Temperature control method and apparatus.

(54) Title: TEMPERATURE CONTROL METHOD AND APPARATUS. (54) Title: TEMPERATURE CONTROL METHOD AND APPARATUS.

(57) Summary

A method of controlling the temperature of a liquid held within a reaction container in a chamber of a thermal cycling apparatus, the method includes determining a chamber temperature detected from a temperature sensor in the chamber, determining a temperature of air using the detected chamber temperature, Determine a liquid temperature using the air temperature and selectively heating or cooling air in the chamber according to the temperature of the liquid.

(57) Abstract

A method of controlling the temperature of a liquid held within a reaction container in a chamber of a thermal cycling apparatus, the method including determining a sensed chamber temperature from a temperature sensor in the chamber, determining an air temperature using the sensed chamber temperature, determining a liquid temperature using the air temperature and selectively heating or cooling air in the chamber in accordance with the liquid temperature.

TEMPERATURE CONTROL METHOD AND APPARATUS

FIELD OF THE INVENTION

The present invention relates to a method and apparatus for controlling the temperature of a liquid and in particular to a method and apparatus for controlling the temperature of a liquid in a term cycling apparatus.

The present invention also relates to a method and apparatus for determining the temperature of a liquid in a thermal cycling apparatus.

BACKGROUND OF THE INVENTION

Reference in this specification to any previous publication (or information derived from it), or to any material that is known, is not and should not be taken as a knowledge or admission or any form of suggestion that the previous publication (or derived information of this) or known subject is part of the general common knowledge in the field of work to which this specification refers.

PCR (Polymerase Chain Reaction) is a technique that involves multiple cycles that result in exponential amplification of certain polynucleotide sequences each time one cycle is completed. The PCR technique is well known and is described in many books, including, PCR: A Practical Approach MJ

McPherson, et al., IRL Press (1991), PCR Protocols: A guide to Methods and Applications by Innis, et al., Academic Press (1990), and PCR Technology: Principáis and Applications for

DNA Amplification HA Erlich, Stockton Press (1989). PCR is also described in many United States patents, including 4,683,195; 4,683,202; 4,800,159; 4,965,188;

4,889,818; 5,075,216; 5,079,352; 5,104,792; 5,091,310; and

5,066,584.

The PCR technique typically involves the step of denaturing a polynucleotide followed by the step of annealing at least one pair of primer oligonucleotides to the denatured polynucleotide, i.e., hybridizing the primer paint to the denatured polynucleotide template. After the annealing step, an enzyme with polymerase activity catalyzes the synthesis of a new polynucleotide filament that incorporates the primer oligonucleotide and uses the original denatured polynucleotide as a synthesis template. This series of steps (denaturation, primer annealing, and primer extension) constitutes a PCR cycle.

As cycles are repeated, the amount of newly synthesized polynucleotide increases exponentially because recently synthesized polynucleotides from a previous cycle can serve as templates for synthesis in subsequent cycles. Primer oligonucleotides are typically selected in pairs that can be annealed to opposite strands of a double-pressed polynucleotide sequence so that the region between the two annealing sites is amplified.

Denaturation of DNA typically occurs at approximately 90 to 95 ° C, annealing of a primer paint to denatured DNA typically runs at approximately 40 to 60 ° C, and the step of spreading annealed primer paints with a polymerase is typically performs at approximately 70 to 75 ° C. Therefore, during a PCR cycle, the temperature of the reaction mixture must be varied, and varied many times during a multi-cycle PCR experiment.

<td>The PCR technique has</td><td>a</td><td>wide</td><td>variety</td><td>of</td>

<td>biological applications, includes</td><td>by</td><td>example,</td><td>analysis</td><td>of</td>

<td>DNA sequence generation</td><td>of</td><td>probe,</td><td>cloning</td><td>of</td>

nucleic acid sequences, site-directed mutagenesis, detection of genetic mutations, diagnosis of viral infections, molecular fingerprint and monitoring of contaminating microorganisms in biological fluids and other sources.

In addition to PCR, other in vitro amplification procedures, including the ligase chain reaction as disclosed in US Patent number

4,988,617 to Landegren and Hood are known and conveniently used in the prior art. More generally, several important methods known in the art of biotechnology, such as nucleic acid hybridization and sequencing depend on the temperature change of the solutions containing the sample molecules in a controlled manner. Conventional techniques are based on the use of individual wells or tubes cycled through different temperature zones. For example, a number of thermal cyclers used for DNA amplification and sequencing are disclosed in the prior art, in which a temperature controlled element or block maintains a reaction mixture, and where the temperature of the block is varied with the pass of the time. An advantage of these devices is that a relatively large number of samples can be processed simultaneously, eg 96 well plates are commonly used.

US-7,645,070 describes an instrument to execute

Highly accurate PCR using an assembly, a heated jacket, and an internal computer. The assembly is made of a sample block, a number of Peltier thermal electrical devices, and a heat exchanger, all these subjects together. A control algorithm manipulates the current supplied to thermoelectric coolers so that the dynamic end performance of a block can be controlled so that pre-defined thermal sample temperature profiles can be executed. The sample temperature is calculated instead of measured using a specific design model as well as equations. The control software includes calibration diagnostics that allow the performance of thermoelectric coolers to be varied from instrument to instrument to be compensated so that all instruments operate identically. The block / heat exchanger assembly can be changed to another of the same design or a different design. The assembly carries the necessary information required to characterize its own performance on an on-board memory device, allowing the assembly to be interchangeable between instruments while preserving its precision operating characteristics.

US-5,475,610 describes an instrument to execute

Highly accurate PCR using a sample block in a microtiter tray format. The sample block has local balance and local symmetry. A computer controlled three zone film heater and computer controlled ramp cooling solenoid valves to damper the flow of refrigerant through the block controls the temperature of the block. Constant bias cooling is used for small changes. The displayed temperature is calculated instead of measured. A platen deforms plastic caps to apply a minimum acceptable threshold force to seat the tubes and thermally insulate them.

A cover insulates the block. Control software includes diagnostics. An installation program tests and characterizes the instrument. A new user interface is used. Disposable multi-piece plastic microtiter trays are shown to give individual freedom to sample tubes.

However, such block devices suffer from several drawbacks since they are relatively slow in cycling the reaction mixtures, they are relatively energy intensive to operate, the temperature control is less than ideal and the detection of the reaction mixture in site is difficult.

In an effort to avoid several of these disadvantages, other thermal cyclists have been developed in which a plurality of containers for holding reaction mixtures is supported on a rotating carousel rotatably mounted within a chamber adapted to be heated and cooled. For example, see US Patent Number 7,081,226 to Wittwer at al. However, these devices still suffer from various drawbacks. For example, control over the temperature of reaction mixtures is less than ideal, control over the rate of heating and cooling of reaction mixtures is less than ideal, and these devices have relatively poor energy efficiency. .

Therefore, there remains a need for PCR thermocyclers that provide improved temperature control of reaction mixtures, that are not complex to use, that can provide real-time analysis of the reaction occurring in sample containers, and that are energy efficient.

SUMMARY OF THE INVENTION

The present invention seeks to overcome or improve at least one of the disadvantages of the aforementioned prior art, or to provide a useful alternative.

In a first broad form, the present invention seeks to provide a method of controlling the temperature of a liquid maintained within a reaction container in a chamber of a thermal cycling apparatus, the method includes:

a) determining a detected chamber temperature from a chamber temperature sensor,

b) determining an air temperature using the detected chamber temperature;

c) determining a liquid temperature using the air temperature; and

d) selectively heating or cooling air in the chamber according to the temperature of the liquid.

Typically the method includes:

a) determining a detected ambient temperature from an out-of-chamber temperature sensor; and

b) determine the air temperature at least in part using the detected ambient temperature and the detected chamber temperature.

Typically, the method includes determining the air temperature using a thermal air model.

Typically the method includes:

a) determine if the chamber is closed; and

b) at least one of:

i) if the chamber is closed, determine the effective air temperature using the detected chamber temperature and a closed chamber model; and ii) if the chamber is open, determine the effective air temperature using the detected chamber temperature, a detected ambient temperature, and an open chamber model.

Typically, the method includes, for the closed chamber model:

a) comparing the detected chamber temperature with a threshold temperature; and

b) at least one of:

i) if the detected chamber temperature is below the threshold temperature, determine the air temperature using a first closed chamber model; and ii) if the detected chamber temperature is above the threshold temperature, determine the air temperature using a second closed chamber model.

Typically, air temperature is determined at least in part using the ratio:

T = ^Jss k_SLT_s+ C_L, if T_s &lt;T_rVs + Q / 5 if T_s &gt; T_r where T_H.H it is an air temperature of the closed chamber model;

T_s is the detected chamber temperature;

T_T it is a threshold temperature;

k_SL it is a first coefficient of the closed chamber model;

k_ITS it is a second coefficient of the closed chamber model;

c_L it is a first compensation value of the closed chamber model;

c¡7 is a second offset value of the closed chamber model.

Typically for the open chamber model, the method includes determining the air temperature at least in part using the relationship:

Toe ⁼ kssTss + k ^ TñM + c_oc

<td>Where:</td><td>Toe</td><td>is</td><td>a</td><td>temperature</td><td>from air</td><td>of the</td><td>model</td><td>of</td><td>camera</td>

<td>open;</td><td>Tss</td><td>is</td><td>a</td><td>temperature</td><td>of air</td><td>of the</td><td>model</td><td>of</td><td>camera</td>

<td>closed;</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td>

<td></td><td>TñM</td><td>is</td><td>a</td><td>temperature</td><td colspan="3">environmental detected;</td><td></td><td></td>

<td></td><td>kss</td><td>is</td><td>a</td><td colspan="2">first coefficient &lt;</td><td>of the</td><td>model</td><td>of</td><td>camera</td>

<td>open;</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td>

<td></td><td>kjiM</td><td>is</td><td>a</td><td colspan="2">second coefficient</td><td>of the</td><td>model</td><td>of</td><td>camera</td>

<td>open;</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td>

<td></td><td>Coc</td><td>is</td><td>a</td><td colspan="2">compensation value</td><td>of the</td><td>model</td><td>of</td><td>camera</td>

open.

Typically the model includes determining air temperature at least in part using the relationship:

) T_H.H, if the chamber is closed T_oc, if the camera is open where: T_ANDff is the air temperature.

Typically, the method includes determining the temperature of the liquid using the air temperature and a thermal model of the liquid.

Typically, the method includes determining the temperature of the liquid using a predetermined liquid temperature.

Typically, the method includes determining the temperature of the liquid at least in part using the relationship:

T_L(n) = (lk_AND-k_L) T_L(nl) + k_LT_L(n-2) + k_ANDT_Eff(n) where: n is a discrete time interval;

T_L(n) is the temperature of the liquid at time n;

T_ANDff (n) is the air temperature at time n;

k_AND it is a first coefficient of the liquid model;

k_L it is a second coefficient of the liquid model.

Typically the method includes:

a) determining a target liquid temperature;

b) determining a target air temperature according to the target liquid temperature; and

c) Selectively heat or cool air in the chamber according to the target air temperature.

Typically the method includes determining the target air temperature at least in part using the temperature of the liquid.

Typically the method includes:

a) determining a change in the temperature of the target liquid;

b) compare the change with a threshold; and

c) at least one of:

i) if the change is less than the threshold, determine the target air temperature to be the target liquid temperature; and ii) if the change is greater than the threshold, determine the target air temperature according to the target liquid temperature and the liquid temperature.

Typically if the change is greater than the threshold, the method includes determining the target air temperature using the ratio:

Tñs (n) = Tis ^ koF (Tls ~ Tlm (n)) where: T_ACE(n) is the target air temperature at any given discrete time n;

T_LS is the temperature of the target liquid;

k₀F is a constant of the overflow factor;

is a liquid temperature at any given discrete time n.

Typically, the method includes determining at least one constant from among the constant reference values.

Typically, the method includes determining constant reference values ​​from a data store.

Typically, at least one constant includes at least one of:

a first coefficient of the closed chamber model ksL!

a second coefficient of the closed chamber model ksu!

a first offset value of the closed chamber model C_L;

a second offset value of the closed chamber model Cu;

a first coefficient of the kss open chamber model!

a second coefficient of the open chamber model kAMr a compensation value of the open chamber model c_ORc!

a first coefficient of the liquid model k_AND;

a second coefficient of the liquid model k_L;

an overflow factor constant k_0F.

Typically, the method includes determining constant reference values ​​during a calibration procedure.

Typically the method includes determining the constants of the closed chamber model by:

a) gradually increase a chamber temperature with the chamber closed;

b) detecting a change in each of at least three markers provided in the chamber, each of at least three markers being adapted to undergo a detectable change at a respective marker temperature;

c) determining a detected chamber temperature for each marker change; and

d) determine the constants of the closed chamber model using the detected chamber temperature and a corresponding marker temperature.

Typically the method includes determining the liquid model constants for a given volume of liquid by:

a) run a number of thermal cycling runs;

b) for each run:

i) monitoring a characteristic of a provided liquid sample when the chamber is closed, the sample characteristic is indicative of a liquid temperature of the liquid sample;

ii) determining at least one liquid temperature using the characteristic;

iii) determining at least one detected chamber temperature corresponding to at least one liquid temperature;

iv) determining an air temperature using at least one detected chamber temperature and a closed thermal model; and

c) run a regression analysis to relate the air temperature to the liquid temperature to determine the constants of the liquid model.

Typically the method includes:

a) determining constants of the liquid model for a determined number of liquid volumes; and

b) interpolate liquid model constants for intermediate liquid volumes.

Typically, the method includes determining open chamber model constants by:

a) change a chamber temperature with the chamber open;

<td rowspan="2">liquid</td><td rowspan="2">b) monitor provided</td><td rowspan="2">a in</td><td colspan="2">characteristic</td><td colspan="2">of a sample of the</td>

<td>the</td><td>camera the</td><td>characteristic</td><td>of</td>

<td>shows</td><td>is indicative</td><td>of</td><td>a</td><td>temperature</td><td>liquid</td><td>the</td>

<td>shows</td><td>of liquid;</td><td></td><td></td><td></td><td></td><td></td>

c) determining a number of liquid temperatures using the characteristic;

d) determining a number of detected chamber temperatures and detected ambient temperatures corresponding to the number of liquid temperatures;

e) determining a number of air temperatures using the number of detected chamber temperatures and a closed thermal model; and

f) determine a number of air temperatures

<td>15 using the number of</td><td>temperatures</td><td>of</td><td>liquid and a</td><td>model</td>

<td>liquid thermal; and</td><td></td><td></td><td></td><td></td>

<td>g) determine</td><td>constants</td><td>of the</td><td>model of</td><td>camera</td>

<td>open using the</td><td>temperatures</td><td>of</td><td>air and the</td><td>camera</td>

detected and ambient temperatures detected.

Typically the method is executed at least in part using a thermal cycling apparatus controller, the controller includes a processor and memory.

Typically the method includes, in the processor, retrieving at least one constant from memory.

Typically the method includes, in the processor:

a) receiving a chamber temperature detected from a temperature sensor in the chamber;

b) determining an air temperature using the detected chamber temperature and a thermal air model stored in memory;

c) determine a liquid temperature using air temperature and a liquid thermal model stored in memory; and

d) controlling at least one of a heater, a fan, and a vent flap to selectively heat or cool air in the chamber according to the temperature of the liquid.

In a second broad form, the present invention seeks to provide an apparatus for controlling the temperature of a liquid maintained within a reaction container in a chamber of a thermal cycling apparatus, the apparatus includes a controller that:

a) determines a chamber temperature detected from a temperature sensor in the chamber;

b) determine an air temperature using the detected chamber temperature;

c) determine a liquid temperature using the air temperature; and

d) Selectively heats or cools air in the chamber according to the temperature of the liquid.

Typically the controller includes a processor and memory.

Typically memory is to store at least one of:

<td></td><td>to)</td><td>a</td><td>model</td><td>finished</td><td>of</td><td>liquid</td><td>r</td>

<td></td><td>b)</td><td>a</td><td>model</td><td>thermal</td><td>of</td><td>air;</td><td></td>

<td></td><td>c)</td><td>a</td><td>model</td><td>thermal</td><td>of</td><td>camera</td><td>closed;</td>

<td> 10</td><td>d)</td><td>a</td><td>model</td><td>thermal</td><td>of</td><td>camera</td><td>open;</td>

e) at least one model constant.

Typically the processor:

a) receives a chamber temperature detected from a temperature sensor in the chamber;

b) determine an air temperature using the detected chamber temperature and a thermal air model stored in memory;

c) determine a liquid temperature using the air temperature and a liquid thermal model stored in memory; and

d) controls at least one of a heater, a fan, and a vent flap to selectively heat or cool air in the chamber according to the temperature of the liquid.

Typically the controller is coupled to at least one of:

a) a chamber temperature sensor to detect a chamber temperature;

b) an ambient temperature sensor to detect an ambient temperature;

c) a heater to heat the chamber;

d) a fan to cycle the ambient air through the chamber; and

e) a vent flap to close the chamber.

In a third broad form, the present invention seeks to provide a method for determining the temperature of a liquid held within a reaction container in a chamber of a thermal cycling apparatus, the method includes:

a) determining a detected chamber temperature from a chamber temperature sensor;

b) determining an air temperature using the detected chamber temperature; and

c) determine a liquid temperature using the air temperature.

Typically, the method includes determining the liquid temperature using the air temperature and a thermal liquid model.

Typically, the method includes determining an air temperature using the detected chamber temperature and a thermal air model.

<td colspan="4">Typically the method</td><td colspan="3">It includes:</td>

<td>to)</td><td>yes</td><td>the</td><td>camera</td><td>is closed,</td><td>decide</td><td>the</td>

<td>temperature</td><td>of the</td><td>air</td><td>effective</td><td>using the</td><td>temperature</td><td>of</td>

<td colspan="2">camera detected</td><td>and a</td><td>model of</td><td>: closed chamber</td><td>: and</td><td></td>

<td>b)</td><td>yes</td><td>the</td><td>camera</td><td>it's open,</td><td>decide</td><td>the</td>

<td>temperature</td><td>of</td><td>air</td><td>effective</td><td>using the</td><td>temperature</td><td>of</td>

chamber detected, a ambient temperature detected, and an open chamber model.

In a fourth broad form, the present invention seeks to provide an apparatus for determining the temperature of a liquid maintained within a reaction container in a chamber of a thermal cycling apparatus, the apparatus includes a processor that:

a) determines a detected chamber temperature from a temperature sensor in the chamber;

b) determine an air temperature using the detected chamber temperature; and

c) Determine a liquid temperature using the air temperature.

It will be appreciated that the broad forms of the invention can be used individually or in combination, and can be used for temperature control in a range of different applications including, but not limited to nucleic acid amplification.

BRIEF DESCRIPTION OF THE FIGURES

Examples of the invention will now be described with reference to the accompanying drawings in which:

Figure 1 is a schematic diagram of an example of apparatus for controlling the temperature of a reaction mixture;

Figure 2 is a flow chart of an example of a process for controlling the temperature of a reaction mixture using the apparatus of Figure 1;

Figure 3 is a schematic side view of a second example of the apparatus for controlling the temperature of a reaction mixture;

Figure 4 is a schematic diagram of an example of a controller for the apparatus of Figure 3;

Figure 5 is a flow chart of an example of a process for controlling the temperature of a reaction mixture using the apparatus of Figure 3;

Figure 6 is a graph showing an example of the temperature response of the apparatus of Figure 3 operating using the control process of Figure 5;

Figure 7 is a flow chart of an example of a process for determining the temperature of a reaction mixture using the apparatus of Figure 3;

<td></td><td>The figure</td><td>8A is</td><td>a</td><td>diagram</td><td>schematic</td><td>of</td><td>a</td>

<td> 5</td><td>flow example</td><td>air in</td><td>the</td><td>apparatus</td><td>figure 3</td><td>with</td><td>the</td>

<td></td><td>closed chamber;</td><td></td><td></td><td></td><td></td><td></td><td></td>

<td></td><td>Figure S</td><td>3B is a</td><td colspan="2">graphic of a</td><td>example of</td><td colspan="2">first</td>

<td></td><td>and second models of</td><td colspan="3">closed chamber;</td><td></td><td></td><td></td>

<td></td><td>The figure</td><td>8C is</td><td>a</td><td>diagram</td><td>schematic</td><td>of</td><td>a</td>

<td> 10</td><td>flow example</td><td>air in</td><td>the</td><td>apparatus</td><td>figure 3</td><td>with</td><td>the</td>

open camera;

Figure 9 is a flow chart of an example of a process for calibrating a closed chamber air thermal model of a thermal cycling apparatus;

Figure 10 is a flow chart of an example of a process to calibrate a thermal model of liquid using a thermal cycling apparatus;

FIG. 11 is a flow chart of an example of a process for calibrating an open chamber air thermal model of a thermal cycling apparatus;

Fig. 12 is a schematic diagram of an example of a heat flow diagram of the liquid thermal model; and

Figure 13 is an image of an exemplary 200 pL reaction container containing a colored liquid and indicating the associated amounts of the thermal liquid model.

DETAILED DESCRIPTION OF IA PREFERRED MODALITY

An exemplary apparatus for detecting and optionally controlling the temperature of a liquid, for example, during a thermal cycling process, will now be described with reference to Figure 1.

In this example, apparatus 100 includes a camera

1010 containing a reaction container 111 having a liquid 110, such as a reaction mixture, therein. The apparatus 100 typically includes a controller 120 coupled to a heater 130 and a temperature sensor 140. The heater

130 typically it is a convection heater, or the like, accommodated to heat air in chamber 101, with temperature sensor 140 being used to detect a chamber temperature.

Apparatus 100 can optionally include a fan 150 and an ambient temperature sensor 160, coupled to controller 120. Fan 150 can be used to allow ambient air to be supplied to chamber 101 to help cool chamber 101, with the ambient air temperature being determined using

4 the ambient temperature sensor 160. However, this is not essential, and other cooling mechanisms can be used as will be described in greater detail below.

It will be appreciated that in one example, multiple reaction containers can be provided in an arrangement within the chamber, allowing the temperature of the liquid in multiple reaction containers to be determined and optionally controlled substantially simultaneously.

In use, controller 120 is adapted to monitor signals from temperature sensor 140, and use them to control heater 130. Accordingly, controller 120 can be any convenient form of controller, such as a conveniently programmed processing system, FPGA (Field Programmable Gate Array), or the like.

An exemplary process for controlling the temperature of liquid 120 will now be described with reference to FIG.

2.

In this example, in step 200, controller 120 determines a detected chamber temperature from temperature sensor 140. In step 210, controller 120 determines an air temperature using the detected chamber temperature. Air temperature is typically determined from the detected chamber temperature using a thermal air model, which defines one or more relationships between the detected chamber temperature and the air temperature. In some examples, the air thermal model can also take into account a detected ambient temperature determined from the ambient temperature sensor 160.

In step 220, controller 120 determines a liquid temperature using the air temperature. Liquid temperature is typically determined from air temperature using a liquid thermal model, which defines one or more relationships between air temperature and liquid temperature.

In step 230, controller 120 optionally selectively heats or cools the air in the chamber according to the temperature of the liquid, for example, selectively controlling heater 130, and / or fan 150.

Accordingly, the process described above operates by calculating the air temperature to which the reaction containers are exposed, based on a chamber temperature detected by a chamber temperature sensor.

Once the air temperature has been calculated, it is used to determine the temperature of the liquid, allowing the temperature of the liquid to be determined accurately without requiring direct measurement of the temperature of the liquid. This has a number of benefits.

For example, accurate determination of liquid temperature allows for improved thermal control of the liquid. This in turn allows for faster heating and cooling, thus reducing thermal cycling times. Additionally, the degree of heating and cooling used to achieve the required liquid temperature control can be reduced, making the thermal control process more energy efficient and thus reducing operating costs. The use of indirect liquid temperature measurement is also particularly beneficial in rotating thermal cycling devices, where a number of reaction containers are mounted on a rotating carousel, and where direct measurement of liquid temperature is problematic.

Therefore, the process described above allows precise thermal · control · of liquid samples in a rotary thermal cycling apparatus, which otherwise cannot be easily accomplished.

Additional features will now be described with reference to the following examples.

An example of the apparatus for controlling the temperature of a reaction process will now be described with reference to Figure 3.

In this example, apparatus 300 includes a body

310 and a cover 312, defining a chamber 311. Chamber 311 includes a mount 320 to receive a carousel 321. Carousel 321 includes a number of openings 322 to receive reaction containers 323, such as tubes

Eppendorf or the like, containing a liquid sample, such as a reaction mixture.

Mount 320 is coupled to shaft 331, which in turn is coupled to drive motor 332, allowing carousel 321 to be rotated within chamber 311. A wall 313 is provided that extends through chamber 311. to separate drive motor 332 from carousel 321. Wall 313 typically includes an opening having a 314 mesh therein to allow air flow through the 314 mesh.

Chamber 311 includes a heater 340, which in this example includes a heating element 341 and a fan 342 for circulating air within chamber 311. A chamber temperature sensor 343, such as a thermistor, is typically provided in the chamber 311 to generate signals indicative of a chamber temperature.

In one example, an optical sensor 360 is also provided mounted to wall 313 to detect the status of a reaction based on the color of an indicator in the reaction mixture. Optical sensor 360 can include an illumination source, such as a laser, and a corresponding optical detector to detect reflected illumination.

Chamber 311 typically also includes a fan 371 provided in a vent 372, to allow ambient air from outside of chamber 311 to be circulated through chamber 311. The vent typically includes a vent flap 373 to close vent 372. In one example, an ambient temperature sensor 374 is provided outside chamber 311 to generate signals indicative of a detected ambient temperature.

It will be appreciated that the apparatus will typically also include a controller, an example of which will now be described with reference to Figure 4.

In this example, controller 400 includes a processor 410, a memory 411, an input / output device 412 such as a keyboard and display, and an interface 413 coupled together via link 414. Interface 413 can be provided to allowing controller 400 to be coupled to any one or more of heater 340, impeller 332, temperature sensors 343, 374, fan 371, and vent flap 373.

The interface may also include an external interface used to provide connection to external peripheral devices, such as a barcode scanner, computer system, or the like. Accordingly, it will be appreciated that controller 400 can be formed from any convenient processing system,

FPGA, or the like.

In use, processor 410 typically executes instructions stored in memory 411 to allow apparatus 300 to be controlled. In this regard, a user will typically select a desired thermal cycling process, including a required temperature profile, using input / output device 412. This allows processor 410 to access the instructions and control of apparatus 300 to thereby cause apparatus 300 to implement the selected thermal cycling process.

In particular, this causes processor 410 to monitor signals from temperature sensors 343, 374 and use these to determine a liquid temperature. Determining the liquid temperature typically involves making the processor 410 access the air and liquid thermal models, along with associated constant reference values ​​from memory 411. In one example, the models are as outlined below, with the reference constants being derived during a calibration and / or setup process, as will also be described in greater detail below. Processor 410 then uses the temperature of the liquid to control the operation of heater 340, the fan

371 and the 373 breather flap, thus allowing the required temperature profile to be implemented.

It will be appreciated that processor 410 can also determine a reaction status, for example, using signals determined from optical sensor 350, and perform additional control, such as actuator control.

332, in order to execute the thermal cycling process. Because such functions are known in the art, this will not be described in greater detail below.

It will be appreciated from the foregoing that the apparatus is particularly intended for thermocyclists for nucleic acid amplification, wherein the reaction containers are supported on a rotary circular carousel mounted rotatably within a chamber.

Particularly preferred thermocyclists for use with the apparatus are the Rotor-Gene ™ family of thermocyclists manufactured and distributed by Qiagen GMBH (www.qiagen.com).

Other similar devices are disclosed in the publication

PCT International number WO 92/20778 and WO 98/49340. However, it will be appreciated that other commercially available thermal cyclers can be modified to operate as described above.

An example of the operation of the apparatus of the figure to control the temperature of the liquid in the reaction container will now be described with reference to figure 5.

In this example, at step 500, controller 400 determines a change in the temperature of the target liquid

ATls, based on a temperature of the target liquid T_Ls (n), for the thermal cycling process. This information is typically determined from a temperature profile stored in memory 411, which is associated with the current thermal cycling process. In step

510, controller 400 compares a change in temperature of the target liquid AT_IS/ with a threshold value ¿\ T_ORsth- This is used to allow the appliance to operate in one of two modes, generally referred to as standby and overflow modes.

In this case, if the magnitude of the change in the temperature of the target liquid AT_Ls is less than the threshold value AT_ORsraz then controller 4 00 operates in standby mode. Accordingly, controller 400 sets a target air temperature T_ACE(n) at the temperature of the target liquid T_LS(n) in step 520, and then selectively heats or cools chamber 311, using heater 340 and / or fan 371 and vent flap 373, based on the target air temperature T_ACE(n)_r at step 530. Accordingly, in the standby mode, changes in air temperature are assumed to be small enough that the liquid temperature remains substantially in equilibrium with the air temperature.

However, if the magnitude of the change in the temperature of the target liquid AT_LS is greater than the LTosth threshold value, then controller 4 00 operates in overflow mode. In overflow mode, in step 540 the controller

400 Determine a temperature of the liquid Ti «(n) using a liquid thermal model, which will be described in more detail below. In step 550, controller 400 then determines a target air temperature T_ACE(n) using the temperature of the liquid Τ_Μ(η), which in one example is achieved using the following relationship:

Tas (s) ⁼ T_LS+ koF · (Tls-Tlm (n)) (1) where: T_ACE(n) is the target air temperature at any given discrete time n;

T_LS is the temperature of the target liquid;

k_0F it is an overflow factor constant;

TiMÍn) is a liquid temperature at any given discrete time n.

In this case, the air temperature is rapidly changing, so that the air temperature in chamber 311 differs significantly from the liquid temperature. This allows the liquid to be heated or cooled

<td>the fastest</td><td colspan="2">possible, taking</td><td>consider</td><td>the</td><td>thermal mass</td><td>of the</td>

<td>liquid and the</td><td>container</td><td>of</td><td>reaction.</td><td>TO</td><td>as</td><td>the</td>

<td colspan="2">liquid temperature</td><td>I know</td><td>approximates</td><td>to</td><td colspan="2">temperature</td>

<td>objective the</td><td>effect of</td><td colspan="2">heating</td><td>or</td><td>cooling</td><td>I know</td>

<td colspan="2">reduces, so that the</td><td colspan="2">temperature</td><td>of the</td><td colspan="2">fresh liquid</td>

reaches the target temperature. An example of the temperature profile is shown in figure 6.

The result of this fix is ​​that when it is in overflow mode:

• For the first 90% of the transition, the heating or cooling power is maximum, to maximize the speed of the transition;

• In the final 10% part of the liquid temperature transition, the heating / cooling rate of the liquid decreases in proportion to how close it is to the target temperature, as there is a gradual reduction in the difference between the set air temperature and target liquid temperature, rather than abrupt change.

<td>Therefore, in this arrangement, the</td><td>temperature</td>

<td>of the liquid gradually approaches the</td><td>temperature</td>

<td>objective, so that it is not far above</td><td>or very</td>

<td>5 below the target temperature, while</td><td>allowed</td>

the heating / cooling rate is raised to the maximum, thus reducing the thermal cycle time. It should also be noted that when heated from 55 ° C to 95 ° C, the 373 cooling vent flap is not open.

This is in contrast to some traditional control processes, the cooling vent flap 373 is open at the transition end to abruptly cool the air, thus resulting in increased overall energy usage for the apparatus. Therefore it will be appreciated that this provides a particularly beneficial thermal control process.

In order to operate in accordance with the above described thermal control process, a temperature of the liquid is determined, and an example of the process for achieving this will now be described with reference to Figure 7.

In this example, in step 700, controller 400 determines a detected chamber temperature T_s from the chamber temperature sensor 343. Since the chamber temperature sensor 343 will detect a localized air temperature within chamber 311, it is necessary to use an air thermal model to derive an air temperature that reflects more accurately the effective air temperature within chamber 311. In this sense, the air temperature is then the effective air temperature to which the reaction containers are exposed. The air temperature is provided by:

<td></td><td>^Tsff</td><td>T_H.H, if the chamber is closed T_oc, if the camera is open</td><td></td><td></td><td> (2)</td><td></td><td></td>

<td>where:</td><td></td><td>is the temperature of the</td><td>air;</td><td></td><td></td><td></td><td></td>

<td></td><td>Tss</td><td>is a temperature of</td><td>air</td><td>of the</td><td>model</td><td>of</td><td>camera</td>

<td>closed;</td><td>Toe</td><td>is a temperature of</td><td>air</td><td>of the</td><td>model</td><td>of</td><td>camera</td>

open;

Therefore, in this example, the air temperature is calculated using a thermal air model that is divided into a closed chamber model and an open chamber model.

/

The closed chamber air model is used whenever the vent flap 373 is closed and the fan 371 is turned off, so that when there is negligible air exchange between the interior and exterior of the chamber. The effective air flow for the closed chamber model is shown schematically in Figure 8A.

In one example, the closed chamber model is a two-part linear model that has first and second models that relate the temperature detected by the chamber temperature sensor 343 to an accepted actual average air temperature to which the exteriors are exposed of the reaction containers. Mathematically the model is provided by:

^ slTs + Cl, ^yes T_s&lt;T_r + ο_υ, if T_s &gt; T_T

3) where T_Ss is an air temperature of the closed chamber model;

Ts is the detected chamber temperature;

Tt is a threshold temperature;

k_YES it is a first coefficient of the closed chamber model;

k_Su is a second coefficient of the closed chamber model;

c_L it is a first compensation value of the closed chamber model; and

Cu is a second offset value of the closed chamber model.

The resulting transfer function is shown in Figure 8B, which highlights that the first and second models intersect at transition temperature T_T. Two first-order models are used in this example to compensate for any non-linearity between the detected chamber temperature and the actual air temperature. This also allows for only 3 temperature points for which the model needs to be calibrated, which can be done using the 3 sets of Thermal Liquid Crystals (TLC) as will be described in more detail below. Calibration is performed to determine closed chamber model constants, including threshold temperature T_T, the first coefficient of the closed chamber model k_LS, the second coefficient of the closed chamber model k_Su, the first offset value of the closed chamber model c_Lr and the second offset value of the closed chamber model c_to. The closed chamber model constants are typically stored in memory 411, so that they can be accessed during the temperature determination process.

In contrast, when the vent flap 373 is open, and the fan 371 is on, the air flow through the chamber is different than for the closed chamber case, and an example of the effective air flow is shown so schematic in figure 8C. The result is that the relationship between the chamber temperature and the air temperature is different, and additionally depends on the ambient air temperature.

Accordingly, controller 400 uses an open chamber model to determine the air temperature of the open chamber model T_oc. The open-chamber thermal model models this difference as a simple linear superposition of the closed-chamber air thermal model and the ambient air temperature, and in this example it is provided by:

<td></td><td>Toe</td><td>= k</td><td colspan="2">'SsTsS + kAMTñM + Coc</td><td> (4)</td><td></td><td></td>

<td>where:</td><td>Toe</td><td>is</td><td>a</td><td>air temperature</td><td>of the model</td><td>of</td><td>camera</td>

<td>open;</td><td>Tss</td><td>is</td><td>a</td><td>air temperature</td><td>of the model</td><td>of</td><td>camera</td>

<td>closed;</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td>

<td></td><td>Tam</td><td>is</td><td>a</td><td colspan="2">ambient temperature detected;</td><td></td><td></td>

<td></td><td>kss</td><td>is</td><td>a</td><td colspan="2">first coefficient of the model</td><td>of</td><td>camera</td>

<td>open;</td><td>kñM</td><td>is</td><td>a</td><td>second coefficient</td><td>of the model</td><td>of</td><td>camera</td>

<td>open;</td><td>Coc</td><td>is</td><td>a</td><td>compensation value</td><td>of the model</td><td>of</td><td>camera</td>

open.

The constants of the open chamber model, including the first coefficient of the open chamber model k_H.H, the second coefficient of the open chamber model k_m, and the compensation value of the open chamber model c_ORc, can be determined during a calibration process, as will be described in greater detail below, and which are stored in memory 411.

It will be appreciated that in the above example, the air temperature of the closed chamber model is used in the open chamber model, and therefore the air temperature of the closed chamber model is determined without regard to whether the vent 373 is open or closed. .

Accordingly, in step 710, processor 410 determines whether the detected chamber temperature T_s, is above or below a threshold temperature T_T. In the event that the threshold temperature is exceeded, processor 410 moves to step 720 to access the first coefficient of the closed chamber model k_SL, and the first compensation of the closed chamber model c_£, from memory 411.

Alternatively, if the detected chamber temperature T_s, is below the threshold temperature, the processor

410 moves to step 730 to access the second closed chamber model coefficient ksu, and the second closed chamber model offset value c_to. In step 740, processor 410 uses the accessible constants to determine the air temperature of the closed chamber model T_H.H.

At 750, the controller 400 determines if the vent flap 373 is open, and if so, the process advances to step 760 in which the processor 410 determines a detected ambient temperature from the ambient temperature sensor 374. In the step 770, the processor 410 has access to the open chamber model constants, including the first coefficient of the open chamber model k_Ss, the second coefficient of the open chamber model km, and the compensation value of the open chamber model c_0C, before calculating the air temperature of the open chamber model T_ORc ·

Following this, or in the case where the vent flap 373 is closed, the processor 410 uses the air temperature T_ANDff, which is based on either the air temperature of the closed chamber model T_H.H, or the air temperature of the open chamber model T_ORc, to determine a temperature of the liquid. In one example, this is accomplished using a liquid thermal model.

The liquid thermal model only has one input, specifically the air temperature T_Eff, with the temperature of the liquid being provided by:

T_L(n) = (lk_AND-k_L) T_L(nl) + k_LT_L(n-2} + k_ANDT_Eff(n) (5) where: n is a discrete time interval;

T_L(n) is the temperature of the liquid at time n;

T_ANDff (n) is the air temperature at time n; k_AND it is a first coefficient of the liquid model;

and k_AND it is a second coefficient of the liquid model.

The derivation of this equation is highlighted below in Appendix A.

The constants of the liquid model including the first coefficient of the liquid model k_AND and the second coefficient of the liquid model k_L they are determined during a calibration process, as will be described in greater detail below, and are stored in memory 411. The model is implemented by controller 400 and is essentially the entire discrete-time liquid thermal model.

The constants of the liquid model depend on the volume of sample used, and optionally the reaction container used and therefore different constants of the liquid model can be stored for different volumes of liquid and / or types of reaction container. In this case, the user can provide relevant details, such as a sample volume and reaction container type when the particular thermal cycling process to be run is selected, thus allowing processor 410 to access the constants of the relevant liquid model from memory 411, in step

790. In case the reference constants are not available for the current liquid volume, they will typically be extrapolated from the available liquid model constants, using linear interpolation or another similar technique.

Once the relevant liquid model constants have been determined, processor 410 calculates the liquid temperature in step 800, allowing controller 400 to control heater 340, fan 371, and vent flap 373 according to the thermal control process of figure 5 above.

Accordingly, it will be appreciated that the process of Figure 7 allows controller 400 to calculate liquid temperature in real time, based on signals from temperature sensors 343, 374, and using air and liquid thermal models. This information can then be used in the control algorithm of Figure 5, thus enabling rapid and accurate liquid temperature control to be achieved.

As mentioned above, the reference constants used in the air and liquid models can be determined during a calibration process, an example of which will now be described with reference to Figures 9 through 11. In this example, the process General will first calibrate a specific 300 thermal cycling apparatus to determine the constants of the closed chamber model.

Once this is complete, the calibration is run on the same page to determine constants for the thermal thermal model, where these results are used to calibrate the open chamber model.

The open and closed chamber model constants refer to the readings from the temperature sensors 343, 374 at the air temperature in the chamber and are therefore specific to the thermal cycling apparatus.

These calibrations are then performed on a per magic basis. In contrast, the liquid model refers to the air temperature to which the reaction containers are exposed for heating the liquid, and therefore independent of the thermal cycling apparatus. However, these constants depend on the volume of liquid in the tube, and optionally the nature of the reaction container itself, and therefore calibration of the liquid model is typically performed for a range of different sample volumes, and optionally containers reaction.

An exemplary process for calibrating closed chamber model constants for a specific thermal cycling apparatus will now be described with reference to Figure 9.

In this example, at step 900, the thermal cycling apparatus 300 is loaded with at least three liquid samples including the respective markers. Each marker is adapted to undergo a detectable change at a respective marker temperature and in the meantime any of the markers can be used, typically the markers in the form of liquid thermal crystals (TLC),

Pyronin-Y, or the like. The markers undergo an optical change, which can be detected by the 360 ​​optical sensor, at a known temperature, allowing three known liquid temperatures to be detected.

In step 910, processor 410 controls heater 340 to cause chamber 311 to gradually rise in temperature, with vent flap 373 closed. By gradually increasing the temperature, the liquid samples are assumed to be in thermal equilibrium with the air in the chamber, so that the temperature of the liquid is effectively equal to the air temperature.

In step 920, processor 410 monitors a signal from optical sensor 360 to determine if a marker change has occurred. If a marker change is not detected, the process returns to step 910, allowing additional heating to occur. Otherwise, once a marker change has been detected, controller 400 records the chamber temperature detected by chamber temperature sensor 343, along with the associated marker temperature of the marker that is undergoing the change, in step 930.

<td>In</td><td>the</td><td>step 940,</td><td>controller 400</td><td colspan="2">determine if</td>

<td>each one of</td><td>the</td><td>markers</td><td>has experienced a</td><td>change,</td><td>and in</td>

<td>case of no</td><td colspan="2">be like this, the</td><td>process returns</td><td>to step</td><td> 910</td>

<td>allowing</td><td>than</td><td>a</td><td colspan="2">additional heating. Of</td><td>other</td>

<td>shape in</td><td>the</td><td>step 950,</td><td>processor 410</td><td>drift</td><td>the</td>

constants of the closed chamber model.

It will be appreciated, from the previous model in equation (3), that two of the three reference temperatures are used to define the first constants of the closed chamber model, with another two of the three reference temperatures being used to define the second constants of the closed chamber model, where each model is based on a linear relationship. The constants determined can then be stored in memory

411 for later recovery and use.

An exemplary process for calibrating the liquid model constants will now be described with reference to Figure 10.

In this example, in step 1000, a thermal cycling apparatus 300 is loaded with liquid samples of a given volume, and into certain reaction containers. Liquid samples have a characteristic that undergoes a detectable change with changes in temperature. In one example, the liquid samples include Pyronin-Y, which undergoes a continuous change in fluorescence with temperature, thus allowing a liquid temperature to be determined based on liquid fluorescence.

It should be noted that in one example, TLCs similar to those used in Figure 9 above are not used in the calibration of the liquid model constants as they do not emulate the thermal properties of a PCR buffer (aqueous solution) as well as a Pyronin-Y solution. However, it will be appreciated that any marker that does not adequately emulate a PCR buffer could also be used.

In step 1010, processor 410 controls heater 340, flap 373, and fan 371 to execute a thermal cycling process, and in particular to cause samples to undergo a sequence of temperature changes. In step 1020, processor 410 monitors the characteristic of the liquid sample, which in this example involves monitoring signals from the optical sensor 360 to determine the fluorescence of the sample, and then using this information to derive a liquid temperature. . At the same time, in step 1030, controller 400 monitors signals from chamber temperature sensor 343 to determine a detected chamber temperature, which is then used to derive an air temperature. Air temperature is determined from the detected chamber temperature using the closed chamber model and the calibration information derived from the process in Figure 9. Consequently, this process is executed when the chamber is closed, and the fluorescence and temperature of the chamber are then not monitored when the chamber is open.

In step 1040, controller 400 determines whether thermal cycling runs are complete, and if not, the process returns to step 1010 allowing the run to continue. Otherwise, in step 1050, processor 410 performs a linear regression based on the air temperature derived from the detected chamber temperature, and the liquid temperature derived from the fluorescence of the liquid sample. Linear regression is used to derive the constants of the liquid model in step 1060, and is described in detail in Appendix Β.

In step 1070, controller 400 determines if all sample volumes and all reaction container types have been tested, and if not, the process returns to step 1000, allowing different sample volumes and / or reaction containers are calibrated. Otherwise, in step 1080 the process ends with the determined liquid model constants being stored in memory 411 as well as optionally exported for use in other thermal cycling devices.

An exemplary process for calibrating open chamber model constants for a specific thermal cycling apparatus will now be described with reference to Figure 11.

In this example, in step 1100, the thermal cycling apparatus 300 is loaded with liquid samples of a given volume, and in certain reaction containers. Liquid samples have a characteristic that undergoes a detectable change with changes in temperature. In one example, the liquid samples include Pyronin-Y, which undergoes a continuous change in fluorescence with temperature, thus allowing a liquid temperature to be determined based on liquid fluorescence.

<td>It should</td><td colspan="2">observe that</td><td>in</td><td>an example the</td><td>TLC</td>

<td>similar to those</td><td>used</td><td>in</td><td>the</td><td>figure 9 above</td><td>not</td>

<td>are used in</td><td>calibration</td><td>of</td><td>the</td><td colspan="2">model constants</td>

<td>of liquid since no</td><td>emulate</td><td colspan="3">thermal properties of</td><td>a</td>

PCR buffer (aqueous solution) as well as a Pyronin-Y solution. However, it will be appreciated that any marker could be used that conveniently emulates a PCR buffer.

In step 1110, processor 410 controls heater 340 to initially heat chamber, before opening flap 373 and activating fan 371 to start a cooling portion of a thermal cycle run, thereby causing chamber 311 to cool. . In step 1120, processor 410 monitors the characteristics of the liquid sample, which in this example involves monitoring signals from the optical sensor 360 to determine the fluorescence of the sample. This is run to determine a number of liquid temperatures at different times.

Simultaneously, in step 1130, processor 410 monitors the chamber temperature detected by chamber temperature sensor 343, and the ambient temperature detected by ambient temperature sensor 374, to thereby determine ambient and chamber temperatures. detected, measured at the corresponding times.

In step 1140, controller 400 determines if the cooling run has ended, and if not, the process returns to step 1110 allowing further cooling to occur.

Otherwise, in step 1150, processor 410 uses the liquid model to derive the air temperature for each detected liquid temperature using the fluorescence of the sample. Using this information, as well as the detected chamber and ambient temperatures and the closed chamber model, processor 410 can determine the constants of the open chamber model in step 1160, with the determined constants being stored in memory 411 for later retrieval. and use.

Accordingly, the above calibration process allows reference constants to be easily determined for the liquid and air thermal models described above, thus allowing the models to be easily implemented.

In any event, it will be appreciated that the method and apparatus described above allow the temperature of a sample liquid to be determined using signals from a chamber temperature sensor and optionally an ambient temperature sensor. The liquid temperature accurately reflects the temperature of the liquid samples within the reaction containers, thus allowing the determined liquid temperature to be used in the control of thermal cycling processes, for example, as used in reactions PCR. In one example, the liquid temperature can then be used in a proportional overflow process similar to that described above with reference to Figure 5, thus allowing rapid and accurate temperature adjustment of the liquid samples to be achieved.

It will be appreciated that although the above described system typically uses an open chamber model as well as a closed chamber model, this may not be required if the chamber remains closed during the thermal cycling process, such as may occur for example if using an alternative cooling mechanism. In this case, if the cooling mechanism is inside the chamber, this can be taken into account by monitoring the temperature changes using the chamber temperature sensor only. Alternatively, other equivalent models can be used.

Although the invention has been described with reference to specific examples, those skilled in the art will appreciate that the invention can be incorporated in many other ways. In particular, features of any of the various described examples can be provided in any combination in any of the other described examples.

APPENDIX A

In the liquid thermal model it is assumed that there are two thermal storages, the plastic tube and the liquid. It is assumed that there are also two corresponding thermal resistances, one from air to plastic, and then one from plastic to liquid. The liquid is also assumed to have a negligible effect on the temperature of the plastic. Figure 12 shows a heat flow diagram of the liquid thermal model, with an image of a typical 2000 pL reaction container containing a colored liquid showing how the quantities of the liquid thermal model are assumed that is related to the real system that is being modeled, being shown in figure 13.

Continuous time equations of the liquid thermal model

The heat flux in the plastic can be represented by the equation:

Paf = G_TOf (T_eee-T_p) (6)

Where P_ñP is the heating power of air to plastic (generally expressed in Watts (W))

G_AP is the thermal conductance of air to plastic (generally expressed in watts per degree centigrade (W / ° C))

T_FFF is the effective air temperature to which the tubes are exposed (usually expressed in degrees centigrade (° C))

T_P is the temperature of the plastic (usually expressed in (° C))

Similarly, the heat flux in the liquid can be represented by an equation in the same way:

P_PL = G_pl (T_p-T_l) (7)

Where P_PL is the plastic to liquid heating power (usually expressed in watts (W)).

G_pl is the plastic to liquid thermal conductance (usually expressed in watts per degree centigrade (W / ° C)).

T_P is the temperature of the plastic (generally expressed in ° C)).

T_L is the temperature of the liquid (generally expressed in ° C))

Continuous time differential equations

The rate of change of temperature of the plastic can be represented by the following equation dT_P _ P_AP dt C_P (8) dT where —- is the rate of change of the temperature of the plastic dt (generally expressed in degrees centigrade per 5 second (° C / s)).

C_P is the heat capacity of the plastic (generally expressed in Joules per degree centigrade (J / ° C)).

Similarly, the rate of change of liquid temperature can be represented by the following equation:

dT _L_ _ -¹ PL dt C, (9) dT_L

Where _is rate of change of the temperature of the liquid dt (generally expressed in degrees centigrade per second (° C / s)).

C_L is the heat capacity of the liquid (generally expressed in Joules per degree centigrade (J / ° C)).

The above equations for heat flux (equations (6) and (7)) and the rate of change of temperature (equations (8) and (9)) can be combined to condense the unknown constants, as follows:

dT_P dt (10) dT, dt ^ωΡΐΑ^ΤΡ ~^ΤΐΑ (11)

Where ω_ΑΡ is a constant that relates the rate of change of the plastic temperature to the difference between the plastic and the effective air temperature. It is also the angular cutoff frequency 3dB of the corresponding low-pass filter. The value of this could be expressed in

Hertz (Hz).

or_PL is a constant that relates the rate of change of the temperature of the liquid to the difference between the liquid and the temperature of the plastic. This is also the corresponding low-pass filter 3dB cutoff angular frequency. The value of this could be expressed in

Hertz (Hz).

The constant ω_ΛΡ also related to G_ñP and

C_P by:

or&gt; ap

<img file="MX2012012172A_D0001.tif" />

(12)

Similarly the constant ω_{Ρ £} also related to G_PL and C_£ by:

'PL

C_L (13)

The constants ω_Αί&gt; already_PLf Inverse time constants can also be considered:

⁵ 1 ^TAP ~

G&gt; ap and

i ^TPL - &lt;»PL

Where τ _AP is the time constant of the relationship between air temperature and plastic temperature. The value of this could be expressed in seconds (s). This is equivalent to the time it takes for plastic to change by 63% of a gradual change in air temperature.

τ _PL is the time constant of the relationship between the temperature of the plastic and the temperature of the liquid. The value of this could be expressed in seconds (s). This is equivalent to the time it takes for the liquid to change by 63% of a gradual change in plastic temperature.

Solutions to differential continuous time equations

The solution to equation (10), assuming the constant is the decreasing exponential function of equation (14).

(14)

T_P(t) = T_{E ££}+ [T_P(t₀) ~ T_{E ££})] e^{akP {t}-^t0}

Similarly, the solution to equation (11), assuming the constant T_P is the decreasing exponential function of equation (15).

T_L(t) = T_P+ [T_L(t₀) ~ T_P] e (15)

Separate discrete-time equations of the liquid thermal model

<td>The</td><td colspan="3">liquid thermal model is typically</td>

<td>implemented</td><td>in</td><td>a microcontroller in the</td><td>circuits</td>

<td>electronic</td><td>of the</td><td>thermal cycling apparatus and, for</td><td>therefore</td>

<td>It should be</td><td>in</td><td>a form of discrete time.</td><td>Time</td>

<td>continuous, t,</td><td colspan="2">then it is related to the</td><td>index of</td>

discrete time sample, n, using the equation:

t = nT (16)

Where T is the discrete time sampling period which in one example is lOOms

T_P(nT) = T_{Ef £}+ [T_P ((n-1) T) - T_EFF)] e '“^ñPTTP (nT) = TEff + TP ((nl) T) e^aAP-TEFFe ~ ^^PT

T_P(nT) = e '^aAPTTP ((nl) Ij + [le ~^akPT] TEff

Replacing 2-e ~ "^ñPT with b_AP:

T_P(nT) = (lh_ñP) T_P ((n-1) T) + h_ñPT_{E ££}

Assuming that T_{E ££} remains constant over the entire sample interval:

TpfnTj = (í-h_AP) T_P ((n-1) T) + h_APT_ANDff (nT)

Replacing the time dependency with the sample index dependency:

Tp (n) = (lh_AP) Tp ((n-1) + h_TOpT_ANDff (n) (17)

And repeating the process in equation (11) produces:

T_L(n) = (lh_PL) T_L((n-1) + h_PET_P (n) (18)

Where h_AP is the discrete time 3dB cutoff angular frequency of the model relating the temperature of the plastic to the air temperature.

h_PL is the angular frequency of cut 3dB of discrete time of the model relating the temperature of the liquid with the temperature of the plastic.

Combined equation of the thermal model of liquid

It is not practical to directly measure the temperature of the plastic (even if the actual system was the same as the model described here), however it is possible and practical to measure the temperature of the liquid. Additionally, the temperature of the liquid is the temperature in which we are interested, and not the temperature of the plastic.

The above two first order equations can be combined to provide a second order equation which removes the discrete time signal from the plastic temperature.

W = (I - W &lt;- ') + /.,. (0 - h.Mr&gt; - [) + V ^ / l)) / Τ / «- ΙΊ_Ζ1

/.(/ ») = (i - /.,.) / (/ 1-0 + / ,,.

/ („) = 0 - / Purchase)) /. (Purchase-0+0 -V (/ (« - 1) - (1 -h,) /. («- 2)) + νΛ)

W = 0-W „-1) + (1 - / iJ (/ (/ il) - / (/) - 2) + / ,,. / (/ I-2)) + / i, .ArW / ( / i) = 0- / i_w.) / (/ i-0 + (/ (n-.0 - /. («- 2) + /.,. / (/ i-2) - //₄„/(/Jl)+/T4,/(/i-2)-M,Wine./(/5-2))+A.Wine.V^(ii)) / («) = (2- /. ,. - // ^ ,.) / (// - 1) + (- 1 + / „, + /.,. -ΑχΛ / Κ ^ - ^ + ^ ΛΛ ^ η)

This can be further simplified by condensing the constants again:

<td> 10</td><td colspan="2">k_L—-L + h_AP+ h_PL-h_APh_PL</td><td> (19)</td>

<td></td><td></td><td>k_AND—H_PLh_AP</td><td> (20)</td>

<td></td><td></td><td>So that:</td><td></td>

<td></td><td></td><td>k_L= -l + h_TOp + hp_L-k_AND</td><td></td>

<td></td><td></td><td>-h_AP-hp_L= -1 -k_AND-k_L</td><td></td>

<td> 15</td><td></td><td>2 —h_TOp — hpi, = l -k_AND-k_L</td><td></td>

<td></td><td></td><td>So the differential equation of</td><td>second</td>

<td></td><td>order of</td><td colspan="2">simplified discrete time describing the model</td>

<td></td><td>thermal</td><td colspan="2">of liquid, which relates the temperature of the</td>

<td></td><td>liquid</td><td>about time with air temperature</td><td>effective</td>

<td> 20</td><td>about him</td><td>time is:</td><td></td>

<td></td><td>T_L(n) =</td><td>(lk_AND-k_L) T_L (n-1) + k_LT_L (n-2) + k_ANDT_ANDff (n)</td><td> (21)</td>

Having the equation in the above form (i.e., no plastic temperature term) allows the constants to be easily calculated from a

<td>set</td><td>data from</td><td>signs</td><td>of</td><td>weather</td><td>discreet</td><td>of</td>

<td colspan="2">liquid temperature</td><td>and air,</td><td>such</td><td>how</td><td>using</td><td>the</td>

<td>regression</td><td colspan="2">linear multi-variant (</td><td colspan="2">as it</td><td>describes in</td><td>the</td>

Appendix Β).

Working backwards to extract discrete time equation constants

The constants of equations (17) and (18) above, h_AP yh_PL, can be derived from the constants of equation (21), k_AND and k_L. The combination of equations: 19) and (20):

k_L - 1 + h_AP + h_pl h_AP h_PL^kL = - ^ + ^hAP ⁺TT ~ -^kAND ^hAP h - k +) - k ^hAP

Multiplied by h_AP:

hñp²-hñPkL + hAP-kE + kEhAP hAp²-hApk_L+ h_ñP-k_ANDh_AP+ k_AND= 0 h_AP²-l · (-k_AND-k_AND-l) h_AP+ k_AND=0

Completing the square using temporary variables a, b and c.

íz = 1 = -k_L - k_AND -1 c =

AP

PL

-b + yjb² -4ac 2a kp ^hAP

Applying these equations to typical fitted constants allows the values ​​of h_AP yh_PL be determined.

Working backwards to extract the constants from the continuous-time equation.

As previously analyzed, there is a relationship:

h_TOp = l ~^and '&amp;_TOpT e ~ ^^T = \ - h_AP\ n (\ - h_APJ-co_APT

0&gt; AP =

-Wh_AP) and

h_PL= \ - e ^^T _- \ n (\ - h_PL) ^ωJ ~ j.

Applying these equations to typical fitted constants allows the values ​​of ω to be found_Αρ ym_PL.

Time constants can also be easily found:

-Τ and

-τ ^TpL~ \ n (\ - h_PL)

Applying these equations to typical fitted constants allows t_TOp and τpl are found. Working backwards it is possible to extract other quantities.

Plastic to Liquid Thermal Conductance

The value of the liquid heat capacity can be estimated in a typical aqueous solution sample, using the value of the sample volume and the specific heat capacity constant of the accepted water:

C_L= C_WV_L (22)

Where_L is the heat capacity of the liquid,

C_M is the specific heat capacity of water.

This has an accepted value at 25 ° C of 4,186J / cm3 / ° C (or more conveniently 4,186mJ / pL / ° C) for volumes in pL.

V_L is the volume of liquid in the sample.

If the value of the constant, mp_L It is known, together with this heat capacity of the liquid, then the thermal conductance of heating of the liquid, G_PL, can be derived using equation (13):

G_pi-OplCl (23)

Liquid heating / cooling power

Here are two methods for determining the heating power that heats a liquid sample in a given time.

If the heating capacity of the liquid is predetermined (as above in equation (22)) and the rate of change of the temperature of the liquid is known at a given moment, then the heating power of the liquid entering the tube at that instant can be calculated using a rearrangement of equation (9):

P = C ^rPL dT_L dt (24)

If at a given instant the thermal conductance of plastic to liquid and the difference between the temperature of the plastic and the temperature of the liquid are known; then the heating power of the liquid entering the tube at that moment can be calculated using equation (7), as previously analyzed.

APPENDIX B

We will now describe an exemplary process for fitting constants for thermal models using multi-variant linear regression.

For this purpose, it is convenient to approximate the behavior of a general real system with a simple linear model which assumes the form:

M y = f (x) = ^_mx_m (25)

Where y is the dependent variable that the model is calculating, x is the vector of independent variables on which the model depends,

M is the size of the vector xk_m is the constant of proportionality for the independent variable x_m x_m is an independent variable in the vector of independent variables x.

Usually the most appropriate values ​​of the constants of proportionality k (i.e., ki k_m) are not clear, but can be adjusted using various real system data samples (x and y) and a linear regression technique (see Appendix B).

Liquid thermal model

The second order liquid thermal model is of the form (equation (21)):

T_L(n) = (lk_AND-k_L) T_L(nl) + k_LT_L(n-2) + k_ANDT_Eff(n)

In order to make it fit the general equation form of equation (25), it needs to be rearranged:

T_AND (n) —T_AND (n-1) -k_ANDT_AND (n-1) -k_LT_L (n-1) + k_ANDT_L (n-2) + k_ANDT_ANDff (n)

T_L (n) -T_L (n-1) = k_AND (T_Eff (n) -T_L (n-1)) + k_L (T_L (n-2) -T_L (n-1)

So now, in terms of equation (25):

M = 2 y = T_L(n) -T_L(nl)

Xi = T_Eff(n) -T_L(nl) x₂ = T_L(n-2) -T_L(nl) ki = k_AND k₂ = k_L

If only closed chamber data from a run are used, then the constants of the liquid model k_L and k_AND they can be calculated using the above method, without having to determine the constants of the open-chamber air thermal model.

Open Chamber Air Thermal Model

Rearranging equation (22):

Tl (u) - (lk_AND-k_AND) T_AND (n-1) + k_ANDTi (n-2) + k_ANDT_EEf (η) k_ANDT_{E ££}(n) = T_L(n) - (lk_AND-k_L) T_L(nl) -k_LT_L(n-2)

T_Eff(n) = T_L (n) - (lk_AND-k_L) T_L (n-1) -k_LT_L (n-2) k_AND

Using the above equation, the effective air temperature can be calculated from the liquid temperature data, in case the constants of the liquid thermal model are known. Once the effective air temperature is known, the open-chamber data (only) can be used to find the constants of the open-chamber air thermal model. Thus, starting from equation (4), in the form of equation (25):

M = 3 y = T_Eff (n) kí = T_H.H(n) * 2 = AkC) * 3 = 1 ki = kss k₂ = k_w k₃ = Coc

Linear least squares solution for multi-variant linear regression

The constants k of the linear model of equation (25) can be adjusted using variant multi5 linear regression when several samples, N, of y and x of the real system are available.

The method of linear least squares to find the constants k is provided by:

k = (X^TX)^_1X^Tand (26)

Where k is a column vector of proportionality constants of size M

X is the matrix of the samples with N rows and M columns of the vector of independent variables, x, where each samples of x occupies one row.

X^T is the transposition matrix of X

X '¹ is the inverse matrix of X and is a column vector of size N containing the corresponding samples of the dependent variable, y, of the real system.

NOVELTY OF THE INVENTION

Having described the present invention, it is considered as a novelty and, therefore, the content of the following is claimed as a priority: