Measurement of a dynamic system

A method for measuring rates of gas consumption or production of a plurality of biological samples in respective fluid-filled wells a multi-well plate, the method comprising:

• placing a lid onto a plate containing biological samples in fluid in respective wells of the plate, wherein the lid
• has a bottom surface exposed to the wells, and a top surface opposite to the bottom surface,
• maintains a sterile barrier between the surface of the fluid in each well and an environment of the plate by blocking any straight gas path between the surface of the fluid in each well and the environment,
• provides at least some indirect gas path between the fluid of each well and the environment,
• comprises a plurality of elongated probes, and attaching the lid to the plate includes inserting each probe into fluid of a respective well such that each probe provides an optical path between the top surface of the lid and an end of the probe inserted into the fluid of the respective well, and
• comprises at least some flexible portions permitting motion of the lid causing vertical movement of the probes while maintaining the sterile barrier and the indirect gas paths;
• placing a device onto the lid such that the lid is held between the device and the plate, wherein the device
• comprises one or more mechanical actuators for causing motion of the lid resulting in vertical movement of the probes in the fluid of the wells, and
• comprises a plurality of optoelectronic sensors, and placing the device onto the lid includes aligning each of the optoelectronic sensors with a respective probe of the lid forming an optical path from the end of the probe inserted into the fluid to the optoelectronic sensor;
• acquiring gas concentration measurements, including controlling the actuators to repeatedly move the probes up and down in the wells, and while moving the probes acquiring concentration measurements via the probes and optoelectronic sensors at varying depths of the probes in the fluid of the respective wells;
• and
• determining a rate of gas consumption or production in the fluid of each well, including determining spatial gradients of gas concentration in each well from the measurements of the gas concentrations and determining the consumption or production rate from the spatial gradient.

A method for sensing biological samples in one or more multi-well plates, the method comprising:

• receiving a first multi-well plate of the one or more multi-well plates, the first multi-well plate having a plurality of biological samples in fluid in respective wells of the first multi-well plate, the first multi-well plate having a top side with openings of the respective wells;
• positioning a first lid over a top side of the first multi-well plate, the first lid having a bottom side proximal to the top side of the first multi-well plate, and a top side opposite to said bottom side, and wherein the first lid has a plurality of elongated probes extend substantially perpendicularly from said bottom side into respective wells for the multi-well plate, and when so placed, said elongated probes extend into the fluid in said respective wells;
• wherein the first lid, when positioned on the first multi-well plate, provides a gas path from each well to an environment providing a reservoir for the gas only via tortuous paths;
• wherein each elongated probe of the plurality of elongated probes comprises an elongated optical channel coupled to optically sensitive sensing material at an end of the elongated probe that is in the fluid of a respective well;
• causing the elongated probes to be displaced up and down in multiple time intervals spanning an overall measurement duration;
• sensing a value of a property of the fluid in each well at multiple displacements of the probes in each interval of the multiple time intervals;
• combining multiple values of the property at respective displacements of the probes for each well to determine a value of a property of the biological sample in said well;
• and
• providing the values of the properties of the plurality of biological samples.