PATENT ABSTRACT
The system and method of the present application predicts if there is sufficient CO 2  absorbent capacity for the next anesthesia case. If insufficient, the canister can be preemptively replaced when no patient is connected to the breathing system. Such prediction also allows clinicians to determine if the CO 2  canister has to be changed during the present case or to wait until the end of the case. In the latter, the clinician may buy time by increasing the fresh gas flow rate to reduce the amount of patient CO 2  gases recirculated. A predictive estimation of CO 2  breakthrough allows more time to prepare for an orderly CO 2  canister replacement during a quiet period in the anesthesia care.

PATENT DESCRIPTION
FIELD 
     The present application is directed to the field of patient ventilators. More specifically, the present application is directed to ventilator circuit carbon dioxide (CO 2 ) removal. 
     BACKGROUND 
     A circle system is used to ventilate patients undergoing general anesthesia. To minimize wastage of excess expired anesthetic breathed out by the patient, the circle breathing system is designed to enable patient expired gases to be rebreathed after carbon dioxide is removed using CO 2  absorbent. In addition, oxygen and anesthetic agent is replenished to maintain desired concentration of gases breathed by the patient. CO 2  absorbent housed in a canister has a finite capacity to remove CO 2  from the expired patient gases. They can be replaced at the start of day or end of day on a routine basis. This is wasteful as unused absorbent capacity is discarded. 
     Alternatively, the absorbent is replaced during an anesthesia case when it is spent. This is detected by measurement of significant inspired CO 2  concentration. A typical threshold value is 0.5% of sustained inspired CO 2  concentration. This cost saving practice exposes the patient while unconscious and requires mechanical ventilation assistance during anesthesia, where the risk is disruption of ventilation that include temporarily pausing ventilation, disconnecting the breathing system, installing a CO 2  canister with fresh absorbent, checking the integrity of the reconnected breathing system, and resuming ventilation. 
     Dye with color changes in the presence of CO 2  is also used to indicate sent absorbent, as is computation of remaining CO 2  absorption capacity based on the absorbent refilled quantity and rate of CO 2  recirculated. Since quantity of refill and efficiency of the packed absorbent is a poor estimate of usable absorbent, the estimator/gauge is inaccurate. 
     SUMMARY 
     The above-mentioned shortcomings, disadvantages and problems are addressed herein which will be understood by reading and understanding the following specification. 
     The system and method of the present application predicts if there is sufficient CO 2  absorbent capacity for the next anesthesia case. If insufficient, the canister can be preemptively replaced when no patient is connected to the breathing system. Such prediction also allows clinicians to determine if the CO 2  canister has to be changed during the present case or to wait until the end of the case. In the latter, the clinician may buy time by increasing the fresh gas flow rate to reduce the amount of patient CO 2  gases recirculated. A predictive estimation of CO 2  breakthrough allows more time to prepare for an orderly CO 2  canister replacement during a quiet period in the anesthesia care. 
     In one aspect of the present application, a computerized method of predicting carbon dioxide (CO 2 ) breakthrough in an anesthesia ventilator comprises inputting into a computing system a pre-determined minimum threshold for a minimum averaged inspired CO 2  concentration (FiCO 2 ) and a CO 2  absorbent replacement, inputting into the computing system a set of data received from the anesthesia ventilator, wherein the set of data includes a measured FiCO 2 , determining whether the measured FiCO 2  exceeds the pre-determined minimum threshold, extrapolating, a number of breaths for the measured FiCO 2  to reach the CO 2  absorbent replacement threshold, and calculating a CO 2  absorbent replacement time with the number of breaths and a breaths interval time. 
     In another aspect of the present application, a non-transitory computer readable medium including instructions that, when executed on a computing system, cause the computing system to receive from a user interlace a pre-determined minimum threshold for a minimum averaged inspired CO 2  concentration (FiCO 2 ) and a CO 2  absorbent replacement, receive a set of data from the anesthesia ventilator, wherein the set of data includes a measured FiCO 2 , determine whether the measured FiCO 2  exceeds the pre-determined minimum threshold, extrapolate a number of breaths for the measured FiCO 2  to reach the CO 2  absorbent replacement threshold, and calculate a CO 2  absorbent replacement time with the number of breaths and a breaths interval time. 
     In another aspect of the present application, an anesthesia ventilator comprises a CO 2  canister containing CO 2  absorbent, a computing system including the storage device and a processor, the storage device including instructions that, when executed on the processor, cause the computing system to receive from a user interface a pre-determined minimum threshold for a minimum averaged inspired CO 2  concentration (FiCO 2 ) and a CO 2  absorbent replacement for the CO 2  absorbent, receive a set of data from the anesthesia ventilator, wherein the set of data includes a measured FiCO 2 , determine whether the measured FiCO 2  exceeds the pre-determined minimum threshold, extrapolate a number of breaths for the measured FiCO 2  to reach the CO 2  absorbent replacement threshold, wherein the extrapolation utilizes a set of predetermined parameters, and calculate a CO 2  absorbent replacement time with the number of breaths and a breaths interval time, and output the CO 2  absorbent replacement time to a user interface. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic illustration of a breathing circuit illustrating an embodiment of the present application; 
         FIG. 2  is a schematic illustration of a breathing circuit illustrating an embodiment of the present application; 
         FIG. 3  is a flow chart illustrating an exemplary method in accordance with an embodiment of the present application; and 
         FIG. 4  is a block diagram illustrating an embodiment of the system of the present application. 
     
    
    
     DETAILED DESCRIPTION 
     In the present description, certain terms have been used for brevity, clearness and understanding. No unnecessary limitations are to be applied therefrom beyond the requirement of the prior art because such terms are used for descriptive purposes only and are intended to be broadly construed. The different systems and methods described herein may be used alone or in combination with other systems and methods. Various equivalents, alternatives and modifications are possible within the scope of the appended claims. Each limitation in the appended claims is intended to invoke interpretation under 35 U.S.C. §112, sixth paragraph, only if the terms “means for” or “step for” are explicitly recited in the respective limitation. 
     In the following detailed description, reference is made to the accompanying drawings that form a part hereof, and in which is shown by way of illustration specific embodiments that may be practiced. These embodiments are described in sufficient detail to enable those skilled in the art to practice the embodiments, and it is to be understood that other embodiments may be utilized and that logical, mechanical, electrical and other changes may be made without departing from the scope of the embodiments. The following detailed description is, therefore, not to be taken as limiting the scope of the invention. 
     Referring to  FIG. 1 , the system and method of the present application relates to an anesthesia ventilator  10  with a circle breathing system  12  having a CO 2  canister  14  with absorbent (abs). The patient  22  is ventilated via mechanically through a volume reservoir (e.g. bellows, inflatable bag, long gas conduit) or manual bag (not shown). Concentrations of inspired and expired gases breathed by the patient  22  are monitored by a gas monitor (not shown). Gas concentrations measured include O 2 , CO 2 , N 2 O, air, and anesthetic gas. Inspired and expired gas flows are measured and gas volumes are computed by integrating the flow over a breath. As in any circle anesthesia breathing system  12 , fresh gases (FG)  16  are added to replenish gases consumed by the patient  22 . Excess FG  16  that is not consumed by the patient  22  is exhausted via an exhaust (exh)  24  having a pop off valve. Recirculated expired CO 2  passes through the CO 2  canister  14  and are absorbed by the CO 2  abs. As absorbent is spent, some CO 2  passes through the CO 2  canister  14  and is diluted by the FG  16  to form part of the inspired patient  22  gases. The measured concentration of inspired CO 2  is reported to a computing system  200  that predicts the rate of concentration increase of CO 2  breakthrough. 
     Referring to  FIG. 1 , the anesthesia ventilator  10  includes a circle breathing system  12  as stated above. The circle breathing system  12  includes an expiratory hose  20 , the inspiratory hose  18 , and the CO 2  canister  14 , that make up the main portion of the circle breathing system  12 . The circle breathing system  12  further includes the breathing hose that leads to the patient  20 , as well as the fresh gases  16  source and the exhaust  24 . As pictures in  FIG. 1 , the gases flow in a clockwise direction in the circle breathing system  12  shown in  FIG. 1 , and the hose that connects the patient  22  to the circle breathing system  12  allows gas flow to and from the circle breathing system  12  as shown in  FIG. 2 . Gas flows in the circle breathing system is directed by two one-way valves typically located in line with the inspiratory ( 18 ) and expiratory ( 20 ) breathing hoses. The fresh gases  16  source flowing from a high pressure supply flow one-way direction into the circle breathing system  12 . Likewise, the exhaust  24  allows one-way flow to ambient or scavenging and away from the circle breathing system  12  which is positively pressured during ventilation. In high flow recirculating anesthesia system a blower fan (flowing in excess of 50 lpm) determines the unidirectional flow of the recirculating gas flows. 
     Referring to  FIG. 2 , it should be noted that all of the references to the various formulas and abbreviations will be described and defined in the following description. Furthermore, it should be noted that the arrows included in the circle breathing system  12  of  FIG. 2  are illustrative of gas flow direction of the circle breathing system  12 . 
     As stated above, current dye solutions to indicate spent absorbent are imprecise and the dye color changes tend to regenerate. Predicting CO 2  expenditure of absorbent based on recirculated CO 2  without considering CO 2  concentration breakthrough is associated with error from uncertain absorption capacity based on quantity of absorbent refilled. Inefficiencies in the CO 2  absorption such as channeling, operating temperatures that contribute to this uncertainty. 
     However, the system and method of the present application utilizes the actual breakthrough CO 2  concentration to extrapolate the instance when a threshold CO 2  will be reached given current or what if operating setting of the breathing system. 
     Knowing when and if the absorbent in the CO 2  canister  14  can last through the next case allows the canister  14  to be replaced when the patient  22  is not connected between anesthesia cases, and when the canister  14  will not last through the next anesthesia case 
     Referring now the  FIGS. 1 and 2 , the derivation of Gas Exchange in the System will be determined as follows: 
     First considering the gas exchange in the lungs; inspired gases breathed into the lungs equal expired gases breathed out of the lungs plus gas entering or leaving the lungs from pulmonary blood. Applying conservation of mass to CO 2  exchange over a breath;
 
Inspired CO 2  volume=expired CO 2  volume+CO 2  from blood
 
     or V T ×FiCO 2 =V T ×FeCO 2 +VCO 2 , where V T  is the tidal volume per breath (in mL/min), FiCO 2  is the averaged inspired CO 2  concentration, and VCO 2  is the CO 2  production (in mL/min), in other words, CO 2  from the pulmonary blood. The product of tidal volume (V T ) and respiratory rate per minutes yield minute ventilation 
     
       
         
           
             
               
                 
                   
                     Rearranging 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         Fe 
                         ⁢ 
                         CO 
                       
                       2 
                     
                   
                   = 
                   
                     
                       
                         Fi 
                         ⁢ 
                         CO 
                       
                       2 
                     
                     - 
                     
                       
                         
                           V 
                           ⁢ 
                           CO 
                         
                         2 
                       
                       
                         V 
                         T 
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     Still referring to  FIGS. 1 and 2 , the movement of CO 2  in the circle breathing system  12  over a breath inspired and expired gas movement to the patient  22  are transported by the ventilator  10  at the rate of minute ventilation which is the product of tidal volume (VT) and respiratory rate per minute. In some high flow recirculating ventilators, the recirculating flows can be much higher than minute ventilation. However, the effective flow of gas exchange with the lungs remains at the rate of minute ventilation. As such, the high flow recirculation helps to even out gas concentration in the circle breathing system  12  but has the same effective gas exchange rate with the patient  22  and consumption of CO 2  absorbent, and is thus considered as equivalent in its gas exchange over a breath as the conventional circle system  12 . 
     Still referring to  FIGS. 1 and 2 , the movement of CO 2  through the CO 2  canister  14  per breath includes applying from the law of conservation applied over a breath, where inflow of CO 2  into the canister  14  equals outflow of CO 2  from the canister  14  plus CO 2  absorbed by the CO 2  absorbent in the canister  14 . Inflow of CO 2  into the absorber  14  equals CO 2  expired by the patient  22  less CO 2  exhausted via the exhaust  24 , so 
                         volume   =       ⁢         V   T     ×     FeCO   2       -       V   exh     ×     FeCO   2                     =       ⁢       (       V   T     -     V   exh       )     ×     FeCO   2                     (   2   )               
where FeCO 2  is the average patient  22  expired gases. FeCO 2  can be derived from the end tidal CO 2  measured using a gas monitor, which is used routinely as a standard of anesthesia care, and using the formula
 
                 FeCO   2     =       E   T     ⁢       CO   2     ⁡     (     1   -       V   D       V   T         )           ,         
where E T CO 2  is the measured end tidal CO 2  and V D  is the deadspace per breath and the ratio of
 
               V   D       V   T           
is typically about 10 to 20%. The outflow of CO 2  from the canister  14 =V R ×F R CO 2 , where
 
                     V   R     =       ⁢     tidal   ⁢           ⁢   volume   ⁢           ⁢   to   ⁢           ⁢   the   ⁢           ⁢   patient   ⁢           ⁢   22   ⁢           ⁢   less   ⁢           ⁢   the   ⁢           ⁢   fresh   ⁢             ⁢             ⁢   gas   ⁢           ⁢   flow                     ⁢     in   ⁢           ⁢   a   ⁢           ⁢   breath   ⁢           ⁢   interval   ⁢           ⁢     (   Vfg   )                     =       ⁢       V   T     -     V   fg         ,     and   ⁢           ⁢   is   ⁢           ⁢   the   ⁢           ⁢   total   ⁢           ⁢   gas   ⁢           ⁢   flow   ⁢           ⁢   from   ⁢           ⁢   the   ⁢           ⁢     CO   2     ⁢           ⁢     absorber   .                   
Now, substituting gas flow into the CO 2  flow through the CO 2  canister  14  yields:
 
( V   T   −V   exh )×FeCO 2 =( V   T   −V   fg )× F   R CO 2   +D CO 2 ,
 
where DCO 2  is the CO 2  absorbed by the CO 2  canister  14  over the breath time. Rearranging and solving for F R CO 2  yields:
 
     
       
         
           
             
               
                 
                   
                     
                       F 
                       R 
                     
                     ⁢ 
                     
                       CO 
                       2 
                     
                   
                   = 
                   
                     
                       
                         
                           ( 
                           
                             1 
                             - 
                             
                               
                                 V 
                                 exh 
                               
                               
                                 V 
                                 T 
                               
                             
                           
                           ) 
                         
                         × 
                         
                           FeCO 
                           2 
                         
                       
                       - 
                       
                         
                           
                             D 
                             ⁢ 
                             CO 
                           
                           2 
                         
                         
                           V 
                           T 
                         
                       
                     
                     
                       ( 
                       
                         1 
                         - 
                         
                           
                             V 
                             fg 
                           
                           
                             V 
                             T 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     Considering the confluence of fresh gas  16  and CO 2  outflow of the CO 2  canister  14  where the fresh as 14 free of CO 2  dilutes the recirculating CO 2  concentration from the CO 2  canister  14  to yield the inspired CO 2  concentration (FiCO 2 ):
 
 V   R   ×F   R CO 2   +V   fg   ×F   fg CO 2   =V   T   ×Fi CO 2   (4)
 
Since fresh gas is free of CO 2 , F fg CO 2 =0 yielding:
 
 V   R   ×F   R CO 2   =V   T   ×Fi CO 2  
 
Substituting V R =V T −V fg  and rearranging yields:
 
                       F   R     ⁢     CO   2       =         F   i     ⁢     CO   2         (     1   -       V   fg       V   T         )               (   5   )               
Further substitute (5) into (3) and solving for F i CO 2  yields:
 
     
       
         
           
             
               
                 
                   
                     
                       Fi 
                       ⁢ 
                       CO 
                     
                     2 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           1 
                           - 
                           
                             
                               V 
                               exh 
                             
                             
                               V 
                               T 
                             
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         FeCO 
                         2 
                       
                     
                     - 
                     
                       
                         
                           D 
                           ⁢ 
                           CO 
                         
                         2 
                       
                       
                         V 
                         T 
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     Still referring to  FIG. 2 , since V exh  is the net excess gas volume popped off from the circle breathing system  12  and the net excess gas volume is made up of fresh gas  16 , patient CO 2  production, O 2  uptake (metabolism), agent exchange and CO 2  absorbed by the CO 2  canister  14 . V exh  can be derived from the equation:
 
 V   exh   =V   CO     2     −D CO 2   +V   fg   −V   O     2     −V   AX   (7)
 
During anesthesia maintenance phase, V CO     2   , V O     2    fairly constant and at agent equilibrium the agent uptake V AX  is fairly constant and small compared to V CO     2    and V O     2   . For simplicity, let V C  represent the net gas exchange from the fresh gas and the patient, i.e.:
 
 V   C   =V   fg   +V   CO     2     −V   O     2     −V   AX , and
 
substituting V C  into (T) and (6) yield:
 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               Fi 
                               ⁢ 
                               CO 
                             
                             2 
                           
                           = 
                             
                           ⁢ 
                           
                             
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   
                                     
                                       
                                         V 
                                         C 
                                       
                                       - 
                                       
                                         
                                           D 
                                           ⁢ 
                                           CO 
                                         
                                         2 
                                       
                                     
                                     
                                       V 
                                       T 
                                     
                                   
                                 
                                 ) 
                               
                               ⁢ 
                               
                                 FeCO 
                                 2 
                               
                             
                             - 
                             
                               
                                 
                                   D 
                                   ⁢ 
                                   CO 
                                 
                                 2 
                               
                               
                                 V 
                                 T 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                             
                           ⁢ 
                           
                             
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   
                                     
                                       V 
                                       C 
                                     
                                     
                                       V 
                                       T 
                                     
                                   
                                 
                                 ) 
                               
                               ⁢ 
                               
                                 FeCO 
                                 2 
                               
                             
                             - 
                             
                               
                                 
                                   
                                     D 
                                     ⁢ 
                                     CO 
                                   
                                   2 
                                 
                                 
                                   V 
                                   T 
                                 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   
                                     FeCO 
                                     2 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   or 
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         Fi 
                         ⁢ 
                         CO 
                       
                       2 
                     
                     = 
                     
                       
                         
                           ( 
                           
                             1 
                             - 
                             
                               
                                 V 
                                 C 
                               
                               
                                 V 
                                 T 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           FeCO 
                           2 
                         
                       
                       - 
                       
                         
                           
                             D 
                             ⁢ 
                             CO 
                           
                           2 
                         
                         
                           V 
                           T 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       since 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         FeCO 
                         2 
                       
                     
                     ≅ 
                     0.05 
                     ⪡ 
                     1. 
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     Considering a sequence of regular breathing during anesthesia, leading, up to the n th  breath where the V T  and V CO     2    remain constant is:
 
 V   T   n   =V   T   n−1   = . . . =V   T  and  V   CO2   n−1   = . . . V   CO2  
 
At CO 2  break through, DCO 2  decreases as additional CO 2  is absorbed in each break.
 
     From C1 we have: 
     
       
         
           
             
               
                 
                   
                     
                       
                         Fe 
                         n 
                       
                       ⁢ 
                       
                         CO 
                         2 
                       
                     
                     = 
                     
                       
                         
                           Fi 
                           n 
                         
                         ⁢ 
                         
                           CO 
                           2 
                         
                       
                       - 
                       
                         
                           
                             V 
                             n 
                           
                           ⁢ 
                           
                             CO 
                             2 
                           
                         
                         
                           V 
                           T 
                           n 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       or 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         Fe 
                         n 
                       
                       ⁢ 
                       
                         CO 
                         2 
                       
                     
                     = 
                     
                       
                         
                           Fi 
                           n 
                         
                         ⁢ 
                         
                           CO 
                           2 
                         
                       
                       - 
                       
                         
                           
                             V 
                             ⁢ 
                             CO 
                           
                           2 
                         
                         
                           V 
                           T 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     From C8 we have: 
                         Fi   n     ⁢     CO   2       =         (     1   -     VC   VT       )     ⁢     Fe     CO   2       n   -   1         -         D   n     ⁢     CO   2         V   T   n           ⁢     
     ⁢   or   ⁢     
     ⁢         Fi   n     ⁢     CO   2       =         (     1   -     VC   VT       )     ⁢     Fe     n   -   1       ⁢     CO   2       -         D   n     ⁢     CO   2       VT                 (   10   )               
That is new inspired FiCO 2  concentration is the result of circulating the partially exhausted and absorbed patient CO 2  breath and further diluted by the fresh gas  16 . Since Fi n CO 2 , Fe n−1 CO 2 , V C , VT are measured, set or approximately known, D n CO 2  can be computed as:
 
                       D   n     ⁢     CO   2       =       {         (     1   -     VC   VT       )     ⁢     Fe     n   -   1       ⁢     CO   2       -       Fi     n   -   1       ⁢     CO   2         }     *   VT             (   11   )               
At the previous (n−1) breath,
 
     
       
         
           
             
               
                 
                   
                     Fi 
                     
                       CO 
                       2 
                     
                     
                       n 
                       - 
                       1 
                     
                   
                   = 
                   
                     
                       
                         ( 
                         
                           1 
                           - 
                           
                             VC 
                             VT 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         Fe 
                         
                           CO 
                           2 
                         
                         
                           n 
                           - 
                           2 
                         
                       
                     
                     - 
                     
                       
                         
                           D 
                           
                             n 
                             - 
                             1 
                           
                         
                         ⁢ 
                         
                           CO 
                           2 
                         
                       
                       VT 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     Depending on the design of the absorber canister  14 , and the absorbent, at CO 2  breakthrough the rate of change of CO 2  depletion as the absorbent is spent can be constant, linearly or nonlinearly proportion to the remaining capacity of the CO 2  absorbent. In this description, assuming that the change in depletion rate per breath is a constant D or,
 
 D   n−1 CO 2   =D   n CO 2   −D   (13)
 
     In order to extrapolate and predict the responses of FiCO 2  and FeCO 2 , D n CO 2  and D must be solved. Substituting (13) into (12) yield: 
     
       
         
           
             
               
                 
                   
                     
                       Fi 
                       
                         n 
                         - 
                         1 
                       
                     
                     ⁢ 
                     
                       CO 
                       2 
                     
                   
                   = 
                   
                     
                       
                         ( 
                         
                           1 
                           - 
                           
                             VC 
                             VT 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         Fe 
                         
                           n 
                           - 
                           2 
                         
                       
                       ⁢ 
                       
                         CO 
                         2 
                       
                     
                     - 
                     
                       
                         
                           
                             D 
                             n 
                           
                           ⁢ 
                           
                             CO 
                             2 
                           
                         
                         - 
                         D 
                       
                       VT 
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     Since D n CO 2  can be found from equation (11), D can be computed using measured and approximated values of Fe n−1 Co 2 , Fe n−2 CO 2 , V C , VT. With D known on a breath-to-breath basis the future response of F i   n+k CO2 can be predicted using the following set of equations: 
     Applying equation (10) to predict k number of breaths into the future yield, 
                       Fi   n     ⁢     CO   2       =         (     1   -     VC   VT       )     ⁢     Fe     n   -   1       ⁢     CO   2       -         D   n     ⁢     CO   2       VT               (     15   ⁢   a     )                   Fi     n   +   1       ⁢     CO   2       =         (     1   -     VC   VT       )     ⁢     Fe   n     ⁢     CO   2       -           D   n     ⁢     CO   2       +   D     VT               (     15   ⁢   b     )               ⋮   ⁢     
     ⁢   ⋮   ⁢     
     ⁢   or           (   15   )                   Fi     n   +   k       ⁢     CO   2       =         (     1   -     VC   VT       )     ⁢     Fe     n   +   k       ⁢     CO   2       -           D   n     ⁢     CO   2       +   kD     VT               (     15   ⁢   k     )               
Likewise applying equation (9) to predict k number of breaths into the future yields,
 
     
       
         
           
             
               
                 
                   
                     
                       Fe 
                       n 
                     
                     ⁢ 
                     
                       CO 
                       2 
                     
                   
                   = 
                   
                     
                       
                         Fi 
                         n 
                       
                       ⁢ 
                       
                         CO 
                         2 
                       
                     
                     + 
                     
                       
                         
                           V 
                           ⁢ 
                           CO 
                         
                         2 
                       
                       VT 
                     
                   
                 
               
               
                 
                   ( 
                   
                     16 
                     ⁢ 
                     a 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       Fe 
                       
                         n 
                         + 
                         1 
                       
                     
                     ⁢ 
                     
                       CO 
                       2 
                     
                   
                   = 
                   
                     
                       
                         Fi 
                         
                           n 
                           + 
                           1 
                         
                       
                       ⁢ 
                       
                         CO 
                         2 
                       
                     
                     + 
                     
                       
                         
                           V 
                           ⁢ 
                           CO 
                         
                         2 
                       
                       VT 
                     
                   
                 
               
               
                 
                   ( 
                   
                     16 
                     ⁢ 
                     b 
                   
                   ) 
                 
               
             
             
               
                 
                   ⋮ 
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   ⋮ 
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   or 
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       Fe 
                       
                         n 
                         + 
                         k 
                       
                     
                     ⁢ 
                     
                       CO 
                       2 
                     
                   
                   = 
                   
                     
                       
                         Fi 
                         
                           n 
                           + 
                           k 
                         
                       
                       ⁢ 
                       
                         CO 
                         2 
                       
                     
                     + 
                     
                       
                         
                           
                             V 
                             ⁢ 
                             CO 
                           
                           2 
                         
                         VT 
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   
                     16 
                     ⁢ 
                     k 
                   
                   ) 
                 
               
             
           
         
       
     
     The system of equations 15 and 16 can be iterated and solved sequentially to predict the CO 2  concentrations at the n+k breath, or the number of breaths k) needed to reach a concentration of FiCO 2  breakthrough. 
     In a particular example, assume that at breath n, the breakthrough inspired CO 2  FiCO 2  is at 0.1% and at breath n+k the breakthrough CO 2  is Fi n+k CO 2  is 0.5%. The time for the FiCO 2  to rise from 0.1% to 0.5% is therefore k times the breath interval. 
     Note that the user can change the values of say Vfg, VT, VCO 2  or other related ventilations parameter to predict “what if” situations if these parameters are varied. Such variation is helpful to assist the clinician to adjust future values of ventilation or the fresh gas  16  setting to prolong or better estimate the duration of CO 2  breakthrough, and for the given CO 2  canister  14  be replaced. 
     For linear and non-linear proportional changes in the depletion rate of absorbent, a similar approach can be used to iteratively solve these two sets of equations to predict future responses of FiCO 2  breakthrough. In this case, several breaths leading to the nth breath may be required to solve for D n CO 2  and the depletion profile of the absorbent. 
     Referring now to  FIG. 3 , a method of the present application is illustrated in the flow chart. In the method  100 , at the start of an anesthesia case, users set or default FiCO 2  thresholds for minimum measureable FiCO 2  and CO 2  absorbent replacement R input. In step  104 , V fg , Vmv, FiCO 2 , FeCO 2  from the anesthesia machine, ventilator and gas monitor are set and/or measured and inputted into the computing system. In step  106 , if the minimum detectable FiCO 2  is met, then the method moves on to step  108 . If the minimum detectable FiCO 2  is not met in step  106 , then the method remains at step  106  until the minimum detectable FiCO 2  is obtained. In step  108 , the CO 2  depletion model is updated and constants that describe the FiCO 2  response are computed, and in step  110 , if the user does not request an “what if” prediction, then the method continues to step  112 . It the user does request as “what if” predictions in step  110 , then the method continues to step  120 . 
     Still referring to the method  100 , in step  120 , the user alternate “what if” parameters are inputted. Examples of such inputs are fresh gas and ventilation parameters and the CO 2 . In step  122 , alternate “what if” parameters are used to extrapolate and compute the number of breaths to reach FiCO 2  threshold to replace the CO 2  absorbent. In step  124 , the replacement time is determined based on the number of breaths to threshold times the breath intervals, and in step  126 , the method reports and displays the “what if” ventilator and fresh gas delivery parameters, and time to replace the CO 2  absorbent. If this is the end of the anesthesia case in step  118 , then the method ends. If this is not the end of the anesthesia case, then the method goes back to step  104 . 
     Still referring to  FIG. 3  and the method  100 , in step  112  the set/measured parameters are used to extrapolate the number of breaths for FiCO 2  to reach a threshold to replace the CO 2  absorbent. In step  114 , the time for replacement is calculated by the number of breaths to the threshold times the breath intervals, and in step  116 , the current ventilator and fresh gas delivery parameters and time to replace the CO 2  absorbent are reported and displayed for the user. Once again, in step  118 , if the end of the anesthesia case has been reached, then the method ends. However, if the end of the anesthesia case has not been reached, then the method continues in step  104 . 
       FIG. 4  is a system diagram of an exemplary embodiment of as computing system  200  as may be used to implement embodiments of the method  100 , or in carrying out embodiments of portions of the anesthesia ventilator  10 . The computing system  200  includes a processing system  206 , storage system  204 , software  202 , communication interface  208 , and as user interface  210 . The processing system  206  loads and executes software  202  from the storage system  204 , including a software module  230 . When executed by the computing system  200 , software module  230  directs the processing system to operate as described herein in further detail in accordance with the method  200 , or a portion thereof. It should be noted that the computing system  200  may be configured in a number of locations proximate or remote from the anesthesia ventilator  10 . For example, the computing system  200  may be included in the ventilator  10  in the RFID reader  30 , and/or in any user workstation proximate to the ventilator  150  or remote in a practitioner&#39;s station, care station, or other computer station. 
     Although the computing system  200  as depicted in  FIG. 4  includes one application module  230  in the present example, it is to be understood that one or more modules could provide the same operations or that exemplary embodiments of the method  100  may be carried out by a plurality of modules  230 . Similarly, while the description as provided herein refers to a computing system  200  and a processing system  206 , it is to be recognized that implementations of such system can be performed by using one or more processors  206 , which may be communicatively connected, and such implementations are considered with be within the scope of the description. Exemplarily, such implementations may be used in carrying out embodiments of the system  10  depicted in  FIGS. 1 and 2 . 
     Referring back to  FIG. 4 , the processing system  206  can comprise a microprocessor or other circuitry that retrieves and executes software  202  from storage system  204 . Processing system  206  can be implemented within a single processing device but can also be distributed across multiple processing devices or sub-systems that cooperate in executing programming instructions. Examples of processing system  206  includes general purpose central processing units, application specific processor, and logic devices, as well as any other type of processing device, combinations of processing device, or variations thereof. The storage system  204  can include any storage media readable by the processing system  206  and capable of storing the software  202 . The storage system  304  can include volatile and non-volatile, removable and non-removable media implemented in any method of technology for storage of information such as computer readable instructions, data structures, program modules or other data. Storage system  204  can be implemented as a single storage device but may also be implemented across multiple storage devices or sub-systems. Storage system  204  can further include additional elements, such as a controller capable of communicating with the processing system  206 . 
     Examples of storage media include random access memory, read only memory, magnetic disc, optical discs, flash memory, virtual and non-virtual memory, magnetic sets, magnetic tape, magnetic disc storage or other magnetic storage devices or any other medium which can be used to store the desired information and that may be accessed by an instruction execution system, as well as any combination or variation thereof, or any other type of storage medium. In some implementations, the storage media can be a non-transitory storage media. It should be understood that in no case the storage media propagated signal. 
     User interface  210  can include a mouse, a keyboard, a voice input device, a touch input device for receiving a gesture from a user, a motion input device for detecting non-touch gestures, and other motions by a user, and other comparable input devices and associated processing elements capable of receiving user input from a user. User interface  210  can also include output devices such as a video display or a graphical display that can display an interface associated with embodiments of the systems and methods as disclosed herein. Speakers, printers, haptic devices, and other types of output devices may also be included in the user interface  210 . The user interface  210  is configured to receive user inputs  240  which in non-limiting embodiments may be irregularity user preferences as disclosed in further detail herein. It is also understood that embodiments of the user interface  210  can include a graphical display that presents the reports or alerts as described in further detail herein. 
     As has been described in further detail herein, the communication interface  208  is configured to receive gas measurement concentrations  220 . The anesthesia ventilator data  225  includes all data set of measured and utilized in the formulas discussed above with respect to  FIG. 2 . Accordingly, the gas measurement concentrations  220  and the rest of the anesthesia ventilator data  225  is inputted into the communication interface  208 . User input  240  as described in the description of  FIG. 2  and the method of  FIG. 3 , is input into the user interface  210 . The computing system  200  processes the measured patient gas concentrations  220  including concentrations of inspired and expired CO 2 , anesthesia ventilator data  225  and user input  240  according to the software  302  and method  100 , and as described in detail herein to produce output data  250  which may be pushed to one or more users through the user interface  310 . The output data  250  may include any analysis conducted by the computing system including current ventilator and fresh gas delivery parameters, time to replace CO 2  absorbent, “what if” ventilator and fresh gas delivery parameters, and “what if” time to replace CO 2  absorbent information. Further as described herein, the computing system  200  can output alerts, and/or reports  250  to the user, and may further accept user input  240 , such as but not limited to, setting off of alerts, modifications of the reports, and other administration of the alerts and data. 
     While the invention has been described with reference to preferred embodiments, those skilled in the art will appreciate that certain substitutions, alterations and omissions may be made to the embodiments without departing from the spirit of the invention. Accordingly, the foregoing description is meant to be exemplary only, and should not limit the scope of the invention as set forth in the following claims. 
     In the foregoing description, certain terms have been used for brevity, clearness, and understanding. No unnecessary limitations are to be inferred therefrom beyond the requirement of the prior art because such terms are used for descriptive purposes and are intended to be broadly construed. The different configurations, systems, and method steps described herein may be used alone or in combination with other configurations, systems and method steps. It is to be expected that various equivalents, alternatives and modifications are possible within the scope of the appended claims.