Scaling tool

Abstract

The present application generally pertains to scaling of a production process to produce a chemical, pharmaceutical and/or biotechnological product and/or of a production state of a respective production equipment. Particularly, there is provided a computer-implemented method of scaling a production process to produce a chemical, pharmaceutical and/or biotechnological product, the scaling being from a source scale to a target scale, wherein the production process is defined by a plurality of steps specified by one or more process parameters controlling an execution of the production process, the method comprising: (a) retrieving: parameter evolution information that describes the time evolution of the process parameter(s); a plurality of recipe templates, wherein a recipe comprises the plurality of steps defining the production process, and wherein a recipe template is a recipe in which at least one of the process parameters specifying the plurality of steps is a parameter being variable and having no predetermined value at the outset; (b) receiving: a source setup specification of a source setup to be used for executing the production process at the source scale, the source setup specification comprising the source scale value; a target setup specification of a target setup to be used for executing the production process at the target scale, the target setup specification comprising the target scale value; a source recipe defining the production process at the source scale; at least one acceptability function defining conditions for the values of the process parameter(s) at the source scale and/or at the target scale; (c) simulating the execution of the production process at the source scale using the source setup specification, the source recipe and the parameter evolution information; (d) determining, from the simulation, one or more source trajectories for the process parameter(s), wherein a trajectory corresponds to a time-based profile of values recordable during the simulated execution of the production process; (e) performing a target determination step comprising: selecting a recipe template pertinent to the production process out of the plurality of recipe templates; providing an input value for the at least one variable parameter in the selected recipe template; simulating the execution of the production process at the target scale using the target setup specification, the selected recipe template, the input value for the at least one variable parameter and the parameter evolution information; determining, from the simulation, one or more target trajectories for the process parameters; comparing the source trajectory(ies) and the target trajectory(ies); computing, based on the comparison and on the at least one acceptability function, an acceptability score for the selected recipe template; computing an optimal value for the at least one variable parameter in the selected recipe template by optimising the acceptability score and/or computing an acceptable range for the at least one variable parameter, wherein values within the acceptable range yield an acceptability score above a specific threshold; (f) if there is at least another pertinent recipe template, repeating the target determination step for at least another pertinent recipe template; (g) selecting at least one of the plurality of recipe templates and corresponding computed value(s) for variable parameter(s) as target recipe based on the acceptability scores computed for one or more recipe templates.

Claims

1. A computer-implemented method of scaling a state of a production equipment for a production process to produce a chemical, pharmaceutical and/or biotechnological product, the scaling being from a source scale to a target scale, wherein the state is defined by a set of state parameters describing a condition and/or a behaviour of the production equipment, the method comprising: retrieving mapping information that describes how the state parameters relate to a set of derived parameters; receiving: a source setup specification of a source setup used for executing the production process at the source scale, the source setup specification comprising the source scale value; a target setup specification of a target setup used for executing the production process at the target scale, the target setup specification comprising the target scale value; a first set of state parameters at the source scale; a second set of state parameters at the target scale, wherein at least one of the state parameters at the target scale is a parameter being variable and having no predetermined value at the outset; at least one acceptability function defining conditions on the values of the state parameter(s) and/or the values of the derived parameter(s) at the source scale and/or at the target scale; calculating a first set of derived parameters at the source scale using the first set of state parameters, the source setup specification and the mapping information; providing an input value for the at least one variable parameter in the second set of state parameters; calculating a second set of derived parameters at the target scale using the second set of state parameters, the input value, the target setup specification and the mapping information; comparing the first set of state parameters with the second set of state parameters and/or comparing the first set of derived parameters and the second set of derived parameters; computing, based on the comparison and on the at least one acceptability function, an acceptability score for the second set of state parameters; computing an optimal value for the at least one variable parameter by optimising the acceptability score and/or computing an acceptable range for the at least one variable parameter, wherein values within the acceptable range yield an acceptability score above a specific threshold; outputting the optimal value and/or the acceptable range for the at least one variable parameter; feeding the optimal value and/or the acceptable range for the at least one variable parameter to a control system; setting up the production equipment at the target scale based on the optimal value and/or the acceptable range fed to the control system.

2. The computer-implemented method of claim 1, wherein a plurality of acceptability functions is received and the second set of state parameters comprises a plurality of variable parameters, and wherein computing the acceptability score comprises: for each pertinent variable parameter of the plurality of variable parameters obtaining a partial acceptability score by: selecting one or more applicable acceptability functions; for each applicable acceptability function calculating an acceptability value; if there is a single applicable acceptability function, setting the acceptability value to the partial acceptability score; if there is a plurality of applicable acceptability functions, aggregating the acceptability values for all applicable acceptability functions to obtain the partial acceptability score; and aggregating the partial acceptability scores for all variable parameters to obtain the acceptability score.

3. The computer-implemented method of claim 1, wherein the mapping information comprises experimental bioreactor data fittings derived from previous executions of the production process and/or equations derived by theoretical models.

4. A non-transitory computer readable medium comprising computer-readable instructions, which, when loaded and executed on a computer system, cause the computer system to perform operations according to the method of claim 1.

5. A computer-implemented method of scaling a state of a production equipment for a production process to produce a chemical, pharmaceutical and/or biotechnological product, the scaling being from a source scale to an intermediate target scale to a final target scale, wherein the state is defined by a set of state parameters describing a condition and/or a behaviour of the production equipment, the method comprising: retrieving mapping information that describes how the state parameters relate to a set of derived parameters; receiving: a source setup specification of a source setup used for executing the production process at the source scale, the source setup specification comprising the source scale value; an intermediate target setup specification of an intermediate target setup to be used for executing the production process at the intermediate target scale, the intermediate target setup specification comprising the intermediate target scale value; a final target setup specification of a final target setup used for executing the production process at the final target scale, the final target setup specification comprising the final target scale value; a first set of state parameters at the source scale; a second set of state parameters at the intermediate target scale, wherein at least one of the state parameters at the intermediate target scale is a first parameter being variable and having no predetermined value at the outset; a third set of state parameters at the final target scale, wherein at least one of the state parameters at the final target scale is a second parameter being variable and having no predetermined value at the outset; at least one acceptability function defining conditions on the values of the state parameter(s) and/or the values of the derived parameter(s) at the source scale and/or at the intermediate target scale and/or at the final target scale; calculating a first set of derived parameters at the source scale using the first set of state parameters, the source setup specification and the mapping information; providing a first input value for the at least one first variable parameter in the second set of state parameters; calculating a second set of derived parameters at the intermediate target scale using the second set of state parameters, the first input value, the intermediate target setup specification and the mapping information; providing a second input value for the at least one second variable parameter in the third set of state parameters; calculating a third set of derived parameters at the final target scale using the third set of state parameters, the second input value, the final target setup specification and the mapping information; making a plurality of pairwise comparisons within all pairs of any two of the first, second and third set of state parameters and/or within all pairs of any two of the first, second and third set of derived parameters, and making at least one three-wise comparison among the first, second and third set of state parameters and/or among the first, second and third set of derived parameters; computing an acceptability score based on at least two comparisons and on the at least one acceptability function; computing a first optimal value for the at least one first variable parameter and a second optimal value for the at least one second variable parameter by optimising the acceptability score and/or computing a first acceptable range for the at least one first variable parameter and a second acceptable range for the at least one second variable parameter, wherein values within the first acceptable range and values within the second acceptable range yield an acceptability score above a specific threshold; outputting the optimal values and/or the acceptable ranges; feeding the optimal values and/or the acceptable ranges to a control system; setting up the production equipment at the target scale based on the optimal values and/or the acceptable ranges fed to the control system.

6. A non-transitory computer readable medium comprising computer-readable instructions, which, when loaded and executed on a computer system, cause the computer system to perform operations according to the method of claim 5.

7. A computer system operable to scale a state of a production equipment for a production process to produce a chemical, pharmaceutical and/or biotechnological product from a source scale to a target scale, wherein the state is defined by a set of state parameters describing a condition and/or a behaviour of the production equipment, the computer system comprising: a retrieving module configured to retrieve mapping information that describes how the state parameters relate to a set of derived parameters; a receiving module configured to receive: a source setup specification of a source setup used for executing the production process at the source scale, the source setup specification comprising the source scale value; a target setup specification of a target setup used for executing the production process at the target scale, the target setup specification comprising the target scale value; a first set of state parameters at the source scale; a second set of state parameters at the target scale, wherein at least one of the state parameters at the target scale is a parameter being variable and having no predetermined value at the outset; at least one acceptability function defining conditions on the values of the state parameter(s) and/or the values of the derived parameter(s) at the source scale and/or at the target scale; and a computing module configured to: calculate a first set of derived parameters at the source scale using the first set of state parameters, the source setup specification and the mapping information; provide an input value for the at least one variable parameter in the second set of state parameters; calculate a second set of derived parameters at the target scale using the second set of state parameters, the input value, the target setup specification and the mapping information; compare the first set of state parameters with the second set of state parameters and/or comparing the first set of derived parameters and the second set of derived parameters; compute, based on the comparison and on the at least one acceptability function, an acceptability score for the second set of state parameters; compute an optimal value for the at least one variable parameter by optimising the acceptability score and/or computing an acceptable range for the at least one variable parameter, wherein values within the acceptable range yield an acceptability score above a specific threshold; an output module configured to output the optimal value and/or the acceptable range for the at least one variable parameter; a control system configured to set up the production equipment at the target scale based on the optimal value and/or the acceptable range output.

8. The computer system of claim 7, wherein the mapping information comprises experimental bioreactor data fittings derived from previous executions of the production process and/or equations derived by theoretical models.

9. A computer system operable to scale a state of a production equipment for a production process to produce a chemical, pharmaceutical and/or biotechnological product from a source scale to an intermediate target scale to a final target scale, wherein the state is defined by a set of state parameters describing a condition and/or a behaviour of the production equipment, the computer system comprising: a retrieving module configured to retrieve mapping information that describes how the state parameters relate to a set of derived parameters; a receiving module configured to receive: a source setup specification of a source setup used for executing the production process at the source scale, the source setup specification comprising the source scale value; an intermediate target setup specification of an intermediate target setup to be used for executing the production process at the intermediate target scale, the intermediate target setup specification comprising the intermediate target scale value; a final target setup specification of a final target setup used for executing the production process at the final target scale, the final target setup specification comprising the final target scale value; a first set of state parameters at the source scale; a second set of state parameters at the intermediate target scale, wherein at least one of the state parameters at the intermediate target scale is a first parameter being variable and having no predetermined value at the outset; a third set of state parameters at the final target scale, wherein at least one of the state parameters at the final target scale is a second parameter being variable and having no predetermined value at the outset; at least one acceptability function defining conditions on the values of the state parameter(s) and/or the values of the derived parameter(s) at the source scale and/or at the intermediate target scale and/or at the final target scale; a computing module configured to: calculate a first set of derived parameters at the source scale using the first set of state parameters, the source setup specification and the mapping information; provide a first input value for the at least one first variable parameter in the second set of state parameters; calculate a second set of derived parameters at the intermediate target scale using the second set of state parameters, the first input value, the intermediate target setup specification and the mapping information; provide a second input value for the at least one second variable parameter in the third set of state parameters; calculate a third set of derived parameters at the final target scale using the third set of state parameters, the second input value, the final target setup specification and the mapping information; make a plurality of pairwise comparisons within all pairs of any two of the first, second and third set of state parameters and/or within all pairs of any two of the first, second and third set of derived parameters, and making at least one three-wise comparison among the first, second and third set of state parameters and/or among the first, second and third set of derived parameters; compute an acceptability score based on at least two comparisons and on the at least one acceptability function; compute a first optimal value for the at least one first variable parameter and a second optimal value for the at least one second variable parameter by optimising the acceptability score and/or compute a first acceptable range for the at least one first variable parameter and a second acceptable range for the at least one second variable parameter, wherein values within the first acceptable range and values within the second acceptable range yield an acceptability score above a specific threshold; an output module configured to output the optimal values and/or the acceptable ranges; a control system configured to set up the production equipment at the target scale based on the optimal values and/or the acceptable ranges output.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Details of exemplary embodiments are set forth below with reference to the exemplary drawings. Other features will be apparent from the description, the drawings, and from the claims. The drawings should be understood as exemplary rather than limiting, as the scope of the invention is defined by the claims.

(2) FIG. 1 shows a computer system for scaling a production process to produce a chemical, pharmaceutical, or biotechnological product.

(3) FIG. 2 shows a method for recipe scaling of a production process.

(4) FIG. 3 shows a block diagram indicating inputs and outputs of the recipe scaling.

(5) FIG. 4 shows part of an exemplary input for recipe scaling.

(6) FIG. 5 shows an acceptability score as a function of time.

(7) FIG. 6 shows exemplary target trajectories.

(8) FIG. 7 shows a method for time-point scaling of a state of a production equipment.

(9) FIG. 8 shows a block diagram indicating inputs and outputs of the time-point scaling.

(10) FIG. 9 shows part of an exemplary input for time-point scaling.

DETAILED DESCRIPTION OF EMBODIMENTS

(11) In the following text, a detailed description of examples will be given with reference to the drawings. It should be understood that various modifications to the examples may be made. In particular, one or more elements of one example may be combined and used in other examples to form new examples.

(12) FIG. 1 shows a computer system 10 for scaling a production process to produce a chemical, pharmaceutical, or biotechnological product.

(13) The computer system 10 may include a processing unit, a system memory, and a system bus. The system bus couples various system components including the system memory to the processing unit. The processing unit may perform arithmetic, logic and/or control operations by accessing the system memory. The system memory may store information and/or instructions for use in combination with the processing unit. The system memory may include volatile and non-volatile memory, such as a random access memory (RAM) and a read only memory (ROM).

(14) The computer system 10 may further include a hard disk drive for reading from and writing to a hard disk (not shown), and an external unit drive for reading from or writing to a removable unit. The drives and their associated computer-readable media provide nonvolatile storage of computer readable instructions, data structures, program modules and other data for the personal computer 920. The data structures may include relevant data for the implementation of the method as described above.

(15) A number of program modules may be stored on the hard disk, external disk, ROM or RAM, including an operating system (not shown), one or more application programs, other program modules (not shown), and program data. The application programs may include at least a part of the functionality as described below.

(16) A user may enter commands and information into the computer system 10 through input devices such as keyboard and mouse. A monitor or other type of display device is also connected to the system bus via an interface, such as a video input/output.

(17) The computer system 10 may communicate with other electronic devices. To communicate, the computer system 10 may operate in a networked environment using connections to one or more electronic devices.

(18) In particular, the computer system may interface and communicate with a source control system 20 and a target control system 30. The computer system 10 may be operable, possibly in conjunction with other devices, to scale a production process.

(19) The source control system 20 may be connected to a bioreactor 40 constituting the source equipment for performing the production process at the source scale. Similarly, the target control system 30 may be connected to a bioreactor 50 constituting the target equipment for performing the production process at the target scale. Although the bioreactor 40 is shown as being smaller than the bioreactor 50, the situation could be reversed.

(20) The source control system 20 and the target control system 30 may be located in the same production facility or in different production facilities at different locations. The source control system 20 and the target control system 30 may be different entities or may coincide, i.e. be a single entity (not shown).

(21) The control systems 20, 30 and the computer system 10 may be located in different rooms of the same facility or in different buildings on a corporate campus. The computer system 10 may be a separate entity from the control systems 20, 30. In other examples (not shown) the computer system 10 may coincide with at least one of the source control system 20 and the target control system 30.

(22) In some examples, a database 60 may be provided. The database may be connected to a network, such that the database is accessible by multiple devices/users. The database may be implemented as a cloud database, i.e. a database that runs on a cloud computing platform. In other words, the database may be accessible over the Internet via a provider that makes shared processing resources and data available to computers and other devices on demand. The database may be implemented using a virtual machine image or a database service. The database may use an SQL based or NoSQL data model.

(23) The database 60 may store any of: sets of values for process parameters, recipes, recipe templates, parameter evolution information, setup specifications, acceptability functions. The database 501 may be accessible from the process control device 503 via the Internet. Communications between the database 60 and the computer system 10 may be secured, e.g. via Internet protocol security (IPSEC) or other security protocols. A virtual private network (VPN) may also be used.

(24) The database 60 may be hosted by a service provider, possibly on a virtual machine, and may be accessible by various users from multiple organizations, possibly located in a variety of different geographic locations around the world. Alternatively, the database 60 may be hosted locally, e.g. in the computer system 10. Accordingly, the computer system 10 and the database 60 may or may not be located in physical proximity. In particular, the database 60 may be located in a location that is geographically distant (e.g. on another continent) from the computer system.

(25) An example of a production process that is scaled by the computer system 10 may be a fed-batch process comprising the following phases: add media to bioreactor condition (set temperature, pH) add inoculum allow to grow in batch phase (control pH, DO, temperature; sample at intervals) when nutrients exhausted, move to fed phase allow to grow in fed phase (control pH, DO, temperature; sample at intervals; supply additional nutrients) harvest product.

(26) In particular, the computer system 10 may perform scaling according to two approaches: recipe scaling, in which whole processes are converted between scales, and instantaneous or time-point scaling, in which settings at a given point in time during a process are converted between scales.

(27) Recipe Scaling

(28) FIG. 2 shows an exemplary method for recipe scaling of a production process. The method will be described in conjunction with FIG. 3, which shows a block diagram indicating inputs and outputs of the recipe scaling.

(29) A production process is defined by a plurality of steps specified by a plurality of process parameters, comprising recipe parameters and dynamic parameters. In the following, the method will be described for a production process in a bioreactor that is to be scaled from a source scale to a target scale.

(30) Examples of recipe parameters include but are not limited to: stir speed (rpm), fill volume (L), total gassing rate (L/hr), gas percentage of O2(%), gas percentage of CO2(%) and parameters defining gassing profile, filling profile, temperature profile, inoculation and induction characteristics and sampling pattern. Profiles may be: constant rate (e.g. constant rate feed) exponential (e.g. feed exponentially increasing, which typically roughly corresponds to what the organism will be doing) polynomial (e.g. order 3 polynomial to correspond to a particular organism growth pattern);
and may be parameterised by one or more recipe parameters.

(31) Examples of dynamic parameters include but are not limited to: tip speed (mps), mixing time (s), k.sub.La (hr.sup.−1), power input (W), power input per volume (Wm.sup.−3), Reynold's number, Froude number, minimum eddy size (μm), superficial gas velocity, cell density, cell metabolic state metric, carbon source availability, nitrogen source availability, secondary nitrogen source availability, inhibitor (toxin) concentration, pH, dissolved oxygen (%), dissolved CO2(%).

(32) Exemplary scenarios for a translation between scales may be the following. A small scale process is established at Ambr® 250 scale and the intention is to transfer the process as a single step to 50 L for production of larger quantities of product to evaluate downstream processing issues (e.g. purification/filtration). In another one, a manufacture process is established in organisation at a given large scale such as 50 L, and there is a need to scale down to e.g. Ambr® 15 or Ambr® 250 scale to perform initial clone selection; the scaled-down process needs to be “representative” otherwise the wrong clones will be selected and production when scaled back up to large scale will be compromised.

(33) The method starts at S101 and the first step at S103 is retrieving parameter evolution information 200 and recipe templates 201. In the current implementation, by way of example, parameter evolution information is retrieved from a set of hard-coded formulae in the software, in conjunction with structured data in XML format stored on a file-system accessible to the software.

(34) The parameter evolution information 200 characterises how the process parameters change with time, exemplarily including initial conditions for the process parameters and relations among process parameters. The parameter evolution information 200 describes physical modelling of the bioreactor in terms of parameters describing the bioreactor state (e.g. of fill volume) or the state of the production as determined by the bioreactor (e.g. power per volume), and biological modelling of the cell culture in the bioreactor (e.g. in terms of growth, oxygen consumption and pH depression).

(35) In particular, the parameter evolution information 200 may comprise relations empirically derived from previous executions of the production process and equations derived by theoretical models about the evolution of the production process.

(36) For example, the parameter evolution information 200 comprises experimental bioreactor data fittings, which are empirically derived mappings between recipe parameters (such as stirring speed, gassing rate and fill volume) and dynamic parameters (such as mixing time, k.sub.La and power input). The experimental bioreactor data fittings link two or more process parameters to each other.

(37) Additionally, the parameter evolution information comprises theoretically-derived equations and starting points both for a cell culture model and a bioreactor physical model. Examples of starting points for the cell culture model may be: growth rate 0.02 hr-1, temperature optimum 36 with growth reduced by 80% for each degree away, pH optimum 7.4 with growth reduced by 50% for each 1/10th of a unit away, specific 1C consumption rate scaled to a unit, growth rate saturating function of 1C source. In an alternative implementation, the cell culture model may be an empirical statistical model.

(38) The bioreactor physical model may cover fill volume, temperature, analyte concentrations, pH, k.sub.La, mixing time, power input and dissolved oxygen. Details about each of these process parameters are provided in the following:

(39) Fill Volume

(40) The starting value for the fill volume is zero. Volume is accumulated due to liquid addition and bolus liquid addition, and reduced due to sampling. Evaporation is not considered in the following, but it may be, for example, by implementing a standard evaporation model whereby input gas is assumed to be devoid of water, and exit gas is assumed to be saturated (in the case with no condenser).

(41) For a bolus addition of volume v.sub.b, the fill volume is considered to update instantaneously, so that:
v.sub.new=v.sub.old+v.sub.b

(42) For the reduction of volume due to sampling, with a sample of volume v.sub.s, the fill volume is considered to update instantaneously, so that:
v.sub.new=v.sub.old−v.sub.s

(43) During continuous liquid addition with a rate profile r(t), the fill volume updates according to the expression:

(44) $\frac{dv}{dt}=r\left(t\right)$

(45) Temperature

(46) The temperature is driven by: an external temperature, modelling a heating/cooling jacket or air stream; temperature changes due to the supply of liquid.

(47) Continuous changes to temperature depend on a single bioreactor-type parameter, indicating the rate of heat transfer between the external and internal temperature:

(48) $\frac{d{T}_{\mathrm{int}}}{dt}=\frac{k_T}{V}\left(T_{\mathrm{ext}}\left(t\right)-T_{\mathrm{int}}\right)$
where T.sub.int is the liquid temperature, k.sub.T the heat transfer coefficient, and T.sub.ext(t) the external temperature.

(49) The equations for temperature changes due to supply of liquid (either bolus supply or profiled supply) are analogous to those for analyte concentrations (see below).

(50) Analyte Concentrations

(51) Analyte concentrations change due to liquid addition and bolus liquid addition.

(52) For bolus liquid addition of volume v.sub.b, for any given analyte at concentration c.sub.b in the bolus, the analyte concentration is considered to update instantaneously, so that:

(53) $c_{new}=\frac{v_{old}{c}_{old}+v_b{c}_b}{v_{old}+v_b}$
where v.sub.old is the volume prior to bolus liquid addition.

(54) For continuous liquid addition with a rate profile r(t) with fill volume expressed as v(t), the concentration for any given analyte, c, at concentration c.sub.a in the supply liquid changes according to the following expression:

(55) $\frac{dc}{dt}=\frac{\left(c_b-c\right)}{v\left(t\right)}r\left(t\right)$

(56) pH

(57) The following is a simplified model of buffering which aims at giving representative results without the need to specify the detailed buffering properties of media in detail. This is achieved by tracking both pH and buffering capacity as two distinct variables. Liquid addition and bolus liquid addition both affect pH. Carbon dioxide mediated (or carbonic acid mediated) effects on pH are not yet considered, but there exist possible sets of theoretical equations for these in the literature which could potentially be included.

(58) The buffering capacity of the media is considered analogous to an analyte, so follows the evolution equations for analyte concentrations given above.

(59) For bolus liquid addition of volume v.sub.b with pH p.sub.b and buffering capacity b.sub.b into medium with volume v.sub.m, pH p.sub.m and buffering capacity b.sub.m, the new medium pH is approximated as:

(60) $p_{m,new}=\frac{b_m{p}_{m,\mathrm{old}}{v}_m+b_b{p}_b{v}_b}{b_m{v}_m+b_b{v}_b}$

(61) Dissolved Oxygen

(62) Dissolved oxygen changes continually in the bioreactor due to the transfer of oxygen from the gas supply, as dictated by the k.sub.La; that is:

(63) $\frac{d\left[\mathrm{DO}\right]}{\mathrm{dt}}=k_{L}a\left(O^{*}-\left[\mathrm{DO}\right]\right)$
where O* is the partial pressure of oxygen in the supply gas, relative to that in air.

(64) The biological model for the cell culture aims at enabling the parsimonious description of a large range of bioprocesses salient for stirred bioreactor culture. The following model does not address, for example: detailed metabolic aspects of the cells: these are relevant only inasmuch as they affect the behaviour of the cells in terms of interaction with the bioreactor or end product; heterogeneity in the bioreactor: it is assumed that consideration of heterogeneity is adequately handled by penalising large mixing times in terms of utilities; specifics and details of any individual process: the aim is to obtain broad but approximate coverage rather than a high degree of detail concerning a particular cell type or product, for example.

(65) The biological model does instead focus on: bioreactor-relevant culture effects, such as pH depression or elevation (which may trigger base or acid addition by the bioreactor system) and oxygen utilisation (which may affect gas flow or stir speed via the intermediary of a DO control loop); end-product-relevant culture dynamics, such as modulation in cell activity or large-scale changes in cell metabolism e.g. to production and away from growth; bioreactor-dependent culture effect, such as pH, DO or nutrient concentration effects.

(66) The model is structured in terms of a number “culture model processes”; these are combined additively to produce a system of ordinary differential equations. Each culture model process has a number of constituent parts that govern its overall rate, multiplied by a maximum rate constant for that process. The constituent parts are functions of critical variables, and the output of these functions is combined multiplicatively.

(67) For example, the rate may be determined as a function of temperature, T, and primary carbon source concentration, c.sub.1C:
r=f.sub.T(T)f.sub.[c1c](c.sub.1c)

(68) The functions f.sub.T and f.sub.[DO] are selected from a (small) repertoire of biologically salient forms with a maximum of unity and minimum of zero. For example, temperature dependency might be described by

(69) $f_T\left(T\right)=\exp \left(-\frac{{\left(T-37\right)}^2}{3}\right)$
to indicate a temperature optimum at 37 degrees but with relatively small sensitivity to deviations from that temperature. Similarly, primary carbon source concentration dependency might be described by

(70) $f_{c1c}=\frac{c_{1c}}{0.5+c_{1c}}$
to indicate a saturating maximum with half of the maximum rate achieved for a concentration of primary carbon source of 0.5 gL.sup.−1.

(71) This rate then determines the rate of change of a set of variables affected by the culture model process. For example, the rate may drive the growth of cell density, such that:

(72) 0$\frac{d\rho }{\mathrm{dt}}=\rho .Math.r$

(73) The full expression for cell growth rate would then become:

(74) $\frac{d\rho }{\mathrm{dt}}=r_g.Math.\exp \left(-\frac{{\left(T-37\right)}^2}{3}\right).Math.\frac{c_{1c}}{0.5+c_{1c}}.Math.\rho$

(75) In the above example, the culture model process has two dependencies (on primary carbon source and temperature) but only a single effect (on cell growth rate). A single culture model process may have multiple effects e.g. on cell growth rate and on primary carbon source consumption, which leads immediately to a system of equations.

(76) $\frac{d\rho }{\mathrm{dt}}=r_g.Math.\exp \left(-\frac{{\left(T-37\right)}^2}{3}\right).Math.\frac{c_{1c}}{0.5+c_{1c}}.Math.\rho$$\frac{d{c}_{1c}}{\mathrm{dt}}=-r_c.Math.\exp \left(-\frac{{\left(T-37\right)}^2}{3}\right).Math.\frac{c_{1c}}{0.5+c_{1c}}.Math.\rho$

(77) A culture model process may depend, in terms of its rate, on one or more driving processes in a hierarchy. In this case, the rates of the driving process may be added (for example, consider when the driving processes relate to nutrient-dependent growth and production respectively, and the derived process is nutrient consumption), or multiplied. The specifics of the responses and the rates are covered in the following sections.

(78) Culture Process Responses:

(79) Temperature

(80) A culture process (such as growth, production, or quiescence/death) may depend on media temperature. It is assumed that the process will be independent of external (jacket, driving) temperature, except inasmuch as this modulates the media temperature.

(81) It is anticipated that temperature dependence will typically comprise either a normal distribution, as described above, or, more usually, an asymmetric normal distribution i.e.

(82) $M\left(x\right)=\{\begin{array}{cc}\exp \left(\frac{-{\left(x-\mu \right)}^2}{{\sigma }_r}\right)& x\ge \mu \\ \exp \left(\frac{-{\left(x-\mu \right)}^2}{{\sigma }_l}\right)& \mathrm{otherwise}\end{array}$

(83) For growth of Cho cells, for example, a normal distribution with μ=37 and σ=2 would be a good starting point.

(84) pH

(85) A culture process (such as growth, production, or quiescence/death) may depend on media pH. It is anticipated that pH dependence will typically comprise a normal or asymmetric normal distribution.

(86) For growth of Cho cells, for example, a normal distribution with μ=7.4 and σ=0.5 would be a good starting point.

(87) DO

(88) A culture process (such as growth, production, or quiescence/death) may depend on dissolved oxygen saturation within the media. It is anticipated that DO dependence will reflect saturation or sigmoidal kinetics, i.e.

(89) $M\left(x\right)=\frac{x}{k+x}\mathrm{or}M\left(x\right)=\frac{1}{1+\exp \left(-\left(\frac{x-k_{\mathrm{crit}}}{k_{\mathrm{sens}}}\right)\right)}$

(90) For growth of Cho cells, for example, saturation kinetics with k.sub.crit=15% and k.sub.sens=5% would be a good starting point.

(91) Cell Metabolic State Response

(92) The single metabolic state variable is used to summarise pertinent properties of the metabolic state of the cells. The meaning of this variable will be culture dependent, but it is primarily intended to summarise the cells' behaviour in terms of relative energetic commitment to growth and production. For example: metabolic state=−1 indicating commitment of 100% energy to growth metabolic state=1 indicating commitment of 100% energy to production.

(93) Simulation starts with metabolic state set to zero and the state remains within the interval from −1 to 1 exclusive.

(94) Clearly this is a vast simplification of the dynamics in real culture. However, it suffices to model the effect of induction and hence knock-on effects in terms of further amplification of the cell density (or otherwise).

(95) The response of culture model processes related to production and growth are anticipated to take the form of a sigmoidal or reversed sigmoidal (i.e. one minus sigmoidal) respectively.

(96) Cell Activity Response

(97) The single cell activity state variable is used to summarise pertinent properties of cell activity, in particular quiescence or recovery from lag, whichever are applicable for the culture in question.

(98) Simulation starts with cell activity set to zero, and the cell activity remains within the interval from −1 and 1 exclusive.

(99) Where the culture exhibits a recovery component, it is anticipated that growth exhibits a sigmoidal response to the cell activity state variable, with other processes responsible for increasing the cell activity; in this case high cell activity state indicates that cells have largely recovered from, for example, defrosting.

(100) Where the culture exhibits a death or quiescence component, it is anticipated that growth (and potentially also production) will exhibit a reverse sigmoidal response to the cell activity state variable, with other processes responsible for increasing the cell activity; in this case high cell activity state indicates a large number of quiescent or senescent cells.

(101) Nutrient Responses

(102) The interactions between cells and media are complex. Setting aside responses to pH, which have already been covered, the biological response to the media can be caricatured as: support of growth by the media e.g. due to the provision of adequate essential nutritive components, typically a sufficient carbon and nitrogen supply; support of production (of final product) by the media, with the same criteria; inhibition of growth by the media e.g. due to the presence of toxic media components; promotion of cell senescence or death by the media e.g. due to the presence of toxic media components; promotion of recovery from lag phase e.g. due to the presence of a supportive nutrient environment; promotion of transition from growth to production.

(103) In many cases these drivers can be modelled as saturation kinetic or sigmoidal responses to concentrations of particular nutrients e.g. saturation kinetic response of growth to primary carbon source saturation kinetic response of growth to primary nitrogen source sigmoidal kinetic response of metabolic state change to inducer concentration either inverse sigmoidal or saturation kinetic response to toxic product or toxins.

(104) In some cases, nutrient responses depend primarily on the ratio of two components of the media. This is particularly the case when multiple carbon sources are present, and one is utilised in preference to the other.

(105) In this case, the cell culture process rate depends on a function (such as sigmoidal, saturation, or reverse sigmoidal) of the quotient of the concentrations of the components.

(106) Culture Process Effects:

(107) Growth Rate

(108) Growth or death cell culture processes effect a change in the cell density, p:

(109) $\frac{d\rho }{\mathrm{dt}}=r_{g}R\rho$
where r.sub.g is the growth rate coefficient associated with the cell culture process, and its product with the rate of the cell culture process (i.e. R, from the cell process responses) indicates the specific growth rate. A constant non-zero R will therefore result in exponential growth (R>1), death (R<1) of the cell density.

(110) The total change in cell density during culture simulation arises from growth and death due to pertinent cell culture processes, change to dilution (e.g. due to liquid bolus or profile liquid addition) and change due to supply of inoculum (i.e. due to the addition of a liquid with non-zero inoculum concentration).

(111) pH Depression Rate

(112) Cell culture processes may depress the media pH. The framework provides two means of modelling depression of pH: pH depression directly by a cell culture process pH depression indirectly due to the consumption or production of an acidic or basic media component due to a cell culture process.

(113) In cases where the cell culture dynamics are considered at a high level (e.g. with an arbitrary carbon source) it is more appropriate to take the former approach.

(114) In this case, pH is modulated according to the following expression:

(115) $\frac{d\left[\mathrm{pH}\right]}{\mathrm{dt}}=\frac{r_{\left[\mathrm{pH}\right]}R\rho }{B}$
where r.sub.[pH] is the pH depression coefficient for the cell culture process, R is the rate of the cell culture process at a given time, and B is the specific buffering capacity of the medium.

(116) O2 Consumption Rate

(117) Growth, maintenance and other metabolic cellular activities consume oxygen from the media. Cell culture processes that involve oxygen uptake modulate the media DO as follows:

(118) $\frac{d\left[\mathrm{DO}\right]}{\mathrm{dt}}=r_{\left[\mathrm{DO}\right]}R\rho$
where r.sub.[DO] is the DO uptake coefficient for the cell culture process and R is the rate of the cell culture process at a given time.

(119) CO2 Production Rate

(120) Similarly, metabolic activity, and in particular oxidative metabolism, produces carbon dioxide. Cell culture processes that involve carbon dioxide evolution modulate the media ppCO.sub.2 as follows:

(121) $\frac{d\left[\mathrm{ppCO}2\right]}{\mathrm{dt}}=r_{\left[\mathrm{ppCO}2\right]}R\rho$

(122) Cell Activity Modification Rate

(123) As previously described, within the framework, cell activity state describes either cells moving out of a lag phase, or into quiescence/senescence. The cell activity state is a measure of the activity of the cells between −1 and 1 exclusive. To maintain the state within this interval, cell culture processes that modulate the state do so as follows:

(124) $\frac{d\left(\tanh \left(A\right)\right)}{\mathrm{dt}}=r_A$
where A is the cell activity state, r.sub.A the cell culture process rate coefficient for cell activity state, and R is the rate of the cell culture process at a given time. No cell-density dependent effect is assumed, as the activity state is considered to apply homogeneously for all cells in the culture.

(125) Cell Metabolic State Modification Rate

(126) Cell metabolic state modification mirrors that for cell activity modification, that is:

(127) 0$\frac{d\left(\tanh \left(M\right)\right)}{\mathrm{dt}}=r_{M}R$
where M is the cell metabolic state, r.sub.M the cell culture process rate coefficient for cell metabolic state, and R as above.

(128) Nutrient Production Rates

(129) A cell culture process may produce or consume components of the media. For example: cell growth and maintenance typically consume a carbon source and potentially a distinct nitrogen source; cell metabolism may produce product cell metabolism may produce toxic by-products.

(130) Any given cell culture process may have zero or more nutrient production rate coefficients, each of which dictates that for the nutrient, i, in question:

(131) $\frac{{\mathrm{dC}}_i}{\mathrm{dt}}=r_{\mathrm{Ci}}R\rho$
where r.sub.ci is the rate coefficient.

(132) Illustrative Culture Processes

(133) The following illustrative culture process demonstrates many of the aspects of the framework described above.

(134) TABLE-US-00001 Cell culture process Responses Effects Comment Cell growth Temperature: Growth rate: 0.5 Growth depends on normal(37, 1) pH depression rate: 1 correct temperature, pH: normal(7, 0.5) o2 consumption rate: pH, and adequate dO: sigmoidal(10, 0.1) 5e3 1C source: −1 dO. It causes met. state: rev. increase in cell count sigmoidal(0.5, 5) and depresses pH act. state: rev. and oxygen. It also sigmoidal(0.5, 5) requires and consumes 1C source: the primary carbon saturation(0.1) source. Cell death Product: act. state: 1 Product causes cell saturation(10) death, modelled as a change in the cell activity state Production Temperature: pH depression rate: 1 Complements growth normal(37, 1) o2 consumption rate: depending on pH: normal(7, 0.5) 5e3 1C source: −1 metabolic state. dO: sigmoidal(10, 0.1) Product: 1 Does not increase met. state: cell count, but does sigmoidal(0.5, 5) increase product act. state: rev. titer. sigmoidal(0.5, 5) 1C source: saturation(0.1) Induction Inducer: met. state: 1 Presence of inducer saturation: 0.001 causes cells to change metabolic state.

(135) Further, recipe templates 201 are retrieved at step S103. Recipes can be seen as a set of instructions dictating how the bioreactor behaves over time. Recipe templates are considered to be recipes with free or variable parameters. These variable parameters may result in very different recipes being produced from a given template (for example, if a path within a template is contingent on a free variable). Recipe templates may contain calculations based on the variable parameters, as well as on other process parameters within the process which they are running. Any of the recipe parameters listed above may be a variable parameter. For examples, profile parameters A, B and C for a feed rate profiled as A+B t+C t.sup.2, wherein t is time, may be left free to vary.

(136) A library of recipe templates 201 may be retrieved, wherein different recipe templates may comprise different steps or instructions and/or may have different variable parameters.

(137) Recipe templates 201 may comprise marks identifying phases of the production process, which are used together with acceptability functions, as explained below.

(138) The acceptability functions 250 are received at step S105. In the exemplary implementation, the software supplies a user interface by which acceptability functions can be selected from a library and then parameterised, or designed graphically. The library in this case provides acceptability functions indicating, amongst others, (a) a range (b) a single point (c) a normal distribution. For further examples see the canonical forms below. The acceptability functions define conditions for the values of the process parameter(s) at the source scale and/or at the target scale, in particular they define how acceptable these values are, when taken alone or in relation to one another. The value for acceptability may be a real number between 0 and 1, boundaries included.

(139) There may be absolute and relative acceptability functions.

(140) An absolute acceptability function maps from one or more process parameters at the same scale to an evaluation. Examples of absolute acceptability functions define conditions for the following parameters: Reynolds number (Rn): 0 for low Rn, increasing to 1 as Rn moves into turbulent zone, then 1 afterwards; k.sub.La: 0 for low k.sub.La, increasing as saturating function to 1 as k.sub.La increases; mixing time: 1 for low mixing time, and then when mixing time exceeds 20 s, equal to 20 s/mixing time (i.e. decreasing towards 0); superficial gas velocity (SGV): 1 for low SGV, with sigmoidal decline with increasing SGV for larger SGV, towards 0, to reflect increased risk of foam with increasing SGV; power per volume: normal distribution around some maximum; stir speed: 0 for 0 . . . 5% and for 95 . . . 100% of bioreactor stir speed, 1 otherwise (preferable to run with the system not at its limits); or linear increase from 0 at 0% to 1 at 5%, then flat until 95%, then linear decrease to 0 at 100%; eddy size: 1 for eddy size greater than 5× organism size, then linearly to 0 for 2× organism size, to reflect increasing risk to organism as eddy size decreases; product concentration at harvest time: 0 for 0, with saturating increase (tends to 1 as product concentration tends to infinity) as titre increases; DO: 0 for 0 . . . 10%, then a sigmoidal curve between 10% and 20% up to 1, and then 1 for >20% to ensure adequate oxygen for organism in sensitive region; SGV+protein concentration: 1 for low SGV or low protein concentration, decreasing to 0 as either become large; similarly stir speed+SGV could also affect risk of foaming; power per volume+cell density: normal distribution around some optimum, but optimum shifts from low to large power per volume as cell density increases (reflecting protective effect of cells on other cells); product concentration+product quality: 0 if either are 0, then increasing as proportional to the product of concentration and quality.

(141) A relative acceptability function maps from a combination of (one or more) process parameters at the source scale and corresponding (one or more) process parameters at the target scale to an evaluation. For example, a way of combining two corresponding process parameters at different scales is to compute their difference or relative difference, i.e. absolute value of (value in source−value in target)/(maximum (value in source, value in target)). Examples of relative acceptability functions define the following conditions: 0 if mixing time is less at source scale than at target scale, otherwise 1 (ensures no loss of mixing when moving up scales); normal distribution of PPV around a delta of 0 (ensures PPV a typical parameter for matching is conserved between scales); 1 for k.sub.La greater at target than source scale, otherwise sigmoidal decrease to 0 as k.sub.La differs increasingly; normal distribution around 0, standard deviation of 0.2 for cell density (ensures growth curves conserved between source and target).

(142) Generally, the acceptability functions may be one-dimensional, two-dimensional or with higher dimensions. Some examples for canonical forms for one-dimensional and two-dimensional acceptability functions are reported below.

(143) A one dimensional acceptability function can take one of the following canonical forms: zero throughout, except at a given exact value, at which it is one (this expresses a need to restrict the solution space to a precise value, for example, if a particular fill volume is needed at the small scale); a normal distribution (this expresses the idea that a parameter value such as k.sub.La has an optimum, but with some room for manoeuvre around this); one within a range, zero outside that range (this expresses the idea that a parameter value should remain within this range, e.g. that mixing time should be less than a given maximum)

(144) A two dimensional acceptability function can take one of the following canonical forms: f(x,y)=0 unless x=y, in which case f(x,y)=1 (this expresses the need to find an exact match between scales e.g. for power input per volume); f(x,y)=0 unless in which case f(x,y)=1 (this expresses the need to restrict solution space to the situation where, at the target scale, the parameter value exceeds that at the source, for example in terms of oxygen transfer) f(x,y)=0 unless in which case f(x,y)=1 (this expresses the need to restrict solution space to the situation where, at the target scale, the parameter value is less than that at the source, for example in terms of mixing time) f(x,y)=N(x−y; m, s) (this expresses a benefit from having as close possible but not necessarily a perfect match between the scales e.g. for power per volume) f(x,y)=N((x−y)/max(x,y); m, s) (as above, but ratiometric).

(145) In the recipe scaling case, acceptability functions may be attached to specified parts of process templates. For example, a process template might specify “start of batch” and “end of batch”, and an acceptability function would then be attached to the interval between these two waypoints, and considered to apply only for those parts of the process. For example, in batch phase, only those acceptability functions may be applied that do not set the acceptability value to depend on cell density, because in batch phase there may be some variability as the cells grow up to use their nutrients up. Conversely, in fed phase, only those acceptability functions may be applied for which the acceptability value depends on cell density, because by start of fed phase, variability due to initial inoculum should have been “evened out” because they were all provided with same amount of nutrient in batch phase. In another example, those acceptability functions for which the acceptability value depends product titre (concentration) may be applied only in harvest phase, because titre is not relevant before the harvest point.

(146) At step S105 also source setup specification 220 and target setup specification 230 are received. In the exemplary implementation, the user selects a source and target setup from a list. The software retrieves information concerning a given source or target setup, including the permitted configurations, minimum stir speed, maximum stir speed, mixing properties, and so on, from structured data in an XML file, which is stored on the file-system in a place accessible to the software.

(147) The setup specifications are description of the scales, namely of the equipment at source scale and target scale, specifying e.g. volumes and number/type of equipment components. A source setup specification 220 may e.g. be Ambr® 250 with mammalian impeller and a target setup specification 230 may e.g. be any of 2 L UniVessel, 50 L STR with 3+6 impeller and combi sparger, 2000 L STR with 3+6 impeller and combi sparger.

(148) Further, at step S105, also a recipe 240 for the source scale is received. In the exemplary implementation, the software provides a user interface by which the user can design a recipe or recipe template by successively adding and removing steps, and by parameterising steps. The software persists the recipe templates in an XML-based repository using the Microsoft .net serialiser to persist the object model for the recipes represented internally as objects within the software implementation.

(149) An example for the source recipe 240 may correspond to the following procedure: “Fill bioreactor with 0.2 L of given media, heat to 35 degrees, inoculate with clone to a density of 1 e6 cells mL-1, incubate stirring at 600 rpm for 36 hrs controlling pH to 7.4 with bottom and top control i.e. addition of acid or base as needed to push pH back to 7.4; maintain temperature; gas at a rate of 0.1 of total volume per minute with air; feed with complex feed for 36 hrs continuing to monitor and control pH, temperature; control DO with stirring and gassing, add inducer to trigger production. Harvest after 36 hrs.”

(150) Then at step S107 the execution of the production process is simulated at the source scale using a combination of the source setup specification 220, the source recipe 240 and the parameter evolution information 200. The source setup specification 220 provides a sort of framework for the simulation, while the source recipe 240 and the parameter evolution information 200 define how the process develops.

(151) The physical, chemical and/or biological aspects of the production process are simulated. In particular, the process simulation comprises purely physical modelling (e.g. of fill volume), bioreactor modelling derived from physical characterisation of bioreactors (e.g. mapping from fill volume and stir speed to power per volume), and biological modelling of the organism (in terms of growth, oxygen consumption and pH depression).

(152) From the simulation at source scale, source trajectories for the process parameters are determined at S109. This means that the values of the process parameters are recorded at different times during the simulation, so that a time dependence of the process parameters can be determined. The data points may be fitted to obtain fitting functions for the time evolution of the parameters. FIG. 6 shows examples of trajectories, which will be discussed below.

(153) Afterwards, at steps S111 and S113, a tentative target recipe is chosen. A recipe template is selected among the plurality of recipe templates 210 and some input values are provided for the variable parameters in the selected recipe template. The combination of the selected recipe template and the provided input values provides a tentative target recipe that can be used at step S115 for simulating the production process at the target scale, similarly to step S107.

(154) FIG. 4 shows part of an exemplary input for recipe scaling, in which parameter evolution information 200, source recipe 240, input values for a selected recipe template 210 and acceptability functions 250 are visible, while the source and target setup specifications are not shown.

(155) Further, at step S117, target trajectories 270 corresponding to the time evolution of process parameters at the target scale are determined, exactly as for the source trajectories.

(156) Then at step S119 the initial guess for the variable parameters provided by the input values is modified to “best” satisfy the conditions given by the acceptability functions 250.

(157) In particular, the simulation may be run multiple times to explore the space available for the variable parameter(s), until preferred points or surfaces in the space are found, i.e. the ones that make the target trajectories 270 most compliant with the acceptability functions 250. The compliance of the target trajectories 270 with the acceptability functions 250 is indicated by an acceptability score 280. Different degrees of compliance may be of interest, such as considering only the values of the variable parameter that maximise the acceptability score 280 or considering also a plurality of values that yield an acceptability score 280 above a certain threshold. The plurality of values may form a single (possibly multi-dimensional) range or non-adjacent ranges.

(158) At step S121 it is checked whether there are other applicable recipe templates that could be used as basis for a target recipe and, if so, steps S111-S115 are repeated.

(159) Finally, at S123, one or more target recipes 260 are selected among the tested tentative target recipes, i.e. the recipe templates with corresponding values for the variable parameters. The selection is based on the acceptability score 280 and may be such that only the tentative target recipe with the highest acceptability score 280 is considered or more tentative target recipes with an acceptability score 280 above a certain threshold are considered.

(160) The method ends at S125.

(161) In some cases, the target recipe(s) 260 may be output, e.g. as a file. An example for an output indicating the target recipe 260 may be: “on the ambr 250, use recipe template named “ramp stir speed”, with the initial inoculum set to 0.2% of the total volume and DO controlled to 35% throughout”. The acceptability score 280 may also be output, e.g. as text “this will give a score of 80% of the optimal translation from your 50 L recipe” or as a plot in function of time, as shown in FIG. 5. Further, the simulated target trajectories 270 may be output e.g. as plots.

(162) FIG. 5 shows an acceptability score as a function of time and FIG. 6 shows exemplary target trajectories.

(163) It can be seen that the acceptability score 280 in FIG. 5 has two troughs around the 4th hour and the 6th hour. The advantage of outputting the target trajectories 270 is that causes for the poor performance in these phases may be readily identified. For example, considering the target trajectories in the upper part of FIG. 6 for the cell density, it is apparent that the cell density evolves similarly at the source scale and at the target scale. Since one of the objectives is to maximise the similarity between the processes at different scale, the cell density will have scored high. Instead, the target trajectories in the lower part of FIG. 6 for k.sub.La show that the evolution of k.sub.La at the target scale is not similar to the one at the source scale. Accordingly, k.sub.La may be at least partly the cause for the troughs in the overall acceptability score 280.

(164) To summarize, the method involves the mapping of a recipe at one scale onto a recipe at a second scale subject to some constraints by means of evaluating the trajectories that result from the simulation of the recipes at each of the scales in question. In particular, trajectories that match best according to the acceptability functions are used to infer values for appropriately populating a recipe template.

(165) The method can be generalised to a train scaling involving an arbitrary number of scales, i.e. a translation that starts from a source scale and arrives at a final target scale by passing through and translating for each of a plurality of intermediate target scales.

(166) When applying the recipe scaling method of FIG. 2, setup specifications for the intermediate target scale(s) are received at S105 and the acceptability functions 250 cover all scales, i.e. define conditions across all scales. In addition, steps S113, S115 and S117 must be performed also for each intermediate target scale. Further, step S119 involves a simultaneous search for “best” values (optimal values or ranges) for all target scales, i.e. the one or more intermediate target scale and the final target scale.

(167) An exemplary scenario for a train scaling may be going from Ambr® 15 to UniVessel® 2 L to STR® 50 L to STR® 1000 L to STR® 2000 L. In particular, each of these scales may belong to a scale group as follows: Configuration 1: Ambr® 250, attached to small scale group Configuration 2: UniVessel® 2 L, attached to small scale and intermediate scale group Configuration 3: STR® 50, attached to intermediate scale and large scale group Configuration 4: STR® 1000, attached to large scale group Configuration 5: STR® 2000, attached to large scale group.

(168) The following acceptability functions 250 are defined for the groups:

(169) 1) Small scale group: relative acceptability function: normal function of delta in k.sub.La with mean 0, standard deviation 1 hr.sup.−1; relative acceptability function: normal function of delta in PPV with mean 0, standard deviation 0.2 Wm.sup.−3; absolute acceptability function: 0 valued when between 0 and 5% and 95% and 100%, 1 otherwise (concerns the stir speed of bioreactor as % of maximum); absolute acceptability function: sigmoidal function with value 0 for 0, a sharp rise around 20 up to 1, for dissolved oxygen.

(170) 2) Intermediate scale group: relative acceptability function: normal function of delta in PPV with mean 0, standard deviation 0.1 Wm.sup.−3

(171) 3) Large scale group: relative acceptability function: normal function of delta in PPV with mean 0, standard deviation 0.1 Wm.sup.−3
absolute acceptability function: 1 kW/(1 kW+power input)

(172) It can be seen that, in the train scaling, particularly, the acceptability functions 250 link the different scales so that the process is scaled for each scale taking into account also the requirements that will arise for following scales.

(173) A train scaling may be computationally expensive, however the acceptability functions can be used when exploring the space of the variable parameters.

(174) By way of example, a simple case with 3 target scales, A, B and C can be considered. A and B are linked by an acceptability function that drops below 0.5 if the k.sub.La differs by more than 1 hr.sup.−1, while an acceptability function linking B and C is such that if the k.sub.La between B and C differs at all, it drops to 0, otherwise it is 1. The variable parameter is the stir speed, so the stir speed for scale A, the stir speed for scale B, and the stir speed for scale C need an input value. A threshold of 0.5 is set for the final acceptability score, and the acceptability score functions are combined by considering the product of the acceptability scores.

(175) After an input value for the stir speed at scale A is chosen and an input value for the stir speed at scale B is chosen, k.sub.La can be computed based on the stir speed values and, in particular, the k.sub.La difference between A and B. There will only be certain regions for which the k.sub.La differs by less than 1 hr.sup.−1 and, thus, the acceptability score is greater than 0.5. Since acceptability scores are by definition all lower or equal to 1, and since the acceptability score functions are combined as a product, it can already be inferred that any values for B that are not in the above-mentioned region will result in a final acceptability score lower than the threshold. Accordingly, a range of feasible input values for B is given on the basis of the input value for A.

(176) In turn, having proposed a candidate stir speed for scale B, this can be immediately propagated to scale C, because only that stir speed which gives identical k.sub.La at scale C is acceptable (using the same logic as before).

(177) The conclusion is that the optimisation should be mainly performed over the value for A, and that the range for the B value for optimisation is diminished as a function of the candidate stir speed for A, and that there is no need to optimise over C because it arises automatically from B. This gives the appropriate set of clues to the optimiser to enable it to move rapidly to a solution, rather than exploring all possible values for stir speed at A, B and C.

(178) Time-Point Scaling

(179) FIG. 7 shows an exemplary method for time-point scaling of a state of a production equipment. The method will be described in conjunction with FIG. 8, which shows a block diagram indicating inputs and outputs of the time-point scaling.

(180) In the following, the method will be described for a production equipment including a bioreactor that may be used to perform any of the production processes discussed with reference to the recipe scaling.

(181) Examples of bioreactor configurations include but are not limited to: Ambr® 15 fermentation, Ambr® 15 cell culture, Ambr® 250 mammalian, Ambr® 250 microbial, UniVessel® 2 L, STR® 50 with ring sparger and 2×3 blade impellers, STR® 200 with micro sparger and 3+6 blade impellers, and STR® 1000 with ring sparger and 2×3 blade impellers.

(182) The state of a production equipment is defined by state parameters, which may include but are not limited to: stir speed (rpm), fill volume (L), total gassing rate (L hr.sup.−1), gas percentage of O2(%) and gas percentage of CO2(%).

(183) The method starts at S701 and the first step at S703 is retrieving mapping information 800. In the exemplary implementation, mapping information is stored alongside bioreactor configuration in an XML file which is accessible to the software.

(184) The mapping information 800 characterises how the state parameters relate to derived parameters, which characterise a given point in time during the production process. The derived parameters include but are not limited to: tip speed (mps), k.sub.La (hr.sup.−1), mixing time (s), power input (W), power input per volume (W/m.sup.3), Reynold's number, Froude number, minimum eddy size (μm) and superficial gas velocity.

(185) In particular, the mapping information 800 may comprise experimental bioreactor data fittings derived from previous executions of the production process and/or equations derived by theoretical models.

(186) The mapping information 800 may comprise different relations between state parameters and derived parameters that apply to different production equipment. Accordingly, in the retrieving step S703, only the relations appropriate for the case at hand may be retrieved.

(187) For example, the time-point scaling may be applied between an Ambr® 250 bioreactor and a UniVessel® 2 L bioreactor. The retrieved mapping information 800 may include a mapping from stir speed, fill volume and gassing rate onto k.sub.La and PPV, as well as the equation linking stir speed and tip speed for a given geometry of the bioreactor.

(188) At step S705, source setup specification 810, target setup specification 820 and acceptability functions 840 are received. In the exemplary implementation, source set up and target set up are specified through the user interface by the user, selecting from a combobox. The details of the source and target setup, in terms of the associated parameters and mapping, are stored in an XML file on the filesystem to which the software has access.

(189) The setup specifications are description of the scales, namely of the equipment at source scale and target scale, specifying e.g. volumes and number/type of equipment components. Continuing the example from above, the source setup specification 810 may be Ambr® 250 and a target setup specification 840 may be UniVessel® 2 L.

(190) The acceptability functions 840 may have any of the canonical forms illustrated previously. For the above example, three acceptability functions 840 may be received: a relative acceptability function being a normal distribution with mean 0 hr.sup.−1 and standard deviation 1 hr.sup.−1 for the difference between k.sub.La at the source scale and at the target scale; a relative acceptability function being a normal distribution with mean 0 s and standard deviation 5 s for the difference between mixing time at the source scale and at the target scale and an absolute acceptability function requiring the tip speed at the target scale to be 5% of the maximum in the bioreactor (i.e. 0 for tip speed lower than 5% and 1 for tip speed higher than 5%).

(191) At step S705, also a first set of state parameters at the source scale and a second set of state parameters at the target scale 830 is received. The first set of state parameters for the above example may be: stir speed 400 rpm, gassing rate 0.02 L min.sup.−1, fill volume 0.2 L, gas 100% air. The second set of state parameters may be: fill volume 2 L, gassing rate 0.2 L min.sup.−1, gas 100% air, with the stir speed left as variable parameter, which will be populated later.

(192) FIG. 9 shows part of an exemplary input for time-point scaling, in which source and target setup specifications 810 and 820, first and second sets of state parameters 830, and acceptability functions 840 are visible, while mapping information 800 is not shown.

(193) Then at step S707 a first set of derived parameters for the source scale is calculated. In the given example, k.sub.La and mixing time are computed at the ambr 250 scale, given stir speed 400 rpm, gassing rate 0.02 L min.sup.−1, fill volume 0.2 L and gas 100% air and using the retrieved mapping information 800.

(194) Then at step S709 input value(s) for the variable parameter(s) are chosen. For example, the input value for the stir speed at the target scale may be 40 rpm, which is the midpoint of the minimum and the maximum stir speed for the UniVessel 2 L. Using the input value(s), at step S711 a second set of derived parameters 860 for the target scale is calculated, similarly to step S707. Accordingly, in the given example, k.sub.La and mixing time are computed at the UniVessel® 2 L scale, given stir speed 40 rpm, gassing rate 0.2 L min.sup.−1, fill volume 2 L and gas 100% air and using the retrieved mapping information 800. Further, the tip speed is computed according to the mapping information 800 from properties of the UniVessel® 2 L scale geometry and the candidate stir speed 40 rpm.

(195) Then at step S713 the initial guess for the variable parameters provided by the input values is modified to “best” satisfy the conditions given by the acceptability functions 840. In particular, the space available for the variable parameter(s) is explored, until preferred points or surfaces in the space are found, i.e. the ones that make the second set of state parameters most compliant with the acceptability functions 840.

(196) The compliance of the state parameters at the target scale with the acceptability functions 840 is indicated by an acceptability score 870. Different degrees of compliance may be of interest, such as considering only the values of the variable parameter that maximise the acceptability score 870 or considering also a plurality of values that yield an acceptability score 870 above a certain threshold. The plurality of values may form a single (possibly multi-dimensional) range or non-adjacent ranges. If each acceptability function 840 gives a partial acceptability score, the total acceptability score may be given by the product or the mean or other combinations of all partial acceptability scores.

(197) The result is an optimised second set of state parameters 850 for the target scale.

(198) In the given example, each time a new input value from the space of the stir speed is chosen, k.sub.La, mixing time and tip speed are derived again and the corresponding acceptability score is computed. The final result is, thus, an optimised stir speed or an acceptable range for the stir speed at the UniVessel 2 L scale.

(199) The method ends at S715.

(200) The method can be generalised to a train scaling involving an arbitrary number of scales, i.e. a translation that starts from a source scale and arrives at a final target scale by passing through and translating for each of a plurality of intermediate target scales.

(201) When applying the time-point scaling method of FIG. 7, setup specifications for the intermediate target scale(s) are received at S705 and the acceptability functions 840 cover all scales, i.e. define conditions across all scales. In addition, steps S709 and S711 must be performed also for each intermediate target scale. Further, step S713 involves a simultaneous search for “best” values (optimal values or ranges) for all target scales, i.e. the one or more intermediate target scale and the final target scale.