as including: emitting light having a first wavelength at a biological body, the first wavelength being associated with a first absorption coefficient for blood components; capturing a first reflected signal as a result of the light having the first wavelength being reflected from the biological body; emitting light having a second wavelength at the biological body, the second wavelength being associated with a second absorption coefficient for the blood components that is less than the first absorption coefficient; capturing a second reflected signal as a result of the light having the second wavelength being reflected from the biological body; obtaining a heart rate signal as a difference between the first reflected signal and the second reflected signal; and determining a heart rate of the biological body based on the heart rate signal. 
     The method may further include: scaling the second reflected signal by a reciprocal of an amplitude adapting coefficient before obtaining the heart rate signal as the difference between the first reflected signal and the second reflected signal using the second reflected signal scaled by the reciprocal of the amplitude adapting coefficient. The amplitude adapting coefficient may be a divisor of the second reflected signal that minimizes a difference in energy between the first reflected signal and the quotient of the second reflected signal and the amplitude adapting coefficient. The method may further include: time shifting the second reflected signal prior to obtaining the heart rate signal using the time shifted second reflected signal. The second reflected signal may be shifted by a time index corresponding to a maximum cross-correlation value between the first reflected signal and the second reflected signal. The method may further include: filtering the first and second reflected signals; and de-trending the first and second reflected signals. 
     A system may be summarized as including: a first light source; a second light source; a photodetector; a processor; and a computer-readable storage medium having stored thereon instructions that, when executed by the processor, cause the processor to: instruct the first light source to emit light having a first wavelength at a biological body, the first wavelength being associated with a first absorption coefficient for blood components; instruct the second light source to emit light having a second wavelength at the biological body, the second wavelength being associated with a second absorption coefficient for the blood components that is less than the first absorption coefficient; receive a first reflected signal captured by the photodetector as a result of the light having the first wavelength being reflected from the biological body and a second reflected signal captured by the photodetector as a result of the light having the second wavelength being reflected from the biological body; obtain a heart rate signal based on the first reflected signal and the second reflected signal; and determine a heart rate of the biological body based on the heart rate signal. 
     The instructions may further cause the processor to obtain the heart rate signal as a difference between the first reflected signal and the second reflected signal. The instructions may further cause the processor to: obtain an amplitude adapting coefficient for the second reflected signal; adjust an amplitude of the second reflected signal by the amplitude adapting coefficient to obtain an amplitude-adjusted second reflected signal; and obtain the heart rate signal as a difference between the first reflected signal and the amplitude-adjusted second reflected signal. The instructions may further cause the processor to: low-pass filter the first and second reflected signals to respectively produce first and second filtered signals; and de-trend the first and second filtered signals ahead of obtaining the heart rate signal. The first wavelength may be between 500 and 580 nanometers (nm) and the second wavelength may be between 680 and 700 nm. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
         FIG. 1  shows a cross-sectional view of a probe of a heart rate measurement device positioned near the skin of a biological body. 
         FIG. 2  shows a diagram of the absorption coefficients of blood components for light of different wavelengths. 
         FIG. 3  shows a block diagram of a heart rate measurement device. 
         FIG. 4  shows a method for determining the heart rate of a biological body. 
         FIGS. 5A and 5B  show a flow diagram of a method for compensating for motion in the heart rate measurement device. 
         FIGS. 6A and 6B  show a flow diagram of a method for compensating for motion in the heart rate measurement device. 
         FIG. 7  shows a flow diagram of a method for determining the heart rate based on a heart rate signal. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  shows a cross-sectional view of heart rate measurement device  100   a  positioned near the skin  103  of a biological body  104 . The heart rate measurement device  100   a  is used to measure the heart rate of the biological body  104  using photopletysmography (PPG). The heart rate measurement device  100   a  includes a probe  102  having a first light source  106   a , a second light source  108   a  and a photodetector  109   a . The probe  102  is positioned near the skin  103  of the biological body  104  (and may, for example, be in contact with the skin  103 ). Light emanating from the first light source  106   a  and the second light source  108   a  is captured by the photodetector  109   a  after having at least partially penetrated the biological body  104  and been reflected by the biological body  104 . 
     PPG is a non-invasive technique for heart rate measurement and detection. PPG relies on the principle that blood components, such as oxyhemoglobin and deoxyhemoglobin, reflect back light having certain wavelengths. Light emitted by the first light source  106   a  or the second light source  108   a  will reach a blood vessel  105  in the dermis  107 . Blood components reflect light having certain wavelengths (for example, green light of 500-550 nanometers (nm) and yellow light of about 580 nm) differently than light having other wavelengths (for example, red light of a wavelength slightly lower than 700 nm). The intensity of light reflected from the biological body changes due to the different absorption coefficients of the colors of light. The intensity of reflected light depends on the volume of blood in a vessel. When the volume of blood in vessel is relatively large the reflected light intensity is low (because the blood absorbs more light) and vice-versa. This variation is correlated with blood flow. Green light is a lot more sensitive to blood than red light because of its associated higher absorption coefficient. The variation of the received light intensity over time is due to volumetric variations. 
     PPG-based heart rate measurements are sensitive to movement of the biological body  104  or the heart rate measurement device  100   a  during measurement. For example, movement of the biological body  104  while a heart rate measurement is being made changes the area of the dermis  107  on which light is shone. As a result of the movement, noise is introduced in the reflected signal. Similarly, movement of the probe  102  (or light source emanating light having a wavelength or photodetector  109   a  thereof) also introduces noise in the reflected signal. 
     The heart rate measurement device  100   a  compensates for the noise, or in general artifacts, introduced in the reflected signal as a result of the movement. The heart rate measurement device  100   a  compensates for the noise by utilizing two light sources that emit light having different wavelengths, whereby one light source (referred to herein as the “first light source”) has a wavelength with relatively high absorption coefficient for blood components and another light source (referred to herein as the “second light source”) has a wavelength with relatively low absorption coefficient for blood components. 
       FIG. 2  shows a diagram of the absorption coefficients of blood components for light of different wavelengths. Graph  202  shows the absorption coefficients for oxyhemoglobin and graph  204  shows the absorption coefficients for deoxyhemoglobin for various light wavelengths. The lower is the absorption coefficient, the greater the transparency of the blood component to light. For example, oxyhemoglobin has high transparency for red light (having a wavelength of about 700 nm) as evidenced by the low absorption coefficient of 0.1. Accordingly, more red light is reflected than blue, green or yellow light (wavelengths in the range of 500-600 nm). Blue, green are largely absorbed by oxyhemoglobin and are not reflected. 
     When the first light source is used to provide light having a wavelength with a high absorption coefficient, the first reflected signal (denoted as R 1 ) has a signal component (S 1 ) that is representative of the heart rate. However, when the second light source is used to provide light having a wavelength with a low absorption coefficient, the second reflected signal (denoted as R 2 ) has a weak signal component (S 2 ) that is not representative of the heart rate because the light is not reflected by the blood components. However, the noise components (N 1  and N 2 ) of the respective first and second reflected signals are similarly affected by movement. 
     By modeling the first reflected signal as R 1 =S 1 +N 1  and the second reflected signal as R 2 =S 2 +N 2 , the difference between the reflected signals is represented as:
 
 R   2   =S   1   +N   1 −( S   2   +N   2 )=( S   1   −S   2 )+( N   1   −N   2 )  Equation (1).
 
     Because the signal component of the second reflected signal (S 2 ) is not reflected by the blood components, S 2  may not influence the signal term (S 1 −S 2 ) of equation (1). The signal term may be simplified as: S 1 −S 2 ≈S 1 . The noise components are both similarly affected by movement of the biological body or the heart rate measurement device  100   a . The noise components should substantially cancel one another out. That is, N 1 −N 2 ≈0. Accordingly, obtaining the difference between the first reflected signal and the second reflected signal may improve the received signal component used to determine the heart rate of the biological body. That is:
 
 R   1   −R   2   ≈S   1   Equation (2).
 
       FIG. 3  shows a block diagram of a heart rate measurement device  100   b . The heart rate measurement device  100   b  comprises a processor  110 , memory  111 , one or more first light sources  106   b , one or more second light sources  108   b , a photodetector  109   b , a motion detector  112  and an output device  114 . The one or more first light sources  106   b  and the one or more second light sources  108   b  may each be a light emitting diode (LED). Further, the photodetector  109   b  may be a photodiode and the motion detector  112  may be an accelerometer or a gyroscope. In addition, the processor  110  may be any type of device that is capable of performing computing functions. For example, the processor  110  may be a microcontroller, microprocessor or digital signal processor (DSP), among others. 
     The memory  111  may be any type of memory, such as volatile memory that includes random access memory (RAM), among others or non-volatile memory that includes read only memory (ROM), among others. The memory  111  may be a non-transitory computer-readable memory. The memory  111  may be used to store instructions that, when executed by the processor  110 , cause the processor  110  to perform the techniques described herein. For example, the memory  111  may store instruction that, when executed by the processor  110 , cause the processor  110  to obtain a heart rate signal or determine a heart rate of a biological body as described herein, among others. The output device  114  may be a display, such as a liquid crystal display, or speakers. In various embodiments, the output device  114  may be a communications port for transferring heart rate measurements to another device. 
     Although not shown in  FIG. 3 , the heart rate measurement device  100   a  may include a front end (for example, an analog front end) disposed between the processor  110  and the photodetector  109   b . The front end may condition or amplify a signal received from the photodetector  109   b  and correct acquisition of the signal received from the photodetector  109   b . In some embodiments, the front end may be part of the processor  110 , whereby the processor amplifies, conditions or corrects the acquisition of the signal from the photodetector  109   b.    
     The heart rate measurement device  100   a  is used to measure the heart rate of a biological body using PPG as described herein. The one or more first light sources  106   b , one or more second light sources  108   b , photodetector  109   b  and motion detector  112  may be part of the probe  102  of the heart rate measurement device  100   b.    
     The one or more first light sources  106   b , one or more second light sources  108   b , photodetector  109   b , motion detector  112  and output device  114  are coupled to the processor  110 . The processor  110  sends a first control signal to the one or more first light sources  106   b  instructing the one or more first light sources  106   b  to emit light having a first wavelength. As described herein, the emitted light may be blue, green or yellow light that has a relatively high absorption coefficient for blood. The first control signal may indicate the period of time for which the light should be emitted or a first light source  106   b  may be configured to emit the light for the period of time in response to receipt of the first control signal. 
     The photodetector  109   b  then captures the first reflected signal resulting from reflection of the first wavelength light by the biological body. The photodetector  109   b  outputs the captured first reflected signal to the processor  110 . 
     The processor  110  then sends a second control signal to the one or more second light sources  106  instructing the one or more second light sources  106   b  to emit light having a second wavelength. As described herein, the emitted light may be red and may have a relatively low absorption coefficient by blood components. The second control signal may indicate the period of time for which the light should be emitted or a second light source  108   b  may be configured to emit the light for the period of time in response to receipt of the second control signal. The photodetector  109   b  then captures the second reflected signal resulting from reflection of second wavelength light by the biological body. The photodetector  109   b  transmits the second reflected signal to the processor  110 . The second reflected signal may be identified as such due to the fact that it has been captured at the same time as or subsequent to emitting light by the second light source  108   b.    
     In one embodiment, the heart rate measurement device  100   b  includes only one first light source  106   b  and only one second light source  108   b . In this case, the first light source  106   b  and the second light source  108   b  may alternate emitting light one at a time with an interval for a break therebetween. The positions of the first light source  106   b  and the second light source  108   b  may be equidistant from the photodetector  109   b . For example, each light source  106   b ,  108   b  may be 3 millimeters (mm) to 5 mm from the photodetector  109   b . The distance between each light source  106   b ,  108   b  and the photodetector  109   b  may be set to 4 mm. The first light source  106   b  and the second light source  108   b  may be positioned on opposite sides of the photodetector  109   b  or on the same side. The distance between the first light source  106   b  and the photodetector  109   b  may be the same as the distance between the second light source  108   b  and the photodetector  109   b . Further, the first light source  106   b  and the second light source  108   b  may be positioned in close proximity to one another (for example, abutting or less than 1 mm apart) and on the same side of the photodetector  109   b.    
     In another embodiment, the heart rate measurement device  100   b  includes two or more first light sources  106   b  and two or more second light sources  108   b , whereby only one of the first light sources  106   b  and second light sources  108   b  emits light at a time. When two or more first light sources  106   b  and two or more second light sources  108   b  are used, the second and subsequent light sources of the two or more second light sources  108   b  may be positioned on opposite sides of the photodetector  109   b  as compared to the first of the two or more second light sources  108   b . However, it may be necessary to have at least one pair (comprising a first light source  106   b  and a second light source  108   b ) positioned adjacent to each other or within close proximity of each other. 
     The motion detector  112  detects whether the heart rate measurement device  100   b  or light sources  106   b ,  108   b  or photodetector  109   b  thereof were moved during the capturing of the reflected signals. If movement is detected, the motion detector  112  sends a signal to the processor  110  indicating that movement was detected. Receipt of the signal by the processor  110  triggers the processor to perform motion compensation using the first and second reflected signals as described herein. 
       FIG. 4  shows a method  400  for determining the heart rate of a biological body. In the method  400 , the first light source  106   b , at  402 , emits light having a first wavelength associated with a first absorption coefficient for blood components. At  404 , the photodetector  109   b  captures the first reflected signal as a result of emitting the light having the first wavelength. Then, at  406 , the second light source  108   b  emits light having a second wavelength associated with a second absorption coefficient for blood components. The second absorption coefficient is less than the first absorption coefficient. At  408 , the photodetector  109   b  captures a second reflected signal as a result of emitting the light having the second wavelength. The first reflected signal and the second reflected signal are provided to the processor  110 . In turn, the processor  110 , at  410  determines the heart rate based on a difference between the first reflected signal and the second reflected signal. It will of course be understood that the steps in  FIG. 4  could be performed in many different orders, such as performing steps  406  and  408  before steps  402  and  404 . 
       FIGS. 5A and 5B  show a flow diagram of a method for compensating for motion in the heart rate measurement device  100   b . In the method  500 , at  502 , the processor  110  receives the first reflected signal and the second reflected signal. The first reflected signal may have been captured by the photodetector  109   b  as a result of reflection of light emitted by the first light source  106   b  and the second reflected signal may have been captured by the photodetector  109   b  as a result of light emitted by the second light source  108   b . The processor  110  then determines, at  504 , whether motion has been detected. Determining whether motion is detected may be based on the output of the motion detector  112 . If motion is not detected, then motion compensation is not necessarily performed. The processor  110 , at  506 , determines the heart rate based on the first reflected signal as a heart rate signal. 
     Conversely, if motion is detected, the processor  110  at  508  applies a low-pass filter to the first reflected signal and the second reflected signal to produce a first filtered signal and a second filtered signal, respectively. The low-pass filter may remove electrical or thermal noise from the first and second reflected signals. The noise may be introduced in the first and second reflected signals by circuit components of the heart rate measurement device  100   b . The low-pass filter may have a cutoff frequency that is higher than a typical heart rate. For example, the human heart rate is typically between 0.5 and 3 Hertz (Hz). If the heart rate measurement device  100   b  is used to measure the human heart rate, the cutoff frequency of the low-pass filter may be set to 4 Hz, thus capturing the 0.5 to 3 Hz band of human heart rate. Accordingly, heart rate information is not filtered out by the low-pass filtering. 
     The processor  110  then de-trends the first and second filtered signals to produce respective first and second de-trended signals at  510 . De-trending the first and second filtered signals removes an identified trend in the signals and enables analysis of the signals to focus on fluctuations or variations in the signals as opposed to a trend in the signals. The first filtered signal may be de-trended by linearly fitting the first filtered signal and subtracting the linearly-fitted signal from the first filtered signal. 
     The processor  110 , at  512 , cross-correlates the first and second de-trended signals. Denoting the first de-trended signal as D 1 (n) and the second de-trended signal as D 2  (n), the cross-correlation function of the first de-trended signal and the second de-trended signal is: 
     
       
         
           
             
               
                 
                   
                     XCorr 
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     The processor  110  then identifies a maximum cross-correlation value and an index of the maximum cross-correlation value at  514 . The maximum cross-correlation value may be the maximum value of the time-series correlation function (XCorr). The index may be the corresponding time index of the maximum cross-correlation value. The index may represent a time shift of the second de-trended signal that, when performed, results in a highest degree of similarity between the first de-trended signal and the second de-trended signal. 
     The processor  110  at  516  determines if the maximum cross-correlation value is greater than a threshold. The threshold may, for example, be a minimum correlation value such as 0.5. The threshold may be determined based on observed correlations in “no motion” conditions. Under these conditions, the first reflected signal has a strong signal component. The second reflected signal, on the other hand, has a poor signal component and has a heavy contribution of the noise component. 
     If the maximum cross-correlation value is below the threshold then the similarities between the first and second reflected signals may not be sufficient for performing motion compensation. Accordingly, if the maximum cross-correlation value is not greater than the threshold, the processor  110  at  518  determines the heart rate based on the first reflected signal as the heart rate signal. 
     If the maximum cross-correlation value is greater than the threshold, the processor  110  performs motion compensation as described herein. In motion compensation, the second de-trended signal is used to remove the additive noise affecting the first de-trended signal as a result of the motion. 
     At  520 , the processor  110  shifts the second de-trended signal by the index of the maximum cross-correlation value. As a result, the first de-trended signal and the second de-trended signal become aligned to maximize their correlation. 
     The processor  110  obtains an adapting amplitude coefficient for the second de-trended signal at  522 . The adapting amplitude coefficient minimizes the difference in energy between the first de-trended signal and the second de-trended signal. To obtain the adapting amplitude coefficient the following energy function is determined: 
     
       
         
           
             
               
                 
                   
                     E 
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     A minimum of the energy function is identified and the adapting amplitude coefficient is the input to the function (Coeff=α) corresponding to the minimum of the energy function. In the above equation, α minimizes the energy using the least squares technique. However, as may be recognized other frameworks for determining an energy minimizing coefficient may be used. 
     The processor  110  at  524  obtains a heart rate signal as the difference between the first de-trended signal and a quotient of the second de-trended signal and the adapting amplitude coefficient. The heart rate signal is accordingly determined as: 
     
       
         
           
             
               
                 
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     The processor  110  at  526  then determines the heart rate based on the heart rate signal (H) as described herein. Determining the heart rate may include counting a number of peaks and/or valleys of the heart rate signal in an interval (for example, a 15 second interval) and obtaining the heart rate based on that number. 
     The method described with reference to  FIGS. 5A and 5B  may be used when the heart measurement device  100   b  utilizes one first light source  106   b  for emitting light captured as the first reflected signal and one second light source  108   b  for emitting light captured as the second reflected signal. When the heart measurement device  100   b  operates two or more first light sources  106   b  and two or more second light sources  108   b , the processor  110  receives from the photodetector  109   b  more than two reflected signals. 
     If two first light sources  106   b  and two second light sources  108   b  are used, the processor  110  receives two first reflected signals (denoted as R 11  and R 12 ) and two second reflected signals (denoted as R 21  and R 22 ). 
       FIGS. 6A and 6B  show a flow diagram of a method for compensating for motion in the heart rate measurement device  100   b . At  602 , the processor  110  receives the first reflected signals (R 11  and R 12 ) and the second reflected signals (R 21  and R 22 ). The processor  110  then determines if motion is detected at  604 . If a negative determination is made, at  606 , the processor  110  determines the heart rate based on a first reflected signal (R 11  or R 12 ) as a heart rate signal. 
     If a positive determination is made, at  608  the processor  110  applies a low pass filter to the first and second reflected signals (R 11 , R 12 , R 21  and R 22 ) to produce filtered signals. At  610 , the processor de-trends the filtered signals to produce first de-trended signals (D 11  and D 12 ) and second de-trended signals (D 21  and D 22 ). Each signal is individually filtered and de-trended. 
     At  612 , the processor  110  cross-correlates the first de-trended signals with the second de-trended signals. The cross-correlation will produce four cross-correlation functions that are as follows: XCorr 1 =XCorr(D 11 , D 21 ), XCorr 2 =XCorr(D 11 , D 22 ), XCorr 3 =XCorr(D 12 , D 21 ) and XCorr 4 =XCorr(D 12 , D 22 ). 
     For each resulting cross-correlation, the processor  110  at  614  identifies a maximum cross-correlation value and index of the maximum cross-correlation value. The indices of the maximum cross-correlation values and the maximum cross-correlation values are obtained as [Ind 1 , Val 1 ]=max(XCorr 1 ), [Ind 2 , Val 2 ]=max(XCorr 2 ), [Ind 3 , Val 3 ]=max(XCorr 3 ) and [Ind 4 , Val 4 ]=max(XCorr 4 ). 
     The processor  110  at  616  determines whether a maximum cross-correlation value of the identified maximum cross-correlation values exceeds a threshold. If a negative determination is made, the processor  110  at  618  determines the heart rate based on a first reflected signal. That is, the heart rate may be determined using R 11  or R 12 . 
     If a positive determination is made, the processor  110  performs motion compensation. The processor  110  shifts the second de-trended signals by a respective index of the maximum cross-correlation value at  620 . D 21  may be shifted by Ind 1  or Ind 3 . Further, D 22  may be shifted by Ind 2  or Ind 4 . 
     At  622 , the processor  110  obtains reconstructed second signals (C 1  and C 2 ) based on the second shifted de-trended signals and the maximum cross-correlation values. The reconstructed second signals are obtained as: 
     
       
         
           
             
               
                 
                   
                     
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                     6 
                     ) 
                   
                 
               
             
           
         
       
     
     At  624 , for each reconstructed second signal, the processor  110  obtains an adapting amplitude coefficient that minimize the difference in energy between a corresponding first de-trended signal and the reconstructed second signal. The difference in energy between a first de-trended signal and a corresponding reconstructed second signal for each pair of the first de-trended signal and the corresponding reconstructed second signal as described herein. The energy is determined as: 
     
       
         
           
             
               
                 
                   
                     
                       
                         E 
                         1 
                       
                       ⁡ 
                       
                         ( 
                         α 
                         ) 
                       
                     
                     = 
                     
                       ∫ 
                       
                         
                           ( 
                           
                             
                               D 
                               11 
                             
                             - 
                             
                               
                                 C 
                                 1 
                               
                               α 
                             
                           
                           ) 
                         
                         2 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         E 
                         2 
                       
                       ⁡ 
                       
                         ( 
                         α 
                         ) 
                       
                     
                     = 
                     
                       ∫ 
                       
                         
                           ( 
                           
                             
                               D 
                               12 
                             
                             - 
                             
                               
                                 C 
                                 2 
                               
                               α 
                             
                           
                           ) 
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     7 
                     ) 
                   
                 
               
             
           
         
       
     
     A first adapting amplitude coefficient (Coeff 1 =a 1 ) that minimizes E 1 (α) is obtained as [a 1 , E 1min ]=min(E 1 (α)) and a second adapting amplitude coefficient (Coeff 2 =α 2 ) that minimizes E 2 (α) is obtained as [α 2 , E 2min ]=min(E 2 (α)). 
     At  626 , the processor  110  obtains heart rate signals. Each heart rate signal is a difference between a first de-trended signal and a quotient of the respective reconstructed second signal and the adapting amplitude coefficient. A first heart rate signal is obtained as 
               H   1     =       D   11     -       C   1       Coeff   1               
and a second heart rate signal is obtained as
 
               H   2     =       D   12     -         C   2       Coeff   2       .             
The processor  110  at  628  determines the heart rate based on a heart rate signal.
 
       FIG. 7  shows a flow diagram of a method for determining the heart rate based on a heart rate signal. In the method  700 , the processor  110  obtains a heart rate signal as described herein at  702 . The processor  110  filters the heart rate signal using a low-pass filter at  704 . The cutoff frequency of the low-pass filter may be higher than a typical range of the heart rate. The processor  110  at  706  identifies a number of peaks and/or valleys in an interval of the filtered heart rate signal. At  708 , the processor  110  determines the heart rate based on the identified a number of peaks and/or valleys in an interval of the filtered heart rate signal. After determining the heart rate, the processor  110  at  710  outputs the heart rate to an output device, such as the output device  114  described with reference to  FIG. 3  herein. The displayed heart rate may be used by health personnel for evaluating the health of the biological body, such as a human being or an animal. 
     The intensity of the emitted light having the first wavelength and the emitted light having the second wavelength may be regulated such that the two lights, when reflected, arrive at a photodetector having comparable DC values. The DC values may be higher than a spectral sensitivity of the photodetector. To ensure that the detected DC values are comparable, the emitted intensity of the light having the first wavelength may be set to be greater than the emitted light having the second wavelength. 
     The various embodiments described above can be combined to provide further embodiments. 
     These and other changes can be made to the embodiments in light of the above-detailed description. In general, in the following claims, the terms used should not be construed to limit the claims to the specific embodiments disclosed in the specification and the claims, but should be construed to include all possible embodiments along with the full scope of equivalents to which such claims are entitled. Accordingly, the claims are not limited by the disclosure.