Patent ID: 11883194
Assignee: THE GOVERNMENT OF THE UNITED STATES, AS REPRESENTED BY THE SECRETARY OF THE ARMY
Field: Medical technology (Instruments)
Classification: CPC A  G | IPC A  G

Claim 16:
17. The system according to claim 13, wherein said alertness model includes

Pc(t)=(S(t)+κC(t))*gPD(t,c)

where S(t) represents the homeostatic component, C(t) represents the circadian component, and gpD(t,c) represents the caffeine component and where, C
   ⁡
   (
   t
   )
  
  =
  
   
    ∑
    
     i
     =
     1
    
    5
   
    
   
    
     a
     i
    
    ⁢
    
     sin
     [
     
      i
      ⁢
      
       
        2
        ⁢
        π
       
       τ
      
      ⁢
      
       (
       
        t
        +
        ∅
       
       )
      
     
     ]
    
   
  
 

where i represents harmonics, a1=0.97, a2=0.22, a3=0.07, a4=0.03, and a5=0.001, τ denotes a period of a circadian oscillator, K represents a circadian amplitude, and Φ denotes a circadian phase, and, S
   ⁡
   (
   t
   )
  
  =
  
   {
   
    
     
      
       
        U
        -
        
         
          (
          
           U
           -
           
            S
            0
           
          
          )
         
         ⁢
         
          exp
          ⁡
          (
          
           
            -
            t
           
           /
           
            τ
            w
           
          
          )
         
        
       
                                                                   
      
     
     
      
       during
       ⁢
          
       wakefulness
      
     
    
    
     
      
       
        
         
          -
          2
         
         ⁢
         U
        
        +
        
         
          (
          
           
            2
            ⁢
            U
           
           +
           
            S
            0
           
          
          )
         
         ⁢
         
          exp
          ⁡
          (
          
           
            -
            t
           
           /
           
            τ
            s
           
          
          )
         
        
        +
       
                                                   
      
     
     
      
       
        during
        ⁢
           
        sleep
       
                      
      
     
    
    
     
      
       
        
         (
         
          
           2
           ⁢
           U
          
          +
          
           L
           0
          
         
         )
        
        [
        
         
          τ
          LA
         
         /
         
          (
          
           
            τ
            LA
           
           -
           
            τ
            s
           
          
          )
         
        
        ]
       
       [
       
        
         exp
         ⁡
         (
         
          
           -
           t
          
          /
          
           τ
           LA
          
         
         )
        
        -
        
         exp
         ⁡
         (
         
          
           -
           t
          
          /
          
           τ
           s
          
         
         )
        
       
       ]
      
     
     
       
     
    
   
  
 

where U and L denote the sleep debt upper asymptote and the sleep debt lower asymptote of process S, respectively, τw and τs denote time constants, and τLA denotes the time constant of an exponential decay of an effect of sleep history on cognitive performance, where, L
   ⁡
   (
   t
   )
  
  =
  
   {
   
    
     
      
       
        
         
          max
          [
          
           
            U
            -
            
             
              (
              
               U
               -
               
                L
                0
               
              
              )
             
             ⁢
             
              exp
              ⁡
              (
              
               
                -
                t
               
               /
               
                τ
                LA
               
              
              )
             
            
           
           ,
           
            
             -
             0.11
            
            ⁢
            U
           
          
          ]
         
                  
        
       
       
        
         during
         ⁢
            
         wakefulness
        
       
      
      
       
        
         max
         [
         
          
           
            
             -
             2
            
            ⁢
            U
           
           +
           
            
             (
             
              
               2
               ⁢
               U
              
              +
              
               L
               0
              
             
             )
            
            ⁢
            
             exp
             ⁡
             (
             
              
               -
               t
              
              /
              
               τ
               LA
              
             
             )
            
           
          
          ,
          
           
            -
            0.11
           
           ⁢
           U
          
         
         ]
        
       
       
        
         
          during
          ⁢
             
          sleep
         
                        
        
       
      
     
     ⁢
     

                    
     where
     ⁢
     

     
      
       g
       PD
      
      (
      
       t
       ,
       c
      
      )
     
    
    =
    
     
      
       
        
         [
         
          1
          +
          
           
            M
            c
           
           ⁢
           
            
             k
             a
            
            
             
              k
              a
             
             -
             
              k
              c
             
            
           
           ⁢
           
            {
            
             
              exp
              [
              
               -
               
                
                 k
                 c
                
                (
                
                 t
                 -
                 
                  t
                  0
                 
                
                )
               
              
              ]
             
             -
             
              exp
              [
              
               -
               
                
                 k
                 a
                
                (
                
                 t
                 -
                 
                  t
                  0
                 
                
                )
               
              
              ]
             
            
            }
           
          
         
         ]
        
        
         -
         1
        
       
       ⁢
          
       for
       ⁢
          
       t
      
      ≥
      
       t
       ⁢
       0
       ⁢
       

                      
       
        M
        c
       
      
     
     =
     
      
       
        
         M
         0
        
        ·
        c
       
       ⁢
          
       and
       ⁢
          
       
        k
        c
       
      
      =
      
       
        k
        0
       
       ⁢
          
       
        exp
        ⁡
        (
        
         
          -
          z
         
         ·
         c
        
        )
       
      
     
    
   
  
 

where Mc and kc denote an amplitude factor and an elimination rate for a caffeine dose c administered at time t0; and M0, k0, z, and ka, respectively, denote an amplitude slope, a basal elimination rate, a decay constant, and an absorption rate.