Patent Publication Number: US-11659834-B2

Title: Apparatus for tissue transport and preservation

Description:
RELATED APPLICATIONS 
     This application is a divisional application of U.S. non-provisional application Ser. No. 16/002795, filed Jun. 7, 2018, which application claims the benefit of and priority to U.S. provisional patent application Ser. Nos. 62/516,581, filed Jun. 7, 2017, 62/584,330, filed Nov. 10, 2017, and 62/650,610, filed Mar. 30, 2018, all of the contents of which are incorporated by reference herein in their entirety. 
    
    
     TECHNICAL FIELD 
     The disclosure relates to systems and methods for the storage and transportation of bodily tissue. 
     BACKGROUND 
     The current invention generally relates to devices, systems, and methods for extracorporeal preservation of bodily tissue. Extracorporeal preservation of bodily tissue is essential in transplant procedures so that donor tissue can be transported to a recipient in a remote location. In order to provide the best graft survival rates, donor tissues must be matched to appropriate recipients. Because of the sudden nature of most tissue donation events, appropriate recipients must be rapidly located and must be within a limited geographic area of the donor. Time limitations on the extracorporeal viability of donor tissue can lead to less than ideal tissue matching and, worse, wasted donor tissue. Prolonging the viability of donor tissue can allow for better matching between donor tissue and recipients and, in turn, can increase graft survival rates and increase availability of donor tissue to the growing waitlists of individuals in need of transplants. 
     The most prevalent current technique for preserving a bodily tissue for transplantation is static cold storage. While hypothermic temperatures decrease the oxygen demand of the bodily tissue, the tissue&#39;s viability is still time-limited by insufficient oxygen levels to meet the tissue&#39;s decreased metabolic needs. Another known technique for preserving a bodily tissue for transplantation includes the use of hypothermic perfusion devices that can perfuse the tissue with oxygenated perfusate, supplying additional oxygen to the tissue&#39;s cells and prolonging tissue viability. The portability of such known devices is limited, however, because such known devices are large and require a significant volume of compressed gas and electrical power. Furthermore, such known devices are very complex, which can lead to increased manufacturing costs and higher failure rates. 
     An additional limitation of hypothermic storage is the tendency to cause edema, or the accumulation of fluid within the bodily tissue. The level of edema generally increases with the length of hypothermic storage, providing another limitation on the amount of time that a tissue can be stored and remain viable. 
     Because of the time limitations on tissue viability, even given modern hypothermic storage and perfusion techniques, tissue and organs are often transported via air and, accordingly, subjected to pressure changes associated with changes in altitude. 
     SUMMARY OF THE INVENTION 
     Systems and methods of the invention are directed to increasing donor tissue viability during and after storage and transport. In particular, systems and methods relate to storage and transport of lungs. As noted above, tissue transported by air may be subjected to changes in pressure associated with increases and decreases in altitude during flight. While changes in pressure may affect any tissue being transported, they can be particularly harmful to lung tissue. In typical donor lung retrieval and preparation, the donor lung is inflated with air and the trachea or bronchus is stapled to hold the air in the partially inflated lung and to keep preservation fluid out of the airways during storage and transport. Unfortunately, this inflation occurs on the ground and, once subjected to decreases in air pressure from flights at high altitude, the pressure differential between the sealed lung airways and surrounding preservation fluid and air can result in over inflation of the lung and damage to the tissue including rupturing of the alveoli or other air passages. Accordingly systems and methods of the invention may be used to monitor and maintain a relatively constant pressure within donor lungs during transport and storage while maintaining a desired level of inflation. Systems and methods can accomplish those tasks while maintaining separation between the non-sterile airway environment and the sterilized outer tissue surfaces and preservation fluid to help prevent infection of the donor tissue or the transplant recipient. Expandable accumulators of the invention may have variable volume and may include a gauge to indicate the volume of the accumulator. In certain embodiments, the accumulator may be filled to a volume based on the atmospheric pressure at the recovery site in order to compensate for various ambient pressures based on altitude or weather conditions in different locations. Methods may include adjusting the volume of the accumulator based on the ambient pressure at the recovery site before organ transport. 
     In certain embodiments, an expandable accumulator is coupled to the airways of the donor lung(s) and sealed in fluid communication therewith. The expandable accumulator may be more compliant than the airways of the donor lung such that the expandable accumulator expands in response to a relative increase in the volume of gas (e.g., through a change in relative pressure) contained in the closed system formed by the lungs airways and accumulator. By expanding, the accumulator can accommodate and absorb the relative increases in gas volume, stabilizing pressure within the system, and preventing over-inflation of and damage to the lung tissue. 
     Another drawback of current lung transport techniques is that lungs are typically transported horizontally on a flat surface or on a bed of crushed ice. Both techniques are far different from the geometry and orientation of the lung&#39;s anatomical home. By resting the lung horizontally, gravity can crush or damage the bottom-most airways. A rough bed of crushed ice only complicates the issue. Accordingly, systems and methods of the invention may include replicating the geometry of the chest cavity and/or the orientation of the lung therein during transport and storage of donor lungs. In certain embodiments, a lung or pair of lungs may be placed horizontally on a smooth surface with a raised central saddle portion to replicate the spine. Alternatively, a lung or pair of lungs may be suspended in an upright position similar to the orientation of the lung in a standing human body. In such instances, the lung or lungs may be suspended by the trachea or bronchus which may be secured to a support tube in fluid communication with, for example, an expandable accumulator as described above. 
     Systems and methods of the invention have application in both static cold storage devices and hypothermic machine perfusion devices. In certain embodiments, hypothermic machine perfusion devices are configured to oxygenate and perfuse a bodily tissue for extracorporeal preservation of the bodily tissue. In lung applications, the perfusate may be pumped through the lung&#39;s vasculature and kept separate from the closed airway-accumulator air system described above. The perfusion apparatuses can include a pneumatic system, a pumping chamber, and an organ chamber. The pneumatic system may be configured for the controlled delivery of fluid to and from the pumping chamber based on a predetermined control scheme. The predetermined control scheme can be, for example, a time-based control scheme or a pressure-based control scheme. The pumping chamber is configured to diffuse a gas into a perfusate and to generate a pulse wave for moving the perfusate through a bodily tissue. The organ chamber is configured to receive the bodily tissue and the perfusate. The organ chamber is configured to substantially automatically purge excess fluid from the organ chamber to the pumping chamber. The pumping chamber may be configured to substantially automatically purge excess fluid from the pumping chamber to an area external to the apparatus. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    shows a system including a contained bellows-type expandable accumulator. 
         FIG.  2    shows a system including an exposed bellows-type expandable accumulator. 
         FIG.  3    shows a system including a rolling diaphragm expandable accumulator with a spring in compression providing expansion resistance. 
         FIG.  4    shows a system including a rolling diaphragm expandable accumulator with a spring in tension providing expansion resistance. 
         FIG.  5    shows a system including a balloon-type expandable accumulator. 
         FIG.  6    shows a system including a contained bellows-type expandable accumulator with a weight providing expansion resistance. 
         FIG.  7    shows a perfusion-type organ storage container with an expandable accumulator providing pressure control for a lumen of a stored organ. 
         FIGS.  8 A and  8 B  show an organ container with a raised central portion. 
         FIG.  9    shows a pair of lungs disposed on the raised central portion of an organ container 
         FIGS.  10 A and  10 B  show an organ adapter. 
         FIG.  11    shows an external view of a closed organ container with an accumulator according to certain embodiments. 
         FIG.  12    shows an exploded view of an organ container with an accumulator according to certain embodiments. 
         FIG.  13    shows a cross-sectional view of a closed organ container with an accumulator according to certain embodiments. 
         FIG.  14    shows an external view of an open organ container with an accumulator according to certain embodiments. 
         FIG.  15    shows an external view of an open organ container with an accumulator and a support tray according to certain embodiments. 
         FIG.  16 A  shows a transverse cross-sectional view of an approximately empty accumulator according to certain embodiments. 
         FIG.  16 B  shows a lateral cross-sectional view of an approximately empty accumulator according to certain embodiments. 
         FIG.  17    shows a lateral cross-sectional view of an approximately half full accumulator according to certain embodiments. 
         FIG.  18    shows a lateral cross-sectional view of an approximately full accumulator according to certain embodiments. 
         FIG.  19    shows an exploded view of an accumulator according to certain embodiments. 
         FIG.  20    shows a pressure vs. volume curve for an ex-vivo lung model. 
         FIG.  21    shows lung pressure and volume across a range of ambient (atmospheric) pressures during transit without an accumulator based on various atmospheric pressures at recovery. 
         FIG.  22    shows lung pressure and volume across a range of ambient (atmospheric) pressures during transit without an accumulator with recovery at 1 atm. 
         FIG.  23    shows lung pressure and volume across a range of ambient (atmospheric) pressures during transit with a spring-based accumulator based on various atmospheric pressures at recovery. 
         FIG.  24    shows lung pressure and volume across a range of ambient (atmospheric) pressures during transit with a spring-based accumulator with recovery at 1 atm. 
         FIG.  25    shows lung pressure and volume across a range of ambient (atmospheric) pressures during transit with a weight-based accumulator based on various atmospheric pressures at recovery. 
         FIG.  26    shows lung pressure and volume across a range of ambient (atmospheric) pressures during transit with a weight-based accumulator with recovery at 1 atm. 
     
    
    
     DETAILED DESCRIPTION 
     Devices, systems and methods are described herein that are configured for extracorporeal preservation and transportation of bodily tissue. Specifically, devices for monitoring and stabilizing pressure within inflated lungs are described. Systems and methods can compensate for pressure changes resulting from, for example, increases and decreases in altitude during air transport of the organ. By bleeding off and returning excess gases, volumetric expansion of the lung (i.e., over-inflation) may be prevented, avoiding damaging the organ which can result in decreased organ viability and decreased survival rates for transplant recipients. Additional aspects include contoured storage and transport chambers that can replicate the in-vivo anatomical orientation and geometry for a given organ. For example, a pair of donor lungs may be placed against a smooth, raised, central saddle designed to replicate the spine that the lungs would be resting against in vivo. Organs, such as lungs or hearts, may be suspended in an upright position to replicate the organ&#39;s orientation in a standing human and to prevent tissue damage caused by pressure from the organ&#39;s own weight resting on itself. 
       FIG.  1    illustrates a tissue preservation and transportation system  101  according to certain embodiments. An organ adapter  107  is adapted to be coupled to the airways (e.g., by the trachea or bronchus) of a lung  103 . The organ adapter  107  may comprise a lumen that, when the organ adapter  107  is coupled to the lung  103 , is in fluid communication with the airways of the lung  103 . 
     The organ adapter  107  is coupled to an expandable accumulator  105  and the lumen of the organ adapter  107  is in fluid communication with a sealed interior volume of the expandable accumulator  105 . The expandable accumulator  105  may be coupled by a valve  109 , to an inlet  113 . The inlet  113  has a lumen that, when the valve  109  is open, is in fluid communication with the interior volume of the expandable accumulator  105 , the lumen of the organ adapter  107 , and the airways of the lung  103 . When the valve  109  is closed, the interior volume of the expandable accumulator  105 , the lumen of the organ adaptor  107 , and the airways of the lung  103  form an air-tight, closed environment that is sealed from the outside environment including, for example, any preservation fluid present within the organ container  111 . The organ container  111  may include one or more boxes or bags configured to contain both the organ and any preservation fluid (e.g., temperature regulated, oxygenated fluid) in a sterilized environment. In preferred embodiments, the organ is placed into one or more sterile bags or boxes. For example, a lung may be placed in three concentric sterile bags fitted with a through-the-bag-wall cannula leading into the trachea plug. The cannula may include a filter for each bag (e.g., a 0.2-micron sterile filter). Accordingly, both the exterior surface and interior, pressure-dampened lumen of the organ are surrounded by three sterile layers. 
     In various embodiments, the accumulator may have an interior volume (fully expanded) of about, 0.5, 0.75, 1, 1.25, 1.5, 1.75, 2, 2.5, 3, 3.5, 4, 4.5, or more liters. In preferred embodiments, the accumulator has a fully expanded interior volume of about 1 liter. 
     System  101  is configured to permit gas to move back and forth between the airways of the lung  103  through the lumen of the organ adapter  107 , and into the interior volume of the expandable accumulator  105 . When the valve  109  is open, the system  101  is configured to permit gas flow from the inlet  113 , through the valve  109 , into the lumen of the organ adaptor  107 , and finally into the airways of the lung  103 . The expansion resistance of the expandable accumulator  105  may be adjustable, fixed, or progressive. 
     The organ adapter  107  may be configured to substantially retain the bodily tissue (e.g., lung) with respect to the expandable accumulator  105 . The organ adapter  107  may be configured to permit movement of a gas from the expandable accumulator  105 , into the airways of the lung  103 , and back. The organ adapter  107  can be configured to be coupled to a bodily tissue such as a lung  103 . The organ adapter  107  can be coupled to the bodily tissue in any suitable manner For example, in some embodiments, the organ adapter  107  can configured to be sutured to the bodily tissue. In another example, the organ adapter  107  is coupleable to the bodily tissue via an intervening structure, such as silastic or other tubing. In some embodiments, at least a portion of the organ adapter  107 , or the intervening structure, is configured to be inserted into the bodily tissue such as the lumen of a trachea, bronchus, or other air passage of a lung  103 . For example, in some embodiments, the lumen of the organ adapter  107  (or a lumen of the intervening structure) is configured to be fluidically coupled to a lumen of the bodily tissue such as an air passage of the lung  103 . 
     In various embodiments including the use of one or more sterile bags or other containers for the organ, the organ adapter may be contained in or integral to the inner most sterile bag and coupled to a through-the-bag-wall cannula that transverses each of the bags or other containers. The cannula, at the outer most bag or other container, may include an adapter to be removably coupled to the accumulator in the systems described herein. Accordingly, the bagged organ may be easily and quickly connected to the accumulator and inflated during loading and easily and quickly disconnected upon arrival at the transplantation site. 
     In some embodiments, the organ adapter (or simply referred as the adapter) can be configured to support the bodily tissue when the bodily tissue is coupled to the adapter. For example, in some embodiments, the adapter can include a retention mechanism (not shown) configured to be disposed about at least a portion of the bodily tissue and to help retain the bodily tissue with respect to the adapter. The retention mechanism can be, for example, a net, a cage, a sling, or the like. In some embodiments, the system can include a basket (not shown) or other support mechanism configured to support the bodily tissue when the bodily tissue is coupled to the adapter or otherwise received in the system. The organ adapter may be rigidly coupled to an interior wall (e.g. a lid) of an organ container such that the organ may be suspended via its connection point to the adapter. 
     The portion of the adapter that is inserted into a lumen of the organ may include a series of tapered steps such that a distal end of the adapter portion is narrower than a proximal end. In this manner, the adapter is configured to be inserted into a range of lumen sizes. 
     The lumen may be secured or sealed to the organ adapter via any means including elastic tension in the organ lumen itself or through the use of sutures, elastic band, or other securing mechanisms on the outside of the lumen applying pressure thereupon to form an air-tight seal between the lumen of the organ and the lumen of the adapter. 
     The expandable accumulator is configured to expand to accept relative increases in gas volume within the closed system in response to pressure differential changes between the closed system and the surrounding environment (e.g., during flight). The interior volume of the expandable accumulator should resist expansion with an opposing force that is less than that of the lung. Accordingly, decreases in internal pressure of the closed system due to decreases in the pressure of the surrounding environment (e.g. during flight) will be borne by the expandable accumulator such that the pressure within the system drops without volumetric expansion of the lung airways (which could cause tissue damage or rupture the airways). 
     The expandable accumulator is configured to be in constant communication with the internal (closed system) pressure and the external (surrounding environment) pressure, and to establish a nearly-constant differential between the two while having compliance higher than the lung&#39;s compliance. The pressure differential is such that the internal pressure is greater than the environment pressure. The pressure differential keeps the lungs inflated. The pressure differential would commonly be referred to as the gauge pressure. When the system is initially prepared, the external pressure may be 1 bar (absolute) and the internal pressure would be 1+x bar, absolute (where the x is a suitable value chosen for best storage performance). The gauge pressure of the closed system is therefore x bar, and the differential pressure across the lung is also x bar. At a later time, in transport, the external pressure may be 0.75 bar for instance due to airplane cabin pressure when in flight. The internal pressure would be 0.75+x bar, so the gauge pressure is again x bar, as is the pressure across the lung. In this manner the expandable accumulator maintains a nearly-constant pressure differential across the lung (from inside to outside). 
     In order to maintain the nearly-constant pressure differential the expandable accumulator will have a very high compliance, for example much higher than the lung compliance. In certain embodiments, the system may be configured to maintain about a 15 cm H 2 O gauge pressure inside the organ. The pressure may be fixed or may be tunable or adjustable using variable weight, spring tension, or other means depending on the accumulator mechanism. Pressure in the system may be set by filling the system to a desired fixed pressure or may be controlled using an adjustable accumulator which may be acted on by a computer based on inputs received from a pressure or other sensor as described below. 
     An inlet of the system may be used to add or remove a gas from the lumen of the organ (e.g., airways of a lung). For example, where donor lungs are at least partially inflated for storage and transport, a retrieved lung may be secured to an organ adapter as shown in  FIGS.  1 - 6   . The inlet may be then connected to a gas source such as a compressed air tank or a source of oxygen or another gas or combinations thereof. In certain embodiments, the gas source may comprise a pump or bulb for manually filling the system with ambient air or other gas. The pump or bulb may be integral to the transport container and travel with the container or may be used to establish pressure and removed after a valve located between the pump or bulb and the organ is closed. The valve connecting the inlet to the closed system of the lung airways, lumen of the adapter, and interior volume of the expandable accumulator may then be opened and oxygen or another gas or mixture of gasses may then be allowed to flow into the closed system. In certain embodiments (e.g., lung transport), gasses such as oxygen may damage the tissue and, as such, the fill gas will be selected accordingly (e.g., ambient air). The closed system may be inflated to a desired pressure which may be monitored with a pressure gauge or sensor located on the gas source or on the closed system. The pressure sensor may be electric and include a wireless sender located on the closed system such that pressure may be wirelessly monitored from outside an organ transport container during transport. 
     During inflation, as gas is admitted to the system, both the lungs and the expandable accumulator will inflate until reaching the desired gauge pressure (designated “x” above). As additional gas is thereafter admitted, the gas would preferentially fill the expandable accumulator given that component&#39;s higher compliance. When the expandable accumulator is entirely filled, the pressure would begin to rise above the “x” target, and the system would not have any remaining capacity. Therefore, when the system is filled the volume of gas may be adjusted such that a movable element of the expandable accumulator rests at a target position (for instance 25% of travel). Once the expandable accumulator is at that target position, the valve can be closed and the closed system is sealed and ready for transport. 
     Once the lung has been inflated to a desired pressure, the valve may be closed, sealing off the closed system. The lung coupled to the expandable accumulator by the organ adapter along with the closed valve and the inlet may be then be placed in an organ container for storage or transport and may be at least partially submerged in a fluid such as a preservation fluid as known in the art. Examples of preservation fluid and static and perfusion-based tissue containers compatible with systems and methods of the invention are described in U.S. application Ser. No. 14/460,489, incorporated herein by reference. 
     The fill of the accumulator can be adjusted at organ recovery according to the local ambient (e.g. barometric) pressure. A smaller accumulator would thereby be able to work identically whether filled in Denver CO, or Boston Mass., whatever the weather conditions. The accumulator may include a scale or other indicator in customary barometric pressure units. An exemplary pressure indicator  1115  is shown in  FIGS.  11 ,  14 ,  15 , and  19   . An ambient pressure sensor or meter may also be included for reading ambient pressure at recovery. The system may then be filled until the piston reaches a mark on the scale or indicator on the accumulator that matches the local barometric pressure reading. If not adjusted to local pressure conditions, a larger accumulator may be used. 
     The expandable accumulator may be of any configuration that permits expansion of its interior volume with less resistance than that of the lung&#39;s airways. Examples of expandable accumulators are shown in  FIGS.  1 - 6   . Materials for transport and storage containers of the invention may be selected to reduce weight in key components such as the accumulator. For example, accumulators such as the rolling diaphragm types depicted in  FIGS.  3  and  4    may comprise a piston that slides within a cylinder to adjust volume to dampen pressure changes in the tissue. The piston or other accumulator components may be constructed of lightweight materials such as aluminum, plastics, or carbon fiber or may be constructed with lightweight techniques including low material thickness with structural bracing for example. Reducing the weight or mass of the moving pieces of the accumulator helps to minimize pressure changes resulting from movement (e.g., tilting) of the container or accumulator therein. Pressure generating force is thereby primarily established by an accumulator spring and relatively unaffected by gravity. 
     The expandable accumulator  105  depicted in  FIG.  1    comprises a bellows-type interior bladder that permits expansion. The bellows may be contained within a shell that may be rigid to preserve an open interior volume into which the bellows can expand. The bellows may rely on inherent shape memory in the material of the bellows itself to provide resistance to expansion or may use, for example, springs opposing the expansion of the bellows via compression or tension. Any known spring type may be used including coiled materials or elastic bands to provide expansion resistance. The spring rate can be selected such that the expansion resistance provided to the interior volume of the accumulator is less than the expansion resistance of the lung&#39;s airways. The expansion resisting force may be a single rate or may be progressive or adjustable. The expansion resisting force can be modeled on the expansion resistance profile of lung airways in order to better maintain a constant pressure within the lung. In various embodiments, a constant force spring can be used to maintain internal pressure. Constant force springs are springs for which the force they exert over their range of motion is relatively constant. Constant force springs may be constructed from rolled ribbons of, for example, spring steel. In certain embodiments, the springs used in the systems depicted in  FIGS.  3  and  4    may be constant force springs. In some embodiments, a pair of constant force springs may be used in a back-to-back orientation. 
       FIG.  2    shows a system  201  including a lung  203 , an organ adapter  207 , an expandable accumulator  205 , a valve  209 , and an inlet  213  all placed within an organ container  211 . The components are configured and relate to each other in a similar manner to that shown in  FIG.  1    aside from differences in the operation of the expandable accumulator  205 . The expandable accumulator  205  comprises a bellows type accumulator  205  that is not contained in a shell such that the outer surface of the expandable accumulator  205  is in direct communication with the interior environment of the organ container  211 . The expandable accumulator  205  may provide expansion resistance through its own material properties or through applied force from, for example, a spring. 
       FIG.  3    shows a system  301  including a lung  303 , an organ adapter  307 , an expandable accumulator  305 , a valve  309 , and an inlet  313  all placed within an organ container  311 . The components are configured and relate to each other in a similar manner to that shown in  FIG.  1    aside from differences in the operation of the expandable accumulator  305 . The expandable accumulator  305  comprises a rolling diaphragm and a spring in compression to provide expansion resistance. 
     The rolling diaphragm contributes to a low-friction, low-hysteresis accumulator advantageous to tissue preservation as described herein, especially in lung preservation and transport apparatuses. The diaphragm may be constructed of any suitable material including latex, rubber, or silicon. 
       FIG.  4    shows a system  401  including a lung  403 , an organ adapter  407 , an expandable accumulator  405 , a valve  409 , and an inlet  413  all placed within an organ container  411 . The components are configured and relate to each other in a similar manner to that shown in  FIG.  3    aside from differences in the operation of the expandable accumulator  405 . The expandable accumulator  405  comprises a rolling diaphragm and a spring in tension to provide expansion resistance. 
     A diaphragm-type accumulator system as exemplified in  FIGS.  3  and  4    may use a constant force spring to maintain a constant internal pressure in the lung or other organ. The diaphragm may be coupled to one or more springs in tension, compression, or some combination thereof (e.g., two opposing springs coupled to the diaphragm and providing expansion resistance through both compression and tension). 
       FIG.  5    shows a system  501  including a lung  503 , an organ adapter  507 , an expandable accumulator  505 , a valve  509 , and an inlet  513  all placed within an organ container  511 . The components are configured and relate to each other in a similar manner to that shown in  FIG.  1    aside from differences in the operation of the expandable accumulator  205 . The expandable accumulator  505  comprises a balloon-type bladder wherein expansion resistance is provided by the elasticity of the material comprising the walls of the expandable accumulator  505 . As shown in  FIG.  5   , the lungs  503  are suspended in a vertical orientation from the organ adapter  507  providing the benefits described above. 
       FIG.  6    shows a system  601  including a lung  603 , an organ adapter  607 , an expandable accumulator  605 , a valve  609 , and an inlet  613  all placed within an organ container  611 . The components are configured and relate to each other in a similar manner to that shown in  FIG.  1    aside from differences in the operation of the expandable accumulator  605 . The expandable accumulator  105  depicted in  FIG.  1    comprises a bellows-type interior bladder that permits expansion. The bellows may be contained within a shell that may be rigid to preserve an open interior volume into which the bellows can expand. The bellows may rely on inherent shape memory in the material of the bellows itself to provide resistance to expansion or may use, for example, gravity to provide the expansion resistance through a weight  615  placed on top of the bellows. 
     As noted, systems of the invention are compatible with and may include any static or perfusion-type preservation apparatus. An example of such a configuration is shown in  FIG.  7   . An apparatus  10  is shown configured to oxygenate a perfusate (not shown) received in a pumping chamber  14  of the apparatus. The apparatus  10  includes a valve  12  configured to permit a fluid (e.g., oxygen) to be introduced into a first portion  16  of the pumping chamber  14 . A membrane  20  is disposed between the first portion  16  of the pumping chamber  14  and a second portion  18  of the pumping chamber. The membrane  20  is configured to permit the flow of a gas between the first portion  16  of the pumping chamber  14  and the second portion  18  of the pumping chamber through the membrane. The membrane  20  is configured to substantially prevent the flow of a liquid between the second portion  18  of the pumping chamber  14  and the first portion  16  of the pumping chamber through the membrane. In this manner, the membrane can be characterized as being semi-permeable. 
     The membrane  20  is disposed within the pumping chamber  14  along an axis Al that is transverse to a horizontal axis A 2 . Said another way, the membrane  20  is inclined, for example, from a first side  22  to a second side  24  of the apparatus  10 . As such, as described in more detail below, a rising fluid in the second portion  18  of the pumping chamber  14  will be directed by the inclined membrane  20  towards a port  38  disposed at the highest portion of the pumping chamber  14 . The port  38  is configured to permit the fluid to flow from the pumping chamber  14  into the atmosphere external to the apparatus  10 . In some embodiments, the port  38  is configured for unidirectional flow, and thus is configured to prevent a fluid from being introduced into the pumping chamber  14  via the port (e.g., from a source external to the apparatus  10 ). In some embodiments, the port  38  includes a luer lock. 
     The second portion  18  of the pumping chamber  14  is configured to receive a fluid. In some embodiments, for example, the second portion  18  of the pumping chamber  14  is configured to receive a liquid perfusate. The second portion  18  of the pumping chamber  14  is in fluid communication with an adapter  26 . The adapter  26  is configured to permit movement of the fluid from the pumping chamber  14  to a bodily tissue T. For example, in some embodiments, the pumping chamber  14  defines an aperture (not shown) configured to be in fluidic communication with a lumen (not shown) of the adapter  26 . The adapter  26  is configured to be coupled to the bodily tissue T. The adapter  26  can be coupled to the bodily tissue T in any suitable manner For example, in some embodiments, the adapter  26  is configured to be sutured to the bodily tissue T. In another example, the adapter  26  is coupleable to the bodily tissue T via an intervening structure, such as silastic or other tubing. In some embodiments, at least a portion of the adapter  26 , or the intervening structure, is configured to be inserted into the bodily tissue T. For example, in some embodiments, the lumen of the adapter  26  (or a lumen of the intervening structure) is configured to be fluidically coupled to a vessel of the bodily tissue T. 
     Where the tissue T is, for example a lung, the airways of the tissue T may be coupled to an expandable accumulator  705  and associated systems as described herein via an organ adapter  707  (e.g., via the trachea or bronchus). 
     In some embodiments, the adapter  26  is configured to support the bodily tissue T when the bodily tissue T is coupled to the adapter. For example, in some embodiments, the adapter  26  includes a retention mechanism (not shown) configured to be disposed about at least a portion of the bodily tissue T and to help retain the bodily tissue T with respect to the adapter. The retention mechanism can be, for example, a net, a cage, a sling, or the like. In some embodiments, the apparatus  10  includes a basket (not shown) or other support mechanism configured to support the bodily tissue T when the bodily tissue T is coupled to the adapter  26  or otherwise received in the apparatus  10 . 
     An organ chamber  30  is configured to receive the bodily tissue T and a fluid. In some embodiments, the apparatus  10  includes a port  34  that is extended through the apparatus  10  (e.g., through the pumping chamber  14 ) to the organ chamber  30 . The port  34  is configured to permit fluid (e.g., perfusate) to be introduced to the organ chamber  30 . In this manner, fluid can be introduced into the organ chamber  30  as desired by an operator of the apparatus. For example, in some embodiments, a desired amount of perfusate is introduced into the organ chamber  30  via the port  34 , such as before disposing the bodily tissue T in the organ chamber  30  and/or while the bodily tissue T is received in the organ chamber. In some embodiments, the port  34  is a unidirectional port, and thus is configured to prevent the flow of fluid from the organ chamber  30  to an area external to the organ chamber through the port. In some embodiments, the port  34  includes a luer lock. The organ chamber  30  may be of any suitable volume necessary for receiving the bodily tissue T and a requisite amount of fluid for maintaining viability of the bodily tissue T. In one embodiment, for example, the volume of the organ chamber  30  is approximately 2 liters. 
     The organ chamber  30  is formed by a canister  32  and a bottom portion  19  of the pumping chamber  14 . In a similar manner as described above with respect to the membrane  20 , an upper portion of the organ chamber (defined by the bottom portion  19  of the pumping chamber  14 ) can be inclined from the first side  22  towards the second side  24  of the apparatus. In this manner, as described in more detail below, a rising fluid in the organ chamber  30  will be directed by the inclined upper portion of the organ chamber towards a valve  36  disposed at a highest portion of the organ chamber. The valve  36  is configured to permit a fluid to flow from the organ chamber  30  to the pumping chamber  14 . The valve  36  is configured to prevent flow of a fluid from the pumping chamber  14  to the organ chamber. The valve  36  can be any suitable valve for permitting unidirectional flow of the fluid, including, for example, a ball check valve. 
     The canister  32  can be constructed of any suitable material. In some embodiments, the canister  32  is constructed of a material that permits an operator of the apparatus  10  to view at least one of the bodily tissue T or the perfusate received in the organ chamber  30 . For example, in some embodiments, the canister  32  is substantially transparent. In another example, in some embodiments, the canister  32  is substantially translucent. The organ chamber  30  can be of any suitable shape and/or size. For example, in some embodiments, the organ chamber  30  can have a perimeter that is substantially oblong, oval, round, square, rectangular, cylindrical, or another suitable shape. 
     In use, the bodily tissue T is coupled to the adapter  26 . The pumping chamber  14  is coupled to the canister  32  such that the bodily tissue T is received in the organ chamber  30 . In some embodiments, the pumping chamber  14  and the canister  32  are coupled such that the organ chamber  30  is hermetically sealed. A desired amount of perfusate is introduced into the organ chamber  30  via the port  34 . The organ chamber  30  can be filled with the perfusate such that the perfusate volume rises to the highest portion of the organ chamber. The organ chamber  30  can be filled with an additional amount of perfusate such that the perfusate flows from the organ chamber  30  through the valve  36  into the second portion  18  of the pumping chamber  14 . The organ chamber  30  can continue to be filled with additional perfusate until all atmospheric gas that initially filled the second portion  18  of the pumping chamber  14  rises along the inclined membrane  20  and escapes through the port  38 . Because the gas will be expelled from the pumping chamber  14  via the port  38  before any excess perfusate is expelled (due to gas being lighter, and thus more easily expelled, than liquid), an operator of the apparatus  10  can determine that substantially all excess gas has been expelled from the pumping chamber when excess perfusate is released via the port. As such, the apparatus  10  can be characterized as self-purging. When perfusate begins to flow out of the port  38 , the apparatus  10  is in a “purged” state (i.e., all atmospheric gas initially within the organ chamber  30  and the second portion  18  of the pumping chamber  14  has been replaced by perfusate). When the purged state is reached, the operator can close both ports  34  and  38 , preparing the apparatus  10  for operation. 
     Oxygen (or another suitable fluid, e.g., gas) is introduced into the first portion  16  of the pumping chamber  14  via the valve  12 . A positive pressure generated by the introduction of oxygen into the pumping chamber  14  causes the oxygen to be diffused through the semi-permeable membrane  20  into the second portion  18  of the pumping chamber. Because oxygen is a gas, the oxygen expands to substantially fill the first portion  16  of the pumping chamber  14 . As such, substantially the entire surface area of the membrane  20  between the first portion  16  and the second portion  18  of the pumping chamber  14  is used to diffuse the oxygen. The oxygen is diffused through the membrane  20  into the perfusate received in the second portion  18  of the pumping chamber  14 , thereby oxygenating the perfusate. 
     In the presence of the positive pressure, the oxygenated perfusate is moved from the second portion  18  of the pumping chamber  14  into the bodily tissue T via the adapter  26 . For example, the positive pressure can cause the perfusate to move from the pumping chamber  14  through the lumen of the adapter  26  into the vessel of the bodily tissue T. The positive pressure is also configured to help move the perfusate through the bodily tissue T such that the bodily tissue T is perfused with oxygenated perfusate. 
     After the perfusate is perfused through the bodily tissue T, the perfusate is received in the organ chamber  30 . In this manner, the perfusate that has been perfused through the bodily tissue T is combined with perfusate previously disposed in the organ chamber  30 . In some embodiments, the volume of perfusate received from the bodily tissue T following perfusion combined with the volume of perfusate previously disposed in the organ chamber  30  exceeds a volume (e.g., a maximum fluid capacity) of the organ chamber  30 . A portion of the organ chamber  30  is flexible and expands to accept this excess volume. The valve  12  can then allow oxygen to vent from the first portion  16  of the pumping chamber  14 , thus, reducing the pressure in the pumping chamber  14 . As the pressure in the pumping chamber  14  drops, the flexible portion of the organ chamber  30  relaxes, and the excess perfusate is moved through the valve  36  into the pumping chamber  14 . The cycle of oxygenating perfusate and perfusing the bodily tissue T with the oxygenated perfusate can be repeated as desired. 
       FIGS.  8 A and  8 B  show an organ container  811  comprising a smooth raised portion  815  or saddle disposed on an interior wall of the organ container and designed to mimic the shape of the spine to replicate the in vivo environment of lungs being stored or transported. Such organ containers  811  are compatible with any other systems described herein including perfusing or static storage containers and various pressure regulating systems.  FIG.  9    shows positioning of a pair of donor lungs  915  on a raised center portion  915  of an organ container  911  intended to mimic the spine in the lungs&#39; in vivo environment. 
     The interior of organ containers of the invention may contain a fixed or removable shelf or tray configured to support cooling materials (e.g., frozen gel packs). Such a tray allows the organ to be loaded into the container before the tray is in place and, once the tray is inserted, the tray supports the cooling materials keeping them proximate to the organ for cooling purposes but prevents the materials from contacting the organ which can cause damage thereto. The tray may further serve to locate the organ within the colder bottom portion of the container. 
       FIGS.  10 A and  10 B  show an organ adapter  1007  configured for insertion into the trachea of a donor lung to be transported using a tissue preservation and transportation system as described above. The organ adapter  1007  may taper as shown in  FIGS.  10 A and  10 B  to form an air-tight seal against the interior surface of the trachea or other organ opening to be transported and may include ridges  1017  to aid retention of the adapter  1007  within the organ opening once inserted. The organ adapter  1007  includes tubing  1015  for connecting to an expandable accumulator as described above and includes an inner lumen  1019  for providing fluid communication between the accumulator and the interior of the organ. Once inserted into the organ, the organ adapter  1007 , interior space of the organ, and the accumulator form a closed, air-tight system. 
     Systems of the invention may include a variety of sensors configured to sense and report, for example, temperature of the tissue, temperature of a preservation fluid or perfusate, pressure within the closed air system, pressure within the fluid, or ambient pressure. Displays for the sensors may be disposed on the outer surfaces of the organ transport or may be wirelessly linked to the internal sensors. 
     In some embodiments, a temperature sensor may include a probe positioned in the transport cavity and attached by a flexible cable to a temperature datalogger. The probe may not be wetted (i.e., the probe would remain outside of any sterile bags or containers) and may be suspended in air by a bracket or support in order to avoid direct contact with any cooling materials. The probe would thereby record and/or report the cavity temperature rather than the lung tissue temperature. 
     In certain embodiments, the sensor may comprise a mechanical flag that indicates the furthest expansion of the expandable accumulator and can therefore indicate if the accumulator reached maximum expansion presenting the possibility that additional pressure was absorbed by the lung tissue through over-inflation. 
       FIG.  11    shows an exemplary organ container  1101  with an accumulator  1105  having an accumulator scale  1115  to indicate barometric pressure. As noted above, the indicator may be used by technicians when adjusting the accumulator to local pressure conditions. The organ container  1101  may include a recess, port, or other feature for retaining the accumulator  1105 , preferably, as shown in  FIG.  11   , in a position that allows for external monitoring of the accumulator  1105 . The organ container may include wheels and an extendable handle as shown for ease of transport and storage. 
       FIG.  12    shows an exploded view of an exemplary organ container  1101 . The organ container  1101  features an accumulator  1105 , a gas source  1113  (e.g., a bulb) for pressurizing the system, and an organ adapter  1107  (e.g., a trachea plug) for interfacing an organ with the system. The organ container  1101  also includes tubing  1111  or connectors for coupling the gas source  1113  and the organ adapter  1107  to the accumulator  1105 . The organ container  1101  may also use a valve  1109  (e.g., a roller clamp) operable to regulate fluid communication between the gas source  1113  and the accumulator  1105  by, for example, acting on the tubing  1111 . 
       FIG.  13    shows a cross-sectional view of an exemplary organ container  1101  illustrating an exemplary configuration of various components described herein including an accumulator  1105  an organ adapter  1107  (not coupled to an organ) and connecting tubing  1111 . A sensor  1117  (e.g., a temperature sensor) as described above, is also included at the bottom of the organ camber and, while potentially wireless in some embodiments, is depicted in  FIG.  13    in a wired format in electronic communication with an external display  1119  (e.g., an LCD screen) to display data obtained from the sensor  1117 . An organ such as a lung would rest on the bottom of the cavity. 
       FIG.  14    shows an external view of an open organ container  1101  with an accumulator  1105  according to certain embodiments. With the lid removed from the exemplary organ container  1101 , it is ready to accept or deliver an organ. The accumulator  1105  with a pressure indicator  1115  is shown placed in a fitted receptacle on the organ container  1101 . A gas source  1113  is connected by tubing  1111  to the accumulator  1105  and that connection is regulated by a valve  1109 . The organ container  1101  also features a storage pocket  1121  for receiving and storing the gas source  1113 , valve  1109 , and tubing  1111  when not in use. The illustrated organ container  1101  does not have an organ loaded and so the organ adapter  1107  inside the cavity is seen. 
       FIG.  15    shows an external view of an open organ container  1101  with an accumulator  1105  with pressure indicator  1115 . A tray  1123  is adapted to be positioned above a loaded organ in the cavity of the organ container  1101  to hold cooling materials such as frozen gel packs off of the organ tissue surface. The tray may be supported by, for example, indentions in the interior walls of the cavity. The gas source  1113  is shown stored in the storage pocket  1121  for transport. 
       FIG.  16 A  shows a transverse cross-sectional view of an approximately empty accumulator  1105  according to certain embodiments and  FIG.  16 B  shows a lateral cross-sectional view. The accumulator  1105  includes a piston  1125  and a rolling diaphragm  1127  as described above. As seen in  FIG.  16 B , a pair of back-to-back constant force springs  1129  comprising rolled ribbons of, for example, spring steel. 
       FIG.  17    shows a lateral cross-sectional view of an approximately half full accumulator  1105  and  FIG.  18    shows a lateral cross-sectional view of an approximately full accumulator  1105 . As seen in  FIGS.  16 B- 18   , as the accumulator  1105  is filled or expands, the rolling diaphragm  1127  unfolds while the ribbons of the constant force springs  1129  unwind thereby providing resistance against said expansion. As noted earlier, the rolling diaphragm  1127  helps maintain a seal between the outer surface of the piston  1125  and the inner wall of the accumulator  1105  while minimizing friction between the two surfaces that might interfere with the expansion or operation of the accumulator  1105 . 
       FIG.  19    shows an exploded view of an accumulator  1105 . The outer barrel of the accumulator  1105  may be constructed of a material such as polycarbonate plastic and is preferably transparent enough for the position of the piston  1125  therein to be externally readable against a pressure indicator  1115  on the accumulator  1105 . For example, the top edge of the piston  1125  may align with a mark on the pressure indicator  1115  to indicate a pressure setting. A clear outer barrel may also allow for monitoring of the state of the piston  1125  within the accumulator  1105  during transport to observe, for example, a maximum displacement thereof.  FIG.  19    shows a pair of constant force springs  1129  and a pair of connectors  1131  configured to couple to tubing to provide fluid communication between the interior of the accumulator  1105  and a gas source and an organ via an organ adapter. 
     As one skilled in the art would recognize as necessary or best-suited for the systems and methods of the invention, systems and methods of the invention may include computers that may include one or more of processor (e.g., a central processing unit (CPU), a graphics processing unit (GPU), etc.), computer-readable storage device (e.g., main memory, static memory, etc.), or combinations thereof which communicate with each other via a bus. Computers may include mobile devices (e.g., cell phones), personal computers, and server computers. In various embodiments, computers may be configured to communicate with one another via a network in order to display image series or allow remote storage, viewing, or selection of images of a given series. 
     A processor may include any suitable processor known in the art, such as the processor sold under the trademark XEON E7 by Intel (Santa Clara, Calif.) or the processor sold under the trademark OPTERON 6200 by AMD (Sunnyvale, Calif.). 
     Memory preferably includes at least one tangible, non-transitory medium capable of storing: one or more sets of instructions executable to cause the system to perform functions described herein (e.g., software embodying any methodology or function found herein); data (e.g., portions of the tangible medium newly re-arranged to represent real world physical objects of interest accessible as, for example, a picture of an object like a motorcycle); or both. While the computer-readable storage device can in an exemplary embodiment be a single medium, the term “computer-readable storage device” should be taken to include a single medium or multiple media (e.g., a centralized or distributed database, and/or associated caches and servers) that store the instructions or data. The term “computer-readable storage device” shall accordingly be taken to include, without limit, solid-state memories (e.g., subscriber identity module (SIM) card, secure digital card (SD card), micro SD card, or solid-state drive (SSD)), optical and magnetic media, hard drives, disk drives, and any other tangible storage media. 
     Input/output devices according to the invention may include one or more of a video display unit (e.g., a liquid crystal display (LCD) or a cathode ray tube (CRT) monitor), an alphanumeric input device (e.g., a keyboard), any temperature, pressure, or other sensor described herein, a cursor control device (e.g., a mouse or trackpad), a disk drive unit, a signal generation device (e.g., a speaker), a touchscreen, a button, an accelerometer, a microphone, a cellular radio frequency antenna, a network interface device, which can be, for example, a network interface card (NIC), Wi-Fi card, or cellular modem, or any combination thereof. 
     One of skill in the art will recognize that any suitable development environment or programming language may be employed to allow the operability described herein for various systems and methods of the invention. For example, systems and methods herein can be implemented using Perl, Python, C++, C#, Java, JavaScript, Visual Basic, Ruby on Rails, Groovy and Grails, or any other suitable tool. For a computer, it may be preferred to use native xCode or Android Java. 
     EXAMPLES 
     Example 1 Modeling of Lung Pressure Changes During Transport 
     Lung volume and pressure conditions were modeled during transport without an accumulator, with a spring-based accumulator, and with a weight based accumulator (as described above). Since PV=nRT (ideal gas law) the trapped volume inside the lung will obey pV/T=constant or p f  V f /T f =p o  V o /T o  where “o” refers to starting and “f” to final conditions. 
     P is the atmospheric pressure, absolute. p is the internal pressure, absolute, biased somewhat above P. V is the contained volume (lung, tubing, accumulator) T is the temperature in Kelvin. 
     For pressure the model defines and uses cmH 2 O and atm (the SI unit standard). Pressure measurements are absolute unless otherwise stated. 
                 cmH   ⁢           ⁢   2   ⁢   O     ≡         gm   ·   g       cm   2       ⁢           ⁢   1   ⁢           ⁢   atm       =       1.033   ×       10   3     ·   cmH     ⁢           ⁢   2   ⁢   O   ⁢           ⁢   1   ⁢           ⁢   atm     =     14.696   ·   psi             
Ambient Condition Ranges:
 
     Ambient Pressure (P) can range between the following (note that weather measurements are usually in inHg)
 
1atm=29.921in_HgPatm min =25.69in_Hg=0.899atmPatm max :=32.06in_Hg=1.071atm
 
Altitude at recovery should be accounted for. For example, the typical pressure in a city such as Denver, Colo. may be calculated as:
 
                   P   atmosphere     ⁡     (   h   )       ⁢     :       =       1   ⁢           ⁢     atm   ⁢           ·     exp   ⁡     (           -   g     ·   0.0289644     ⁢       kg   mol     ·   h         8.31447   ⁢       J     K   ·   mol       ·   288.15     ⁢           ⁢   K       )         ⁢       P   atmosphere     ⁡     (     5280   ⁢           ⁢   ft     )         =     0.826   ⁢           ·           ⁢   atm             
The range of P o  is from ˜0.8 to ˜1.08 atm. Lung temperature (T) can range between the following (assumes that recovery occurs in cold operating rooms and transport is under not as cold conditions):
 
T o_min :=2° C.=275.15K and T o_max :=65° F.=291.483K
 
Travel Conditions:
 
     To model transit conditions, it is assumed that T stays approximately constant. Allowing T f  to rise to 8° C. is conservative. Extremes of pressure will be seen in airplane cabins and is approximated as follows for various aircraft (Cabin Pressure is typically measured in equivalent altitude): 
     Regulatory Maximum=2400 m (p atmosphere (2400 m)=0.752 atm) 
     Boeing 767=2100 m (p atmosphere (2100 m)=0.780 atm) (typical of older airliners) 
     Airbus A380=1868 m (p atmosphere (1868 m)=0.801 atm) 
     Boeing 747-400=1572 m (p atmosphere (1572 m)=0.830 atm) 
     So flight pressures can range from 0.752 up to 0.830 atm. 
     Range Values for Exploring Solution Space: 
     i:=0 . . . 50 (where i is the ambient pressure index); j:=0 . . . 2 (where j is the initial conditions index for solutions of multiple cases simultaneously); P min :=0.75 atm and P max :=1.10 atm 
                 P     travel   1       ⁢     :     =     P   min       +         (       P   max     -     P   min       )     50     ·   1           
Lung Parameters:
 
     The lung values used herein are taken from literature. The volumes at 40 cmH 2 O and above are extrapolated. The resulting interpolated lung pressure-volume model is large: volume is 4.74 liters at 15 cmH2O. The pressure-volume model was scaled to establish a resting volume of 3.5 L at 15 cmH2O.″ 
     
       
         
           
             
               Lung 
               p 
             
             := 
             
               
                 
                   [ 
                   
                     
                       
                         
                           - 
                           20 
                         
                       
                     
                     
                       
                         
                           - 
                           16 
                         
                       
                     
                     
                       
                         
                           - 
                           12 
                         
                       
                     
                     
                       
                         
                           - 
                           8 
                         
                       
                     
                     
                       
                         
                           - 
                           4 
                         
                       
                     
                     
                       
                         0 
                       
                     
                     
                       
                         4 
                       
                     
                     
                       
                         8 
                       
                     
                     
                       
                         12 
                       
                     
                     
                       
                         16 
                       
                     
                     
                       
                         20 
                       
                     
                     
                       
                         24 
                       
                     
                     
                       
                         28 
                       
                     
                     
                       
                         32 
                       
                     
                     
                       
                         36 
                       
                     
                     
                       
                         40 
                       
                     
                     
                       
                         50 
                       
                     
                     
                       
                         60 
                       
                     
                     
                       
                         70 
                       
                     
                     
                       
                         85 
                       
                     
                     
                       
                         100 
                       
                     
                   
                   ] 
                 
                 ⁢ 
                 cm 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 H 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 2 
                 ⁢ 
                 O 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   Lung 
                   v 
                 
               
               := 
               
                 
                   [ 
                   
                     
                       
                         0.600 
                       
                     
                     
                       
                         0.635 
                       
                     
                     
                       
                         0.670 
                       
                     
                     
                       
                         0.695 
                       
                     
                     
                       
                         0.710 
                       
                     
                     
                       
                         0.815 
                       
                     
                     
                       
                         1.100 
                       
                     
                     
                       
                         2.400 
                       
                     
                     
                       
                         3.900 
                       
                     
                     
                       
                         4.600 
                       
                     
                     
                       
                         5.040 
                       
                     
                     
                       
                         5.250 
                       
                     
                     
                       
                         5.370 
                       
                     
                     
                       
                         5.470 
                       
                     
                     
                       
                         5.500 
                       
                     
                     
                       
                         5.525 
                       
                     
                     
                       
                         5.543754952 
                       
                     
                     
                       
                         5.557634961 
                       
                     
                     
                       
                         5.567219684 
                       
                     
                     
                       
                         5.572870767 
                       
                     
                     
                       
                         5.574845677 
                       
                     
                   
                   ] 
                 
                 ⁢ 
                 L 
               
             
           
         
       
     
     V rest :=3.5 L; P rest :=15 cmH 2 O 
     LungV (p, P):=interp[1spline(Lung p , Lung v) , Lung p , Lung v , (p-P)] 
     LungV(P rest , 0 cmH2O)=4.474 L 
     Vlung max =5 L (this simulates a volume constraint from a perfectly rigid lung) The scaled, max-limited Lung Volume formula is then: 
     
       
         
           
             
               
                 V 
                 lung 
               
               ⁡ 
               
                 ( 
                 
                   p 
                   , 
                   P 
                 
                 ) 
               
             
             ⁢ 
             
               
                 : 
               
               = 
               
                 min 
                 ⁡ 
                 
                   ( 
                   
                     
                       Vlung 
                       max 
                     
                     ⁢ 
                     Lung 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         V 
                         ⁡ 
                         
                           ( 
                           
                             p 
                             , 
                             P 
                           
                           ) 
                         
                       
                       · 
                       
                         
                           V 
                           rest 
                         
                         
                           Lung 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             V 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   P 
                                   rest 
                                 
                                 , 
                                 
                                   0 
                                   ⁢ 
                                   cmH 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                   ⁢ 
                                   O 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   ) 
                 
               
             
           
         
       
     
     (where =internal and P =external pressure, absolute) 
     A graph of the lung curve can be modeled using the following equation: 
     
       
         
           
             
               Δ 
               ⁢ 
               
                   
               
               ⁢ 
               
                 Plung 
                 min 
               
               ⁢ 
               
                 : 
               
               = 
               
                 min 
                 ⁡ 
                 
                   ( 
                   
                     Lung 
                     p 
                   
                   ) 
                 
               
             
             = 
             
               
                 
                   - 
                   20 
                 
                 · 
                 cmH 
               
               ⁢ 
               
                   
               
               ⁢ 
               2 
               ⁢ 
               O 
             
           
         
       
       
         
           
             
               Δ 
               ⁢ 
               
                   
               
               ⁢ 
               
                 Plung 
                 max 
               
               ⁢ 
               
                 : 
               
             
             = 
             
               
                 max 
                 ⁡ 
                 
                   ( 
                   
                     Lung 
                     p 
                   
                   ) 
                 
               
               = 
               
                 
                   100 
                   · 
                   cmH 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 2 
                 ⁢ 
                 O 
               
             
           
         
       
       
         
           
             
               Δ 
               ⁢ 
               
                   
               
               ⁢ 
               
                 Plung 
                 i 
               
               ⁢ 
               
                 : 
               
             
             = 
             
               
                 Δ 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   Plung 
                   min 
                 
               
               + 
               
                 
                   
                     ( 
                     
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           Plung 
                           max 
                         
                       
                       - 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           Plung 
                           min 
                         
                       
                     
                     ) 
                   
                   50 
                 
                 · 
                 i 
               
             
           
         
       
     
     A graph of the target volume, pressure and target compliance can be created as follows: 
     
       
         
           
             
               
                 K 
                 target 
               
               ⁢ 
               
                 : 
               
             
             = 
             
               
                 200 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 mL 
               
               
                 cmH 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 2 
                 ⁢ 
                 O 
               
             
           
         
       
       
         
           
             Target 
             ⁢ 
             
                 
             
             ⁢ 
             Line 
             ⁢ 
             
                 
             
             ⁢ 
             Y 
             ⁢ 
             
               : 
             
             = 
             
               ( 
               
                 
                   
                     
                       10 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       L 
                     
                   
                 
                 
                   
                     
                       V 
                       rest 
                     
                   
                 
                 
                   
                     
                       
                         - 
                         1 
                       
                       ⁢ 
                       L 
                     
                   
                 
               
               ) 
             
           
         
       
       
         
           
             
               Target 
               ⁢ 
               
                   
               
               ⁢ 
               Line 
               ⁢ 
               
                   
               
               ⁢ 
               X 
               ⁢ 
               
                 : 
               
             
             = 
             
               [ 
               
                 
                   
                     
                       
                         P 
                         rest 
                       
                       + 
                       
                         
                           ( 
                           
                             
                               Target 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 LineY 
                                 0 
                               
                             
                             - 
                             
                               V 
                               rest 
                             
                           
                           ) 
                         
                         
                           K 
                           target 
                         
                       
                     
                   
                 
                 
                   
                     
                       P 
                       rest 
                     
                   
                 
                 
                   
                     
                       
                         P 
                         rest 
                       
                       + 
                       
                         
                           ( 
                           
                             
                               Target 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 LineY 
                                 2 
                               
                             
                             - 
                             
                               V 
                               rest 
                             
                           
                           ) 
                         
                         
                           K 
                           target 
                         
                       
                     
                   
                 
               
               ] 
             
           
         
       
     
     The curve of an ex-vivo lung model, volume vs. pressure is shown in  FIG.  20   . The target shown is a lung volume of 3.5 L at 15 cmH2O. The curve is taken from literature and scaled (on Yaxis) to pass through target. Values for pressure&gt;36 cmH2O are extrapolated. 
     Accumulator parameters for the model were varied based on the accumulator used as follows: 
     1) No Accumulator: 
     AccumPresent=0(When this is zero, there&#39;s no accumulator in the system). 
     Vacm1tr min =50 mL Vacm1tr max =1500.0 mL (These values represent the designed volume range) 
                     Vacmltr   recovery     =       (         1.000           0.350           0.050         )     ·   L                             
(this is set by the recovery team, e.g. system is filled with air until accumulator is at the stipulated volume, which may vary based on ambient pressure at time/place of recovery)
 
             Kacmltr   =     400.0   ·     mL     cmH   ⁢           ⁢   2   ⁢   O               
(Higher numbers here represent a weight-loaded design; lower numbers represent a spring-loaded design)
 
ΔP acm1tr =15·cmH2O
 
     (This is the nominal accumulator pressure, at Vacm1tr recovery1 , e.g., when the piston is at the target volume for the nominal pressure case. It is set by the weight or spring) 
     
       
         
           
             
               
                 V 
                 acmltr 
               
               ⁡ 
               
                 ( 
                 
                   p 
                   , 
                   P 
                 
                 ) 
               
             
             ⁢ 
             
               : 
             
             ⁢ 
             
               = 
               
                 max 
                 [ 
                 
                   
                     Vacmltr 
                     min 
                   
                   , 
                   
                     
                       
                         min 
                         ⁡ 
                         
                           [ 
                           
                             
                               Vacmltr 
                               max 
                             
                             , 
                             
                               
                                 Vacmltr 
                                 
                                   recovery 
                                   1 
                                 
                               
                               + 
                               
                                   
                                 
                                   Kacmltr 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       p 
                                       - 
                                       P 
                                       - 
                                       
                                         ΔP 
                                         acmltr 
                                       
                                     
                                     ) 
                                   
                                 
                                 ] 
                               
                             
                           
                           ] 
                         
                       
                       ⁢ 
                       
                         
 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           Hacmltr 
                           max 
                         
                         ⁢ 
                         
                           : 
                         
                       
                     
                     = 
                     
                       
                         20 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         cm 
                         ⁢ 
                         
                           
 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             Hacmltr 
                             max 
                           
                           ⁢ 
                           
                             : 
                           
                         
                       
                       = 
                       
                         
                           7.874 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           in 
                           ⁢ 
                           
                             
 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             Dacltr 
                             ⁢ 
                             
                               : 
                             
                           
                         
                         = 
                         
                           
                             
                               
                                 4 
                                 ⁢ 
                                 
                                   Vacmltr 
                                   max 
                                 
                               
                               
                                 π 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   Hacmltr 
                                   max 
                                 
                               
                             
                           
                           = 
                           
                             
                               
                                 9.772 
                                 ⁢ 
                                 
                                     
                                 
                                 · 
                                 cm 
                               
                               ⁢ 
                               
                                 
 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 Fspring 
                                 max 
                               
                               ⁢ 
                               
                                 : 
                               
                             
                             = 
                             
                               
                                 Δ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   P 
                                   acmltr 
                                 
                                 ⁢ 
                                 
                                   
                                     π 
                                     4 
                                   
                                   · 
                                   
                                     Dacltr 
                                     2 
                                   
                                 
                               
                               = 
                               
                                 
                                   
                                     2.48 
                                     ⁢ 
                                     
                                         
                                     
                                     · 
                                     lbf 
                                   
                                   ⁢ 
                                   
                                     
 
                                   
                                   ⁢ 
                                   
                                     Fspring 
                                     max 
                                   
                                   ⁢ 
                                   
                                     : 
                                   
                                 
                                 = 
                                 
                                   
                                     
                                       Fspring 
                                       min 
                                     
                                     + 
                                     
                                       
                                         
                                           ( 
                                           
                                             
                                               Vacmltr 
                                               max 
                                             
                                             - 
                                             
                                               Vacmltr 
                                               min 
                                             
                                           
                                           ) 
                                         
                                         Kacmltr 
                                       
                                       · 
                                       
                                         ( 
                                         
                                           
                                             π 
                                             4 
                                           
                                           · 
                                           
                                             Dacltr 
                                             2 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                   = 
                                   
                                     
                                       
                                         3.08 
                                         ⁢ 
                                         
                                             
                                         
                                         · 
                                         
                                             
                                         
                                         ⁢ 
                                         lbf 
                                       
                                       ⁢ 
                                       
                                         
 
                                       
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       Kspring 
                                       ⁢ 
                                       
                                         : 
                                       
                                     
                                     = 
                                     
                                       
                                         
                                           
                                             Fspring 
                                             max 
                                           
                                           - 
                                           
                                             Fspring 
                                             min 
                                           
                                         
                                         
                                           Hacmltr 
                                           max 
                                         
                                       
                                       = 
                                       
                                         0.076 
                                         ⁢ 
                                         
                                             
                                         
                                         · 
                                         
                                           lbf 
                                           in 
                                         
                                       
                                     
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
             
           
         
       
     
     Hspring min :=1 in (This is the spring height at max compression) 
                 H     spring   free       ⁢     :       =         Hspring   min     +     Hacmltr   max     +       Fspring   min     Kspring       =     41.456   ⁢           ·           ⁢   in             
(This is the free height of the spring and not meaningful for weight-biased designs)
 
2) Spring-Based Accumulator:
 
     Parameters are same as for no accumulator above aside from the following: 
                     ⁢       Accum   ⁢           ⁢   Present     =   1                         ⁢     Kacmltr   =     350.0   ⁢     mL     cmH   ⁢           ⁢   2   ⁢   O                           Fspring   max     ⁢     :       =         Fspring   min     +         (       Vacmltr   max     -     Vacmltr   min       )     Kacmltr     ·     (       π   4     ·     Dacltr   2       )         =     3.165   ⁢           ·           ⁢   lbf                           ⁢       Kspring   ⁢     :       =           Fspring   max     -     Fspring   min         Hacmltr   max       =     0.087   ⁢           ·           ⁢     lbf   in                           Hspring   free     ⁢     :       =         Hspring   min     +     Hacmltr   max     +       Fspring   min     Kspring       =     37.383   ⁢           ·           ⁢   in             
3) Weight-Based Accumulator:
 
     Parameters are same as for no accumulator above aside from the following 
                     ⁢       Accum   ⁢           ⁢   Present     =   1                         ⁢       Vacmltr   recovery     =       (         0.900           0.300           0.010         )     ·   L                           ⁢     Kacmltr   =     10000.0   ⁢     mL     cmH   ⁢           ⁢   2   ⁢   O                           Fspring   max     ⁢     :       =         Fspring   min     +         (       Vacmltr   max     -     Vacmltr   min       )     Kacmltr     ·     (       π   4     ·     Dacltr   2       )         =     3.165   ⁢           ·           ⁢   lbf                           ⁢       Kspring   ⁢     :       =           Fspring   max     -     Fspring   max         Hacmltr   max       =       3.045   ⁢   x   ⁢           ⁢     10     -   3       ⁢     lbf   in     ⁢     
     ⁢     Hspring   free     ⁢     :       =         Hspring   min     +     Hacmltr   max     +       Fspring   min     Kspring       =     823.427   ⁢           ·   in                   
Initial Conditions:
 
               T   o     =         [         4           4           4         ]     ⁢   °   ⁢           ⁢     C   .           ⁢     P   o         =       [         0.860           1.000           1.080         ]     ⁢           ⁢   atm             
where P o  is the external environmental pressure.
 
     The accumulator&#39;s behavior was used to determine P o  and V o , e.g., the initial internal pressure volume at the above P o  and T o  given all other parameters. The accumulator is filled to the target volume, which sets the internal pressure. 
     
       
         
           
             
               
                 
                   P 
                   o 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   := 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   
                     
                       Vacmltr 
                       recovery 
                     
                     Kacmltr 
                   
                   · 
                   0 
                 
               
               + 
               
                 Δ 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   P 
                   acmltr 
                 
               
               + 
               
                 P 
                 o 
               
             
             = 
             
               
                 
                   
                     
                       ( 
                       
                         
                           
                             903.576 
                           
                         
                         
                           
                             1048.227 
                           
                         
                         
                           
                             1130.886 
                           
                         
                       
                       ) 
                     
                     · 
                     cmH 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   2 
                   ⁢ 
                   
                     Cp 
                     o 
                   
                 
                 - 
                 
                   P 
                   o 
                 
               
               = 
               
                 
                   
                     ( 
                     
                       
                         
                           15 
                         
                       
                       
                         
                           15 
                         
                       
                       
                         
                           15 
                         
                       
                     
                     ) 
                   
                   · 
                   cmH 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 2 
                 ⁢ 
                 O 
               
             
           
         
       
     
     The lung volume was determined by the initial and external pressures as:
 
Vlung initial =V lung (p o , P o )=3.5L
 
     The Contained Volume V o  is the sum of accumulator and lung volumes. This is the initial volume of air inside the system. This mass of air will remain unchanged, so the ideal gas law governs its subsequent behavior (relationship of pressure to volume). V o  can be defined as follows for the various accumulator types: 
     No Accumulator: 
                   V   o     ⁢           ⁢     :=     ⁢           ⁢     AccumPresent   ·     Vacmltr   recovery         +     Vlung   initial       =       (         3.500           3.500           3.500         )     ⁢   L           
Spring-Based Accumulator:
 
                   V   o     ⁢           ⁢     :=     ⁢           ⁢     AccumPresent   ·     Vacmltr   recovery         +     Vlung   initial       =       (         4.500           3.850           3.550         )     ⁢   L           
Weight-Based Accumulator:
 
     
       
         
           
             
               
                 
                   V 
                   o 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   := 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   AccumPresent 
                   · 
                   
                     Vacmltr 
                     recovery 
                   
                 
               
               + 
               
                 Vlung 
                 initial 
               
             
             = 
             
               
                 ( 
                 
                   
                     
                       4.400 
                     
                   
                   
                     
                       3.800 
                     
                   
                   
                     
                       3.510 
                     
                   
                 
                 ) 
               
               ⁢ 
               L 
             
           
         
       
     
     The equation for final volume Vf is based on the ideal gas law for contained volume, 
                   p   f     ·     V   f         T   f       =         p   o     ·     V   o         T   o             
solved for Vf:
 
     
       
         
           
             
               V 
               f 
             
             = 
             
               
                 
                   
                     p 
                     o 
                   
                   · 
                   
                     V 
                     o 
                   
                 
                 
                   T 
                   o 
                 
               
               · 
               
                 
                   T 
                   f 
                 
                 
                   p 
                   f 
                 
               
             
           
         
       
     
     The adapted equation was used in the solve function below:
 
P guess :=1.2·p o     2   
 
given:
 
                   po   ·   Vo     To     ·     Tf     p   guess         =       AccumPresent   ·       V   acmltr     ⁡     (       p   guess     ,   Ptravel     )         +       V   lung     ⁡     (       p   guess     ,   Ptravel     )               
with the following constraint added:
 
P guess &gt;Ptravel
 
providing a solution of:
 
ptravel(po, Vo, To, Tf, Ptravel):=Find)p guess )
 
     The inputs to this function are the initial conditions together with travel pressure and temperature. The output of this function is the internal pressure. 
     The solution for a defined range of conditions can then be found:
 
p travel     i,j   =ptravel(p o     j   ,V o     j   ,T o     j   , T f ,P travel     i   )
 
Vlung travel     i,j   =V lung (p travl     i,j   ,p travel     i   )
 
Vacmltr travel     i,j   =AccumPresent V acm1tr (P travel     i,j   , P travel     i   )
 
ΔP lung     i,j   =ptravel i,j =P travel     i   
 
       FIGS.  21  and  22    show lung pressure and volume in no-accumulator systems given various parameters. Lung pressure and volume were plotted in  FIG.  21    given the following: 
     Initial conditions: 
               P   o     ≡       (         .86           1           1.08         )     ⁢   1   ⁢           ⁢   atm   ⁢           ⁢         Atmospheric               Pressure   ⁢           ⁢   at     ⁢                       Recovery   ⁢                                   T   o     ≡       (         4           4           4         )     ⁢   °   ⁢           ⁢     C   .           ⁢           Internal   ⁢                       Temperature   ⁢           ⁢   at               Recovery   ⁢                             
Lung parameters:
         Vlung max =5L   limiting bag/box voume
 
Accumulator design parameters:
       

             AccumPresent   ≡     0   ⁢           ⁢     (     0   =     no   ⁢           ⁢   accum       )                   Kacmltr   ≡     400   ·     mL     cmH   ⁢           ⁢   2   ⁢   O                       Realistic   ⁢           ⁢   spring     ∼     400   ⁢           ⁢   mL   ⁢     /     ⁢   cmH   ⁢           ⁢   2   ⁢     O   .     
     ⁢   Weighted     ⁢           ⁢   piston     &gt;     5000   ⁢           ⁢   mL   ⁢     /     ⁢   cmH   ⁢           ⁢   2   ⁢   O   ⁢     
     ⁢     Δ   ⁢           ⁢     P   acmltr         ≡     15   ⁢           ⁢   cmH   ⁢           ⁢   2   ⁢   O   ⁢           ⁢   recovery   ⁢           ⁢   pressure   ⁢     
     ⁢     Vacmltr   max       ≡     1.5   ⁢           ⁢   L   ⁢           ⁢   maximum   ⁢           ⁢   volume                   Vacmltr   min     ≡     50   ⁢           ⁢   mL   ⁢           ⁢   minimum   ⁢           ⁢   volume   ⁢     
     ⁢     Vacmltr   recovery       ≡       (           1000   ⁢           ⁢   mL               350   ⁢           ⁢   mL               50   ⁢           ⁢   mL           )     ⁢           ⁢             Accum   .     ⁢                       volume   ⁢           ⁢   as   ⁢           ⁢   set                 by   ⁢           ⁢   recovery     ⁢                       team   ⁢                           
In-transit temperature:
         T f =8° C.
 
Airplane cabin pressures:
   Regulatory Minimum=0.75 atm   Older Airplanes=0.78 atm   Newer Airplanes=0.80-0.83 atm       

     Given the above values,  FIG.  21    shows lung pressure and volume across a range of ambient (atmospheric) pressures during transit without an accumulator based on three different atmospheric pressures at recovery (0.86 atm, 1 atm, and 1.08 atm). Lung volume, recovery at 0.86 Patm  1201 , lung volume, recovery at 1 Patm  1202 , lung volume, recovery at 1.08 Patm  1203 , and accumulator volume  1207  (set to zero here to represent a lack of accumulator) are plotted against the left hand scale. Lung pressure, recovery at 0.86 Patm  1204 , lung pressure recovery at 1 Patm  1205 , and lung pressure, recovery at 1.08 Patm  1206  are plotted against the right hand scale. 
       FIG.  22    shows lung pressure and volume across a range of ambient (atmospheric) pressures during transit without an accumulator with recovery at 1 atm. The values are the same as given for the nominal (1 atm recovery pressure) plot in  FIG.  21   . 
     As shown in  FIGS.  21  and  22   , the lung volume and pressure vary markedly in response to changes in the in-transit ambient pressure from airplane ascent and descent. These changes can cause damage to the lung tissue and negatively impact viability of the organ for transplant. 
       FIGS.  23  and  24    show lung pressure and volume in spring-based accumulator systems given various parameters. Lung pressure and volume were plotted in  FIG.  23    given the following: 
     Initial Conditions: 
               P   o     ≡       (         .86           1           1.08         )     ⁢   1   ⁢           ⁢   atm   ⁢           ⁢         Atmospheric               Pressure   ⁢           ⁢   at     ⁢                       Recovery   ⁢                                   T   o     ≡       (         4           4           4         )     ⁢   °   ⁢           ⁢     C   .           ⁢           Internal   ⁢                       Temperature   ⁢           ⁢   at               Recovery   ⁢                             
Lung Parameters:
         Vlung max =5 L
 
Accumulator Design Parameters:
       

             AccumPresent   ≡     1   ⁢           ⁢     (     0   =     no   ⁢           ⁢     accum   .         )                   Kacmltr   ≡     350   ·     mL     cmH   ⁢           ⁢   2   ⁢   O                       Realistic   ⁢           ⁢   spring     ∼     400   ⁢           ⁢   mL   ⁢     /     ⁢   cmH   ⁢           ⁢   2   ⁢     O   .     
     ⁢   Weighted     ⁢           ⁢   piston     &gt;     5000   ⁢           ⁢   mL   ⁢     /     ⁢   cmH   ⁢           ⁢   2   ⁢   O   ⁢     
     ⁢     Δ   ⁢           ⁢     P   acmltr         ≡     15   ⁢           ⁢   cmH   ⁢           ⁢   2   ⁢   O   ⁢           ⁢   recovery   ⁢           ⁢   pressure   ⁢     
     ⁢     Vacmltr   max       ≡     1.5   ⁢           ⁢   L   ⁢           ⁢   maximum   ⁢           ⁢   volume                   Vacmltr   min     ≡     50   ⁢           ⁢   mL   ⁢           ⁢   minimum   ⁢           ⁢   volume   ⁢     
     ⁢     Vacmltr   recovery       ≡       (           1000   ⁢           ⁢   mL               350   ⁢           ⁢   mL               50   ⁢           ⁢   mL           )     ⁢           ⁢             Accum   .     ⁢                       volume   ⁢           ⁢   as   ⁢           ⁢   set                 by   ⁢           ⁢   recovery     ⁢                       team   ⁢                           
In-transit temperature:
         T f =8° C.
 
Airplane cabin pressures:
       

     Regulatory Minimum=0.75 atm 
     Older Airplanes=0.78 atm 
     Newer Airplanes=0.80-0.83 atm 
     Given the above values,  FIG.  23    shows lung pressure and volume across a range of ambient (atmospheric) pressures during transit with a spring-based accumulator based on three different atmospheric pressures at recovery (0.86 atm, 1 atm, and 1.08 atm). Lung volume, recovery at 0.86 atm, 1 atm, and 1.08 atm  1401  and accumulator volume  1407  are plotted against the left hand scale. Lung pressure, recovery at 0.86 atm, 1 atm, and 1.08 atm  1406  are plotted against the right hand scale. Of note compared to  FIG.  21   , the lung volume, lung pressure, and accumulator volume curves are consistent across the various atmospheric pressure conditions at recovery because the accumulator volume set at the time of recover compensates for these differences. Furthermore, as shown in  FIGS.  23 - 26   , the lung volume and lung pressure curves are much flatter than those in  FIGS.  21  and  22    (without an accumulator) while the accumulator volume changes to offset pressure differentials caused by changes in cabin pressure. 
       FIG.  24    shows lung pressure and volume across a range of ambient (atmospheric) pressures during transit without an accumulator with recovery at 1 atm. The values are the same as given for the nominal (1 atm recovery pressure) plot in  FIG.  23   . 
       FIGS.  25  and  26    show lung pressure and volume in weight-based accumulator systems given various parameters. Lung pressure and volume were plotted in  FIG.  25    given the following: 
     Initial Conditions: 
               P   o     ≡       (         .86           1           1.08         )     ⁢   1   ⁢           ⁢   atm   ⁢           ⁢         Atmospheric               Pressure   ⁢           ⁢   at     ⁢                       Recovery   ⁢                                   T   o     ≡       (         4           4           4         )     ⁢   °   ⁢           ⁢     C   .           ⁢           Internal   ⁢                       Temperature   ⁢           ⁢   at               Recovery   ⁢                             
Lung Parameters:
         Vlung max =5 L limiting bag/box volume
 
Accumulator Design Parameters:
   Vlung max =5 L limiting bag/box volume
 
Accumulator Design Parameters
       

             AccumPresent   ≡     1   ⁢           ⁢     (     0   =     no   ⁢           ⁢     accum   .         )                   Kacmltr   ≡     10000   ·     mL     cmH   ⁢           ⁢   2   ⁢   O                       Realistic   ⁢           ⁢   spring     ∼     400   ⁢           ⁢   mL   ⁢     /     ⁢   cmH   ⁢           ⁢   2   ⁢     O   .     
     ⁢   Weighted     ⁢           ⁢   piston     &gt;     5000   ⁢           ⁢   mL   ⁢     /     ⁢   cmH   ⁢           ⁢   2   ⁢   O   ⁢     
     ⁢     Δ   ⁢           ⁢     P   acmltr         ≡     15   ⁢           ⁢   cmH   ⁢           ⁢   2   ⁢   O   ⁢           ⁢   recovery   ⁢           ⁢   pressure   ⁢     
     ⁢     Vacmltr   max       ≡     1.5   ⁢           ⁢   L   ⁢           ⁢   maximum   ⁢           ⁢   volume                   Vacmltr   min     ≡     50   ⁢           ⁢   mL   ⁢           ⁢   minimum   ⁢           ⁢   volume   ⁢     
     ⁢     Vacmltr   recovery       ≡       (           900   ⁢           ⁢   mL               300   ⁢           ⁢   mL               10   ⁢           ⁢   mL           )     ⁢           ⁢             Accum   .     ⁢                       volume   ⁢           ⁢   as   ⁢           ⁢   set                 by   ⁢           ⁢   recovery     ⁢                       team   ⁢                           
In-transit temperature:
 
     T f =8° C. 
     Airplane cabin pressures: 
     
         
         
           
             Regulatory Minimum=0.75 atm 
             Older Airplanes=0.78 atm 
             Newer Airplanes=0.80-0.83 atm 
           
         
       
    
     Given the above values,  FIG.  25    shows lung pressure and volume across a range of ambient (atmospheric) pressures during transit with a weight-based accumulator based on three different atmospheric pressures at recovery (0.86 atm, 1 atm, and 1.08 atm). Lung volume, recovery at 0.86 atm, 1 atm, and 1.08 atm  1601  and accumulator volume  1607  are plotted against the left hand scale. Lung pressure, recovery at 0.86 atm, 1 atm, and 1.08 atm  1606  are plotted against the right hand scale. As with  FIG.  23   , the lung volume, lung pressure, and accumulator volume curves are consistent across the various atmospheric pressure conditions at recovery because the accumulator volume, set at the time of recover compensates for these differences. The lung volume and pressure curves are slightly flatter than the spring-based accumulator curves in  FIG.  23   . 
       FIG.  26    shows lung pressure and volume across a range of ambient (atmospheric) pressures during transit without an accumulator with recovery at 1 atm. The values are the same as given for the nominal (1 atm recovery pressure) case in the plot in  FIG.  25   . 
     INCORPORATION BY REFERENCE 
     References and citations to other documents, such as patents, patent applications, patent publications, journals, books, papers, web contents, have been made throughout this disclosure. All such documents are hereby incorporated herein by reference in their entirety for all purposes. 
     EQUIVALENTS 
     Various modifications of the invention and many further embodiments thereof, in addition to those shown and described herein, will become apparent to those skilled in the art from the full contents of this document, including references to the scientific and patent literature cited herein. The subject matter herein contains important information, exemplification and guidance that can be adapted to the practice of this invention in its various embodiments and equivalents thereof.