Computational fluid dynamics models and methods of use

Abstract

Methods for predicting freeze-thaw curves across scales and geometries, generating predetermined freeze-thaw curves in scaled scale experiments using computational fluid dynamics models, and predicting equal scale freeze-thaw curves using scaled scale freeze-thaw curves are provided.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims the benefit of U.S. Provisional Application No. 63 / 429,778, filed December 2, 2022, which is incorporated herein by reference in its entirety. Technical Field

[0003] The present application relates to methods for optimizing the freeze-thaw process to maintain the quality and stability of a compound. The methods described herein can also be used to optimize the freeze-thaw process to maintain the quality and stability of a pharmaceutical agent. Background Art

[0004] Freeze-thaw processes enable operational flexibility to maintain quality attributes when manufacturing compounds, and particularly pharmaceuticals. For example, freezing can stabilize bulk pharmaceuticals and reduce the likelihood of microbial contamination during transport. Immobilizing protein molecules in a freezing matrix minimizes diffusional collisions, which can cause pharmaceutical aggregation. Freezing also reduces the rate of degradation reactions, particularly those involving free water, such as peptide bond hydrolysis and aspartate isomerization. Thus, batch freezing of large quantities of pharmaceuticals enables formulation, filling, and finishing processes to be tailored to real-time commercial and clinical needs.

[0005] The freeze-thaw process can also have an adverse effect on the quality attributes of compounds and particularly medicaments. Too cold temperatures can cause proteins to unfold spontaneously (e.g., cold denaturation), and the freeze-thaw rate can change the physical and chemical properties of the solution in a way that damages protein stability. Therefore, optimizing the freeze-thaw process can optimize the quality attributes of medicaments during manufacturing, storage, transportation, and delivery. The experiment can characterize the freeze-thaw process under a series of conditions and determine the impact of the freeze-thaw process on the quality attributes of the medicament. Because the characteristics of the freeze-thaw process depend on the scale at which the freeze-thaw process occurs, scaled experiments should be carried out. However, in the early stages of development, bulk medicaments may not be used for at-scale research. Money, time, and labor costs can also limit the investigation of at-scale freeze-thaw situations.

[0006] It will be appreciated that there is a need for improved methods to characterize freeze-thaw processes across scale using a range of conditions and to determine the impact of freeze-thaw processes on the quality attributes of compounds, and in particular pharmaceutical agents. Summary of the Invention

[0007] Optimizing freeze-thaw process is to keep the quality attribute of compound (such as medicament, and especially biopharmaceutical), is the key problem in pharmaceutical manufacturing process, storage, transportation and delivery.It is necessary to characterize the freeze-thaw process of using multiple conditions across scale and determine the improvement method of the impact of freeze-thaw process on the quality attribute of medicament.The application provides the method for predicting the feature of freeze-thaw process using various conditions across scale and copying the feature of freeze-thaw process in the freeze-thaw process of scaled-down.Therefore, even if only a small amount of medicament is available, it is also possible to determine the impact of freeze-thaw process on medicament quality attribute with minimum money, time and labor cost.

[0008] The present application provides a method for freezing a solution. In some exemplary embodiments, the method includes (a) using a computational fluid dynamics model to predict a first freezing curve for a scaled volume of the solution subjected to a first freezing operating condition, wherein the first freezing curve includes a predicted average temperature and a total freezing time of the solution during freezing; (b) using the computational fluid dynamics model to fit a transient temperature boundary equation to the first freezing curve; (c) using the computational fluid dynamics model to predict a set temperature sequence that produces a predicted second freezing curve for a scaled volume of the solution, wherein: (i) the transient temperature boundary equation is a condition for predicting the set temperature sequence; and (ii) the second freezing curve includes a predicted average temperature and a total freezing time of the solution during freezing; and (d) freezing the scaled volume of the solution using the set temperature sequence.

[0009] In one aspect, the method further comprises determining at least one quality attribute of the solution after freezing the scaled-down volume.

[0010] In one aspect, the solution comprises a pharmaceutical agent, a pharmaceutical product, a drug, a chemical compound, a nucleic acid, a toxin, a peptide, a protein, a fusion protein, an antibody, an antibody fragment, a Fab region of an antibody, an antibody-drug conjugate, a biopharmaceutical, a pharmaceutical protein product, or an antibody.

[0011] In one aspect, the method further comprises operating a temperature regulation system using the computational fluid dynamics model to generate a set temperature sequence for freezing the scaled volume.

[0012] In one aspect, the method further comprises measuring the temperature of at least one point of interest in the scaled volume throughout the freezing process.

[0013] In one aspect, the scaled volume is from about 0.2L to about 20L.

[0014] In one aspect, the scaled volume is from about 20 mL to about 100 mL.

[0015] In one aspect, the scale volume is in a scale container having a volume of about 1 L to 20 L.

[0016] In one aspect, the scaled volume is in a scaled container having a volume of about 30 mL to 100 mL.

[0017] In one aspect, the scale container is selected from the group consisting of 1 L polycarbonate bottles, 2 L polycarbonate bottles, 5 L polycarbonate bottles, 10 L polycarbonate bottles, 20 L polycarbonate bottles, 1 L bags, 2 L bags, 8.3 L bags, and 16.6 L bags.

[0018] In one aspect, the scale-down container is selected from the group consisting of a 30 mL bag and a 100 mL bag.

[0019] The present application provides a method for melting a solution. In some exemplary embodiments, the method includes (a) using a computational fluid dynamics model to predict a first melting curve for a scaled volume of the solution subjected to a first melting operating condition, wherein the first melting curve includes a predicted average temperature of the solution during melting and a total melting time; (b) using the computational fluid dynamics model to fit a transient temperature boundary equation to the first melting curve; (c) using the computational fluid dynamics model to predict a set temperature sequence, the set temperature sequence generating a predicted second melting curve for a scaled volume of the solution, wherein: (i) the transient temperature boundary equation is a condition for predicting the set temperature sequence; and (ii) the second melting curve includes a predicted average temperature of the solution during melting and a total melting time; and (d) using the set temperature sequence to melt the scaled volume of the solution.

[0020] In one aspect, the method further comprises determining at least one quality attribute of the reduced-scale volume of the solution after thawing.

[0021] In one aspect, the solution comprises a pharmaceutical agent, a pharmaceutical product, a drug, a chemical compound, a nucleic acid, a toxin, a peptide, a protein, a fusion protein, an antibody, an antibody fragment, a Fab region of an antibody, an antibody-drug conjugate, a biopharmaceutical, a pharmaceutical protein product, or an antibody.

[0022] In one aspect, the method further comprises operating a temperature regulation system using the computational fluid dynamics model to generate a set temperature sequence for melting the scaled volume.

[0023] In one aspect, the method further comprises measuring the temperature of at least one point of interest in the scaled volume throughout the melting process.

[0024] In one aspect, the scaled volume is from about 0.2L to about 20L.

[0025] In one aspect, the scaled volume is from about 20 mL to about 100 mL.

[0026] In one aspect, the scale volume is in a scale container having a volume of about 1 L to 20 L.

[0027] In one aspect, the scaled volume is in a scaled container having a volume of about 30 mL to 100 mL.

[0028] In one aspect, the scale container is selected from the group consisting of 1 L polycarbonate bottles, 2 L polycarbonate bottles, 5 L polycarbonate bottles, 10 L polycarbonate bottles, 20 L polycarbonate bottles, 1 L bags, 2 L bags, 8.3 L bags, and 16.6 L bags.

[0029] In one aspect, the scaled-scale container is selected from the group consisting of a 30 mL bag and a 100 mL bag. The present application provides a method for freezing a solution. In some exemplary embodiments, the method comprises: (a) using a computational fluid dynamics model to predict a freezing curve for a scaled-scale solution subjected to a set of freezing operating conditions; (b) determining whether freezing will occur within a necessary time period; and (c) freezing a scaled-scale volume of the solution using the set of freezing operating conditions.

[0030] The present application provides a method for freezing and thawing a solution. In some exemplary embodiments, the method includes (a) using a computational fluid dynamics model to predict a first freezing and thawing curve for a scaled volume of the solution subjected to a first freezing and thawing operating condition, wherein the first freezing and thawing curve includes a predicted average temperature of the solution during freezing and thawing and a total freezing and thawing time; (b) fitting a transient temperature boundary equation to the first freezing and thawing curve using the computational fluid dynamics model; (c) using the computational fluid dynamics model to predict a set temperature sequence, the set temperature sequence generating a predicted second freezing and thawing curve for a scaled volume of the solution, wherein: (i) the transient temperature boundary equation is a condition for predicting the set temperature sequence; and (ii) the second freezing and thawing curve includes a predicted average temperature of the solution during freezing and thawing and a total freezing and thawing time; and (d) using the set temperature sequence to freeze and thaw the scaled volume of the solution.

[0031] In one aspect, the method further comprises determining at least one quality attribute of the solution in a scaled volume after freezing and thawing.

[0032] In one aspect, the solution comprises a pharmaceutical agent, a pharmaceutical product, a drug, a chemical compound, a nucleic acid, a toxin, a peptide, a protein, a fusion protein, an antibody, an antibody fragment, a Fab region of an antibody, an antibody-drug conjugate, a biopharmaceutical, a pharmaceutical protein product, or an antibody.

[0033] In one aspect, the method further comprises operating a temperature regulation system using the computational fluid dynamics model to generate a set temperature sequence for freezing and thawing the scaled volume.

[0034] In one aspect, the method further comprises measuring the temperature of at least one point of interest in the scaled volume throughout the freezing and thawing process.

[0035] In one aspect, the scaled volume is from about 0.2L to about 20L.

[0036] In one aspect, the scaled volume is from about 20 mL to about 100 mL.

[0037] In one aspect, the scale volume is in a scale container having a volume of about 1 L to 20 L.

[0038] In one aspect, the scaled volume is in a scaled container having a volume of about 30 mL to 100 mL.

[0039] In one aspect, the scale container is selected from the group consisting of 1 L polycarbonate bottles, 2 L polycarbonate bottles, 5 L polycarbonate bottles, 10 L polycarbonate bottles, 20 L polycarbonate bottles, 1 L bags, 2 L bags, 8.3 L bags, and 16.6 L bags.

[0040] In one aspect, the scale-down container is selected from the group consisting of a 30 mL bag and a 100 mL bag.

[0041] The present application provides a method for freezing and thawing a solution. In some exemplary embodiments, the method includes: (a) using a computational fluid dynamics model to predict a freeze and thaw curve for a scaled-scale solution subjected to a first freeze and thaw operating condition; (b) determining whether freezing and thawing will occur within a necessary time period; and (c) freezing and thawing a scaled-scale volume of the solution using the first freeze and thaw operating condition.

[0042] The present application provides a method for melting a solution. In some exemplary embodiments, the method includes: (a) using a computational fluid dynamics model to predict a melting curve of a scaled volume of the solution subjected to a first melting operating condition; (b) determining whether melting will occur within a necessary time period; and (c) melting a scaled volume of the solution using the first melting operating condition.

[0043] The present application provides a method for freezing a solution. In some exemplary embodiments, the method includes: (a) using a computational fluid dynamics model to predict a freezing curve of a scaled-scale solution subjected to a first freezing operating condition; (b) determining whether freezing will occur within a necessary time period; and (c) freezing a scaled-scale volume of the solution using the first freezing operating condition.

[0044] In one embodiment, the computational fluid dynamics model can take into account environmental factors. Environmental factors can include, for example, airflow, proximity to other surfaces of different temperatures, relative humidity, pressure, and any combination thereof. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 An overview of a computational fluid dynamics model framework according to an exemplary embodiment is illustrated.

[0046] Figure 2 Shown are models of a full-scale solution within a full-scale vessel and a scaled-scale solution within a scaled-scale vessel generated by a computational fluid dynamics model of the present disclosure, according to exemplary embodiments.

[0047] Figure 3 1. Shown is a spatial domain within a geometrically scaled container partitioned into discrete volumes after spatial discretization, according to an exemplary embodiment.

[0048] Figure 4 Shown are the predicted thermodynamic temperatures at a point within a scaled solution during the freezing process, according to an exemplary embodiment.

[0049] Figure 5 Shown are predicted velocities at a point within a scale-scale container partially filled with solution during a freeze-thaw process, according to an exemplary embodiment.

[0050] Figure 6 Shown are the predicted thermodynamic temperatures at two points within a scale-scale container partially filled with a scale-scale solution during a freezing process, according to an exemplary embodiment.

[0051] Figure 7 An exemplary embodiment is shown in which the computational fluid dynamics model of the present disclosure can determine the 5L Nalgene TM Polycarbonate Biotainer TM Can a 3.5 L vial containing high or low concentrations of drug substance or free drug substance be frozen within 48 hours under refrigeration operating conditions?

[0052] Figure 8Shown is a scaled-down solution at one point in a scaled-down container during the freezing process, the predicted thermodynamic temperature, and the last freezing point (eg, red sphere), according to an exemplary embodiment.

[0053] Figure 9 The weighted spatial averaging of geometric-scale freeze-thaw processes, the generation of set temperature sequences for temperature regulation systems, and the prediction of expected temperature profiles for geometric-scale and scaled-scale freeze-thaw processes by the computational fluid dynamics model of the present disclosure are shown, enabling the scaled-scale freeze-thaw process to represent the spatially averaged volume of geometric-scale freeze-thaw processes across scales and geometries according to exemplary embodiments.

[0054] Figure 10 An example of a transient equation fitted to the predicted temperature of a full-scale solution during a freezing process by a computational fluid dynamics model of the present disclosure is shown, according to an exemplary embodiment, the transient equation being set as a transient temperature boundary condition when predicting a temperature progression profile of a temperature regulation system in a scaled-scale experiment designed to reproduce the freeze-thaw rates of a full-scale process, and the temperature regulation system being adjusted to produce the predicted temperature progression profile during the scaled-scale experiment.

[0055] Figure 11 An exemplary embodiment is shown in which a computational fluid dynamics model can estimate the physical quantities of the freeze-thaw process of isoscale solutions and scale-scale solutions in 1L-5L polycarbonate bottles and 30mL bags, respectively, and reproduce the freeze-thaw curves of isoscale solutions in scale-scale solutions using a benchtop freezing platform.

[0056] Figure 12 Shown are the ratios of total freezing times for solutions in full-scale and scaled-scale vessels to the total freezing times predicted by a computational fluid dynamics model, according to exemplary embodiments. DETAILED DESCRIPTION

[0057] Maintaining the quality and stability of compounds, and in particular biopharmaceuticals, during the manufacturing process, storage, transportation, and patient administration can be difficult but crucial. Bulk drug substances undergo a series of processing steps to convert the purified drug substance into the final dosage form (e.g., formulation, filling, and finishing processes) in an appropriate container closure system or delivery device. The formulation, filling, and finishing processes include freezing and thawing of the bulk pharmaceutical substance (e.g., bulk freeze-thaw), preparing the purified drug substance to the desired concentration with excipients, filtering, filling into a container closure system, freeze drying (if necessary), inspection, labeling and packaging, storage, transportation, and delivery (e.g., patient administration). Therefore, biopharmaceuticals are susceptible to many sources of chemical and physical instability during the formulation, filling, and finishing processes that may compromise their efficacy.

[0058] Low temperature can make protein spontaneously unfold (for example, cold denaturation) by weakening hydrophobic interaction. The cold denaturation temperature can be explained by the Gibbs free energy function (Gibbs free energy function) with an inverted parabola. The negative free energy of unfolding is conducive to thermal denaturation at temperatures above and below the high temperature threshold and low temperature threshold, respectively. For example, although there is a preference for polar residues and non-polar residues for alternative geometric positions, the hydrophobic effect stabilizes spherical globular proteins with an internal hydrophobic core. Therefore, lowering the temperature will reduce the stability provided by the hydrophobic effect and lead to cold denaturation below the low temperature threshold. In addition to the absolute temperature, the rate at which freezing occurs can also have an adverse effect on protein stability by changing the physical and chemical properties of the solution.

[0059] A slow freezing rate can exclude proteins and excipients from the ice-liquid interface, resulting in an increase in the concentration of excipients and proteins in the liquid near the ice crystals (e.g., cryoconcentration). This increase in excipient concentration can change the structure of the protein. Increasing the concentration of excipients near the ice crystals can change the pH and make the protein unstable because low-solubility buffer components may precipitate. In addition, the increased protein concentration can increase the possibility of aggregation and precipitation. Like a slow freezing rate, a slow melting rate can stress and damage proteins. Tiny ice crystals can recrystallize during the slow melting process, and proteins can denature at the ice-liquid interface.

[0060] The cryoconcentration produced during freezing can destabilize the protein again during thawing. Therefore, a faster thawing process that minimizes recrystallization and cryoconcentration is generally preferred. For example, a mixing process that is sufficient to homogenize the solution without shearing and denaturing the protein at the air-liquid interface can accelerate the thawing process without negatively affecting product quality. Similarly, faster freezing rates can reduce cryoconcentration; however, rapid freezing processes can compromise protein stability.

[0061] Rapid freezing rates expose proteins to a large ice-liquid interface by forming tiny ice crystals that adsorb proteins on their surfaces. Proteins concentrated on the crystal surfaces at the ice-liquid interface can partially unfold and aggregate. In addition, rapid freezing rates can trap air in the ice, and subsequent thawing can denature proteins at the air-liquid interface. Therefore, during biopharmaceutical manufacturing, careful evaluation and optimization of freeze-thaw process parameters prevent the bulk freeze-thaw process from compromising the quality of the drug substance.

[0062] Measuring the temperature of a solution at one or more points of interest during the freeze-thaw process can determine a freeze-thaw curve. These data can determine the average temperature and rate at which the solution freezes or melts over the duration of the freezing or thawing process. Large-scale production can expand the formation of cryoconcentrates. Therefore, experiments are conducted to examine the formation of cryoconcentrates during the scaled freeze-thaw process. Therefore, examining the effects of various freeze-thaw operating conditions on the quality attributes of a pharmaceutical protein product during the scaled freeze-thaw process can require a large amount of material and labor. However, during the early development stages, it may be impossible to obtain a large amount of pharmaceutical protein product, thereby making it impossible to optimize the freeze-thaw operating conditions for the scaled manufacturing process, storage, and transportation.

[0063] Disclosed herein is a method for predicting the freeze-thaw rate of a scaled solution subjected to a set of freeze-thaw operating conditions, reproducing the freeze-thaw rate of a scaled volume solution using a scaled solution, and determining the effect of the freeze-thaw rate on the quality attributes of the scaled volume solution. The example described below demonstrates that the total freezing time of a scaled freezing process differs by approximately 3.57% from the prediction of a computational fluid dynamics model of the present invention. In addition, the computational fluid dynamics model of the present invention reproduces the freezing rate of the scaled freezing process in a scaled freezing experiment. The actual total freezing time and the predicted total freezing time of the scaled freezing process differ by approximately 2.86% and approximately 2.38% from the total freezing time of the scaled freezing process, respectively. Therefore, the method of the present invention can be used to determine the effect of a scaled freeze-thaw process on the quality attributes of a pharmaceutical product without the cost of a scaled study. The present disclosure also provides a method for determining whether a set of freezing operating conditions is suitable for freezing or thawing a certain volume of solution within a predetermined amount of time.

[0064] Unless otherwise described, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. Although methods and materials similar or equivalent to those described herein can be used in practice or testing, specific methods and materials are now described.

[0065] The terms "a" and "an" should be understood to mean "at least one" and the terms "about" and "approximately" should be understood to allow for standard variations, as understood by those of ordinary skill in the art, and where ranges are provided, include the endpoints. As used herein, the terms "include," "includes," and "including" are intended to be non-limiting and may be understood to mean "comprise," "comprises," and "comprising," respectively.

[0066] In an exemplary embodiment, the present disclosure provides a method for freezing or thawing a solution. The solution can include, for example, a component, a pharmaceutical agent or pharmaceutical product, an active ingredient, a drug, a biotherapeutic agent, a small molecule drug, a drug substance, an excipient, or any combination thereof, having at least one quality attribute that can be maintained, replicated, or predicted during the freezing or thawing process. The drug can be a pharmaceutical formulation comprising an excipient.

[0067] As used herein, the term "composition" refers to a pharmaceutical product formulated together with one or more pharmaceutically acceptable vehicles.

[0068] As used herein, the terms "pharmaceutical" and "pharmaceutical product" may include biologically active components of pharmaceutical products. Pharmacological agents and pharmaceutical products may refer to any substance or combination of substances used in pharmaceutical products that is intended to provide pharmacological activity or that otherwise has a direct or indirect effect on the diagnosis, cure, alleviation, treatment or prevention of a disease, or that has a direct or indirect effect on the recovery, correction or alteration of physiological functions in an animal. Non-limiting methods for preparing medicaments and pharmaceutical products may include the use of fermentation processes, recombinant DNA, separation and recovery from natural resources, chemical synthesis, biosynthesis, polymerase chain reaction, or a combination thereof. In some exemplary embodiments, medicaments and pharmaceutical products are drugs, chemical compounds, nucleic acids, nucleotides, nucleosides, oligonucleotides, toxins, peptides, proteins, fusion proteins, antibodies, antibody fragments, the Fab region of an antibody, antibody-drug conjugates, or pharmaceutical protein products, or a combination thereof.

[0069] As used herein, the terms "protein" and "pharmaceutical protein product" may include any amino acid polymer having covalently linked amide bonds. Proteins comprise one or more amino acid polymer chains, commonly referred to in the art as "polypeptides." "Polypeptides" refer to polymers composed of amino acid residues, related naturally occurring structural variants, and synthetic non-naturally occurring analogs thereof, related naturally occurring structural variants, and synthetic non-naturally occurring analogs thereof, linked via peptide bonds. "Synthetic peptides or polypeptides" refer to non-naturally occurring peptides or polypeptides. Synthetic peptides or polypeptides can be synthesized, for example, using an automated peptide synthesizer. Various solid-phase peptide synthesis methods are known to those skilled in the art. Proteins can comprise one or more polypeptides to form a single functional biomolecule. Proteins can include antibody fragments, nanobodies, recombinant antibody chimeras, cytokines, chemokines, peptide hormones, and the like. Proteins of interest can include any biotherapeutic protein, recombinant protein for research or treatment, trap proteins and other chimeric receptor-Fc fusion proteins, chimeric proteins, antibodies, monoclonal antibodies, polyclonal antibodies, human antibodies, and bispecific antibodies. Proteins can be produced using recombinant cell-based production systems, such as insect baculovirus systems, yeast systems (e.g., species of the genus Pichia), mammalian systems (e.g., CHO cells and CHO derivatives such as CHO-K1 cells). For a recent review discussing biotherapeutic proteins and their production, see Ghaderi et al., "Production platforms for biotherapeutic glycoproteins. Occurrence, impact, and challenges of non-human sialylation" (Darius Ghaderi et al., 28 Biotechnology and Genetic Engineering Reviews 147-176 (2012), the entire teaching of which is incorporated herein). Proteins can be classified according to composition and solubility, and thus can include simple proteins such as globular proteins and fibrous proteins; conjugated proteins such as nucleoproteins, glycoproteins, mucins, chromoproteins, phosphoproteins, metalloproteins, and lipoproteins; and derived proteins such as primary derived proteins and secondary derived proteins.

[0070] In some exemplary embodiments, the proteins and pharmaceutical protein products can be recombinant proteins, antibodies, bispecific antibodies, multispecific antibodies, antibody fragments, monoclonal antibodies, fusion proteins, scFv, and combinations thereof.

[0071] As used herein, the term "recombinant protein" refers to a protein produced by transcription and translation of genes carried on a recombinant expression vector introduced into a suitable host cell. In certain exemplary embodiments, the recombinant protein can be an antibody, such as a chimeric antibody, a humanized antibody, or a fully human antibody. In certain exemplary embodiments, the recombinant protein can be an antibody selected from the isotype of the group consisting of: IgG (e.g., IgG1, IgG2, IgG3, IgG4), IgM, IgA1, IgA2, IgD, or IgE. In certain exemplary embodiments, the antibody molecule is a full-length antibody (e.g., IgG1 or IgG4 immunoglobulin), or the antibody can be a fragment (e.g., Fc fragment or Fab fragment).

[0072] As used herein, the term "antibody" includes immunoglobulin molecules and multimers thereof (e.g., IgM) comprising four polypeptide chains (two heavy (H) chains and two light (L) chains) interconnected by disulfide bonds. Each heavy chain comprises a heavy chain variable region (abbreviated herein as HCVR or VH) and a heavy chain constant region. The heavy chain constant region comprises three domains: CH1, CH2, and CH3. Each light chain comprises a light chain variable region (abbreviated herein as LCVR or VL) and a light chain constant region. The light chain constant region comprises one domain (CL1). The VH and VL regions can be further subdivided into hypervariable regions called complementarity determining regions (CDRs), which are interspersed with more conserved regions called framework regions (FRs). Each VH and VL is composed of three CDRs and four FRs arranged from amino terminus to carboxyl terminus in the following order: FR1, CDR1, FR2, CDR2, FR3, CDR3, and FR4. In various embodiments of the present invention, the FRs of the anti-big-ET-1 antibody (or its antigen-binding portion) may be identical to human germline sequences, or may be naturally or artificially modified. An amino acid consensus sequence may be defined based on a side-by-side analysis of two or more CDRs. As used herein, the term "antibody" also includes antigen-binding fragments of intact antibody molecules. As used herein, the terms "antigen-binding portion of an antibody," "antigen-binding fragment of an antibody," etc. include any naturally occurring, enzymatically obtainable, synthetic, or genetically engineered polypeptide or glycoprotein that specifically binds to an antigen to form a complex. Antigen-binding fragments of antibodies can be derived from whole antibody molecules, for example, using any suitable standard technique (e.g., proteolytic digestion or recombinant genetic engineering techniques involving manipulation and expression of DNA encoding antibody variable domains and, optionally, antibody constant domains). Such DNA is known and / or can be readily obtained, for example, from commercial sources, DNA libraries (including, for example, phage-antibody libraries), or can be synthesized. The DNA can be sequenced and manipulated chemically or by using molecular biology techniques, for example, to arrange one or more variable and / or constant domains into a suitable configuration, or to introduce codons, create cysteine ​​residues, modify, add or delete amino acids, etc.

[0073] As used herein, an "antibody fragment" comprises a portion of an intact antibody, such as an antigen-binding region or variable region of an antibody. Examples of antibody fragments include, but are not limited to, Fab fragments, Fab' fragments, F(ab')2 fragments, scFv fragments, Fv fragments, dsFv diabodies, dAb fragments, Fd' fragments, Fd fragments, and isolated complementarity-determining regions (CDRs), as well as triabodies, tetrabodies, linear antibodies, single-chain antibody molecules, and multispecific antibodies formed from antibody fragments. An Fv fragment is a combination of immunoglobulin heavy and light chain variable regions, and an ScFv protein is a recombinant single-chain polypeptide molecule in which the immunoglobulin light and heavy chain variable regions are connected by a peptide linker. In some exemplary embodiments, an antibody fragment comprises sufficient amino acid sequence of a parent antibody such that the fragment binds to the same antigen as the parent antibody; in some exemplary embodiments, the fragment binds to the antigen with the same affinity as the parent antibody and / or competes with the parent antibody for antigen binding. Antibody fragments can be produced by any means. For example, an antibody fragment can be produced enzymatically or chemically by fragmentation of an intact antibody, and / or it can be produced recombinantly from genes encoding a partial antibody sequence. Alternatively or additionally, antibody fragments can be produced synthetically in whole or in part. Antibody fragments may optionally comprise single-chain antibody fragments. Alternatively or additionally, antibody fragments may comprise multiple chains linked together, for example, by disulfide bonds. Antibody fragments may optionally comprise multimolecular complexes. Functional antibody fragments typically comprise at least about 50 amino acids and more typically comprise at least about 200 amino acids.

[0074] The term "bispecific antibody" includes antibodies that can selectively bind to two or more epitopes. Bispecific antibodies generally comprise two different heavy chains, wherein each heavy chain specifically binds to different epitopes - on two different molecules (e.g., antigens) or on the same molecule (e.g., on the same antigen). If a bispecific antibody can selectively bind to two different epitopes (a first epitope and a second epitope), the affinity of the first heavy chain for the first epitope is generally lower than the affinity of the first heavy chain for the second epitope by at least one to two or three or four orders of magnitude, and vice versa. The epitopes recognized by the bispecific antibody can be on the same or different targets (e.g., on the same or different proteins). Bispecific antibodies can be prepared, for example, by combining heavy chains that recognize different epitopes of the same antigen. For example, nucleic acid sequences encoding heavy chain variable sequences that recognize different epitopes of the same antigen can be fused with nucleic acid sequences encoding different heavy chain constant regions, and such sequences can be expressed in cells expressing immunoglobulin light chains.

[0075] A typical bispecific antibody has two heavy chains and an immunoglobulin light chain, each of which has three heavy chain CDRs, followed by a CH1 domain, a hinge, a CH2 domain, and a CH3 domain. The immunoglobulin light chain does not confer antigen binding specificity, but can bind to each heavy chain, or can bind to each heavy chain and can bind to one or more epitopes bound by the heavy chain antigen binding region, or can bind to each heavy chain and enable one or both of the heavy chains to bind to one or two epitopes. bsAbs can be divided into two major categories, those with an Fc region (IgG-like) and those lacking an Fc region, the latter of which is generally smaller than IgG and IgG-like bispecific molecules containing Fc. IgG-like bsAbs can have different formats, such as, but not limited to, three monoclonal antibodies (triomabs), knob-and-hole IgG (kih IgG), crossMab, orth-Fab IgG, dual variable domain Ig (DVD-Ig), two-in-one or dual-action Fab (DAF), IgG single-chain Fv (IgG-scFv), or κλ bodies. Different non-IgG-like formats include tandem scFv, diabody formats, single-chain diabodies, tandem diabodies (TandAb), dual affinity retargeting molecules (DART), DART-Fc, nanobodies or antibodies generated by the dock-and-lock (DNL) approach (Gaowei Fan, Zujian Wang and Mingju Hao, Bispecific antibodies and their applications, 8 JOURNALOF HEMATOLOGY & ONCOLOGY 130; Dafne Müller and Roland E. Kontermann, Bispecific Antibodies, HANDBOOK OF THERAPEUTIC ANTIBODIES 265-310 (2014), the entire teachings of which are incorporated herein).

[0076] As used herein, "multispecific antibodies" refers to antibodies that have binding specificities for at least two different antigens. Although such molecules will typically bind only two antigens (e.g., bispecific antibodies, bsAbs), antibodies with additional specificities, such as trispecific antibodies and KIH trispecific antibodies, can also be processed by the systems and methods disclosed herein.

[0077] The term "monoclonal antibody" as used herein is not limited to antibodies produced by hybridoma technology. Monoclonal antibodies can be derived from a single clone (including any eukaryotic clone, prokaryotic clone, or phage clone) by any means available or known in the art. Monoclonal antibodies that can be used with the present disclosure can be prepared using a variety of techniques known in the art, including the use of hybridoma, recombinant and phage display technologies, or a combination thereof.

[0078] In some exemplary embodiments, proteins and pharmaceutical protein products can be produced from mammalian cells. Mammalian cells can be of human or non-human origin and can include primary epithelial cells (e.g., keratinocytes, cervical epithelial cells, bronchial epithelial cells, tracheal epithelial cells, renal epithelial cells, and retinal epithelial cells), established cell lines and strains thereof (e.g., 293 embryonic kidney cells, BHK cells, HeLa cervical epithelial cells and PER-C6 retinal cells, MDBK (NBL-1) cells, 911 cells, CRFK cells, MDCK cells, CHO cells, BeWo cells, Chang cells, Detroit 562 cells, HeLa 229 cells, HeLa S3 cells, Hep-2 cells, KB cells, LSI80 cells, LS174T cells, NCI-H-548 cells, RPMI2650 cells, SW-13 cells, T24 cells, WI-28VA13, 2RA cells, WISH cells, BS-CI cells, LLC-MK2 cells, clone M-3 cells, 1-10 cells, RAG cells, TCMK-1 cells, Yl cells, LLC-PKi cells, PK(15) cells, GHi cells, GH3 cells, L2 cells, LLC-RC 256 cells, MHiCi cells, XC cells, MDOK cells, VSW cells and TH-1, B1 cells, BSC-1 cells, RAf cells, RK cells, PK-15 cells or their derivatives), fibroblasts from any tissue or organ (including but not limited to heart, liver, kidney, colon, intestine, esophagus, stomach, nervous tissue (brain, spinal cord), lung, vascular tissue (artery, vein, capillary), lymphoid tissue (lymph gland, adenoids, tonsil, bone marrow and blood), spleen), and fibroblast cell lines and fibroblast-like cell lines (e.g.,CHO cells, TRG-2 cells, IMR-33 cells, Don cells, GHK-21 cells, citrullinemia cells, Dempsey cells, Detroit 551 cells, Detroit 510 cells, Detroit 525 cells, Detroit 529 cells, Detroit 532 cells, Detroit 539 cells, Detroit 548 cells, Detroit 573 cells, HEL 299 cells, IMR-90 cells, MRC-5 cells, WI-38 cells, WI-26 cells, Midi cells, CHO cells, CV-1 cells, COS-1 cells, COS-3 cells, COS-7 cells, Vero cells, DBS-FrhL-2 cells, BALB / 3T3 cells, F9 cells, SV-T2 cells, M-MSV-BALB / 3T3 cells, K-BALB cells, BLO-11 cells, NOR-10 cells, C3H / IOTI / 2 cells, HSDMiC3 cells, KLN205 cells, McCoy cells, mouse L cells, line 2071 (mouse L) cells, line LM (mouse L) cells, L-MTK' (mouse L) cells, NCTC clones 2472 and 2555, SCC-PSA1 cells, Swiss / 3T3 cells, Indian muntjac cells, SIRC cells, Cn cells and Jensen cells, Sp2 / 0, NS0, NS1 cells or their derivatives).

[0079] In some exemplary embodiments, the compositions can be used for the treatment, prevention and / or amelioration of a disease or condition. Exemplary, non-limiting diseases and conditions that can be treated and / or prevented by administering the pharmaceutical formulations of the present invention include: infections; respiratory diseases; pain caused by any condition associated with neurogenic, neuropathic or nociceptive pain; genetic conditions; congenital conditions; cancer; herpetiform diseases; chronic idiopathic urticaria; scleroderma, hypertrophic scars; Whipple's Disease; benign prostatic hyperplasia; pulmonary conditions such as mild, moderate or severe asthma, allergic reactions; Kawasaki disease, sickle cell disease; Churg-Strauss syndrome; Graves' disease; disease; preeclampsia; Sjögren's syndrome; autoimmune lymphoproliferative syndrome; autoimmune hemolytic anemia; Barrett's esophagus; autoimmune uveitis; tuberculosis; kidney disease; arthritis, including chronic rheumatoid arthritis; inflammatory bowel disease, including Crohn's disease and ulcerative colitis; systemic lupus erythematosus; inflammatory diseases; HIV infection; AIDS; LDL apheresis; conditions due to PCSK9 activating mutations (gain of function mutations, "GOF"), conditions due to heterozygous familial hypercholesterolemia (heFH); primary hypercholesterolemia; dyslipidemia; cholestatic liver disease; nephrotic syndrome; hypothyroidism; obesity; atherosclerosis; cardiovascular disease; neurodegenerative diseases; neonatal-onset multisystem inflammatory disorder (NOM) ID / CINCA); Muckle-Wells Syndrome (MWS); Familial Cold Autoinflammatory Syndrome (FCAS); Familial Mediterranean Fever (FMF); Tumor Necrosis Factor Receptor-Associated Periodic Fever Syndrome (TRAPS); Systemic Onset Juvenile Idiopathic Arthritis (Still's Disease); Type 1 and Type 2 Diabetes Mellitus; Autoimmune Diseases; Motor Neuron Diseases; Eye Diseases; Sexually Transmitted Diseases; Tuberculosis; Diseases or Conditions Ameliorated, Inhibited, or Alleviated by VEGF Antagonists; Diseases or Conditions Ameliorated, Inhibited, or Alleviated by PD-1 Inhibitors; Diseases or Conditions Ameliorated, Inhibited, or Alleviated by Interleukin Antibodies; Diseases or Conditions Ameliorated, Inhibited, or Alleviated by NGF Antibodies; Diseases or Conditions Ameliorated, Inhibited, or Alleviated by PCSK9 Antibodies; Diseases or Conditions Ameliorated, Inhibited, or Alleviated by ANGPTL Antibodies; Diseases or Conditions Ameliorated, Inhibited, or Alleviated by Activin Antibodies; Diseases or Conditions Ameliorated, Inhibited, or Alleviated by GDF Antibodies; Diseases or Conditions Ameliorated, Inhibited, or Alleviated by Fel d 1 Diseases or conditions that are improved, inhibited or alleviated by the antibody;Diseases or conditions that are improved, inhibited or alleviated by CD antibodies; diseases or conditions that are improved, inhibited or alleviated by C5 antibodies, or a combination thereof.

[0080] In some exemplary embodiments, the composition can be administered to the patient. It can be administered via any route acceptable to those skilled in the art. Non-limiting routes of administration include oral, topical or parenteral. Administration via certain parenteral routes can involve the introduction of the preparation of the present invention into the patient's body by a needle or catheter propelled by a sterile syringe or some other mechanical device such as a continuous infusion system. A syringe, injector, pump or any other device recognized in the art for parenteral administration can be used to administer the composition. The composition can also be administered as an aerosol to absorb in the lungs or nasal cavity. Solutions can also be administered to absorb through the mucous membrane, such as in buccal administration.

[0081] In some exemplary embodiments, the formulation may further comprise excipients, including but not limited to buffers, fillers, tonicity adjusters, solubilizers, and preservatives. Other additional excipients may also be selected based on function and compatibility with the formulation, as can be found, for example, in the following literature: Remington: the science and practice of pharmacy, (2005); US Pharmacopeia: National formulary; Louis Sanford Goodman et al., Goodman & Gilmans, The Pharmacological Basis of Therapeutics (2001); Kenneth E. Avis, Herbert A. Lieberman and Leon Lachman, Pharmaceutical dosage forms: parenteral medications (1992); Praful Agrawala, Pharmaceutical Dosage Forms: Tablets. Vol. 1, 79 Journal of Pharmaceutical Sciences 188 (1990); Herbert A. Lieberman, Martin M. Rieger and Gilbert S. Banker, Pharmaceutical dosage forms: disperse systems (1996); Myra L. Weiner and Lois A. Kotkoskie, Excipient toxicity and safety (2000), which is incorporated herein by reference in its entirety.

[0082] As used herein, the volume of an "isometric solution" can have a volume of about 0.2 L to about 100 L, about 1 L to about 75 L, about 2 L to about 50 L, about 5 L to about 25 L, about 0.2 L, about 0.5 L, about 1 L, about 2 L, about 3 L, about 4 L, about 5 L, about 7.5 L, about 10 L, about 15 L, about 16.6 L, about 20 L, about 25 L, about 30 L, about 40 L, about 50 L, about 60 L, about 70 L, about 75 L, about 80 L, about 90 L, or about 100 L.

[0083] The isoscale solution can be in a container (e.g., an isoscale container) having a volume of about 0.2 L to about 100 L, about 1 L to about 75 L, about 2 L to about 50 L, about 5 L to about 25 L, about 0.2 L, about 0.5 L, about 1 L, about 2 L, about 3 L, about 4 L, about 5 L, about 7.5 L, about 8.3 L, about 10 L, about 15 L, about 16.6 L, about 20 L, about 25 L, about 30 L, about 40 L, about 50 L, about 60 L, about 70 L, about 75 L, about 80 L, about 80 L, or about 100 L.

[0084] As used herein, the volume of a "scale solution" can be from about 1 mL to about 200 mL, from about 5 mL to about 100 mL, from about 10 mL to 75 mL, from about 25 mL to about 50 mL, about 1 mL, about 2 mL, about 3 mL, about 4 mL, about 5 mL, about 7.5 mL, about 10 mL, about 15 mL, about 20 mL, about 25 mL, about 30 mL, about 40 mL, about 50 mL, about 60 mL, about 70 mL, about 75 mL, about 80 mL, about 90 mL, about 100 mL, about 125 mL, about 150 mL, about 175 mL, or about 200 mL.

[0085] The scale-down solution can be in a container (e.g., a scale-down container) having a volume of about 30 mL to about 250 mL, about 50 mL to about 200 mL, about 75 mL to about 175 mL, about 100 mL to about 150 mL, about 30 mL, about 40 mL, about 50 mL, about 75 mL, about 100 mL, about 125 mL, about 150 mL, about 200 mL, or about 250 mL.

[0086] As used herein, "freezing curve" refers to any one or more quantitative measurements of a freezing process that can be used to quantitatively determine at least one freezing rate. Exemplary embodiments quantitatively determine the freezing rate over the entire freezing process until the solution freezes. In some embodiments, the freezing rate can be measured directly. In some embodiments, the freezing rate can be determined indirectly by measuring at least one physical quantity of the freezing process. Exemplary, non-limiting examples of quantitative measurements that can be used to determine the melting rate include thermodynamic temperature, electrical conductivity, osmolarity, osmolality, evaporation, condensation, direct or indirect observation of crystal formation, density, flow rate, viscosity, and any combination thereof.

[0087] As used herein, "freezing rate" refers to the rate at which the thermodynamic temperature of a solution decreases. For example, the freezing rate can be the instantaneous rate at which the thermodynamic temperature of a point in the solution decreases during the freezing process, the instantaneous rate at which the average thermodynamic temperature of a volume of the solution decreases during the freezing process, the average rate at which the thermodynamic temperature of a point in the solution decreases over the entire freezing process (e.g., from the time the solution is initially subjected to freezing conditions to the time the entire solution is initially frozen), or the average rate at which the average thermodynamic temperature of a volume of the solution decreases over the entire freezing process (e.g., from the time the solution is initially subjected to freezing conditions to the time the entire solution is initially frozen).

[0088] As used herein, "melt curve" refers to any quantitative measurement of the melting process that can be used to quantitatively determine at least one melting rate. Exemplary embodiments quantitatively determine the freezing rate throughout the melting process until the solution melts. In some embodiments, the melting rate can be measured directly. In some embodiments, the melting rate can be determined indirectly by measuring at least one physical quantity of the melting process. Exemplary, non-limiting examples of quantitative measurements that can be used to determine the melting rate include thermodynamic temperature, electrical conductivity, osmolality, osmolality, evaporation, condensation, direct or indirect observation of crystalline melting, density, flow rate, viscosity, and any combination thereof.

[0089] As used herein, "melt rate" refers to the rate at which the thermodynamic temperature of a solution increases. For example, the melt rate can be the instantaneous rate at which the thermodynamic temperature of a point in the solution increases during the melting process, the instantaneous rate at which the average thermodynamic temperature of a volume of the solution increases during the melting process, the average rate at which the thermodynamic temperature of a point in the solution increases over the entire melting process (e.g., from the time the solution is initially subjected to melting conditions to the time the entire solution initially melts), or the average rate at which the average thermodynamic temperature of a volume of the solution increases over the entire melting process (e.g., from the time the solution is initially subjected to melting conditions to the time the entire solution initially melts).

[0090] As used herein, "freezing operating conditions" refers to the thermal and mechanical properties of the material inputs into the freezing system and the freezing system operating conditions (e.g., freezing operating conditions) that can affect the freezing process. Exemplary, non-limiting freezing operating conditions that may be included in the freezing operating conditions include temperature, convection pattern, solution volume, solution mechanical properties, solution thermal properties, solution geometry, container volume, container mechanical properties, container thermal properties, container geometry, the air between the fill level and the upper boundary of the container, adjacent airflow mechanisms, proximity of the container to other containers in the freezing environment, and any combination thereof.

[0091] As used herein, "melt operating conditions" refers to the thermal and mechanical properties of the material inputs into the melt system and the operating conditions of the melt system (e.g., melt operating conditions) that can affect the melting process. Exemplary, non-limiting melt operating conditions that can be included in the melt operating conditions include temperature, convection pattern, solution volume, mechanical properties of the solution, thermal properties of the solution, solution geometry, container volume, mechanical properties of the container, thermal properties of the container, container geometry, air between the fill level and the upper boundary of the container, adjacent airflow mechanisms, proximity of the container to other containers in the melt environment, and any combination thereof.

[0092] As used herein, " transient temperature boundary equation " is the equation that is fitted with the predicted average thermodynamic temperature of the isotropic solution in the freeze-thaw process. Prediction of the freeze-thaw curve of isotropic solution can provide the predicted average thermodynamic temperature of isotropic solution during the freeze-thaw process (for example, the instantaneous thermodynamic temperature of solution during the freeze-thaw process) in the whole freeze-thaw process. The computational fluid dynamics model of the present disclosure can replicate the predicted average thermodynamic temperature of isotropic solution during the freeze-thaw process in the scaled-down solution by predicting and subjecting the scaled-down solution to a set temperature sequence. The computational fluid dynamics model of the present disclosure can set the transient temperature boundary equation to the boundary condition when predicting the set temperature progression of the freeze-thaw curve of the isotropic solution in the scaled-down solution. Therefore, the transient temperature boundary equation provides information about average thermodynamic temperature for the computational fluid dynamics model of the present disclosure, and the set temperature progression must be generated at each point in the scaled-down solution during the freeze-thaw process to reproduce the isotropic freeze-thaw curve.

[0093] It will be understood that the present invention is not limited to any of the aforementioned solutions, compositions, medicaments, pharmaceutical products, proteins, pharmaceutical protein products, proteins, polypeptides, synthetic polypeptides, recombinant proteins, antibodies, antigen-binding portions, antigen-binding fragments, antibody fragments, bispecific antibodies, multispecific antibodies, formulations, excipients, cells, full-scale solutions, scaled-down solutions, freezing curves, freezing rates, melting curves, melting rates, freezing operating conditions, melting operating conditions, or transient temperature boundary equations and that the solutions, compositions, medicaments, pharmaceutical products, proteins, pharmaceutical protein products, proteins, polypeptides, synthetic polypeptides, recombinant proteins, antibodies, antigen-binding portions, antigen-binding fragments, antibody fragments, bispecific antibodies, multispecific antibodies, formulations, excipients, cells, full-scale solutions, scaled-down solutions, freezing curves, freezing rates, melting curves, melting rates, freezing operating conditions, melting operating conditions, or transient temperature boundary equations may be selected by any suitable means.

[0094] Existing methods for determining the freeze-thaw rate of a scaled freeze-thaw process and its impact on pharmaceutical quality attributes require a large amount of pharmaceutical materials. The problem is that producing the necessary amount of pharmaceutical materials for scaled testing requires a large amount of money, labor, material resources, time and other resources. Therefore, resource limitations can hinder the optimization of scaled freeze-thaw operating conditions. In contrast, exemplary embodiments of the present disclosure can provide location-specific modeling of pharmaceutical freeze-thaw processes in containers across scales and geometries under a range of freeze-thaw operating conditions. In addition, exemplary embodiments of the present disclosure can reproduce the freeze-thaw rate of a scaled pharmaceutical freeze-thaw process in a scaled-down experiment. Therefore, the impact of scaled freeze-thaw rate on pharmaceutical quality attributes can be determined with a minimum amount of pharmaceutical material. Therefore, exemplary embodiments of the present disclosure enable more stringent and cost-effective optimization of scaled pharmaceutical freeze-thaw operating conditions than existing methods.

[0095] For example, Figure 1 An overview of a computational fluid dynamics model of the present disclosure according to an exemplary embodiment is shown. A set of equations representing the physical properties of a material input subjected to freeze-thaw operating conditions can control the computational fluid dynamics model of the present disclosure. User input can provide information about the material input under freeze-thaw operating conditions to the computational fluid dynamics model of the present disclosure. Information about the material input subjected to freeze-thaw operating conditions can include the geometry of the container and the mechanical and thermal properties of the material input, including but not limited to any and all parts of the composition formulation. For example, Figure 2 Shown is a representation of a full-scale solution (e.g., about 0.2 L to about 100 L) in a full-scale container (e.g., about 0.5 L to about 100 L) having a cuboid geometry within a computational fluid dynamics model of the present disclosure, according to an exemplary embodiment. Figure 2Also shown is a representation of a scaled-down solution in a scaled-down container (e.g., about 30 mL to about 250 mL) with an expansion bag geometry within a computational fluid dynamics model of the present disclosure according to an exemplary embodiment. User input can also provide information about freeze-thaw operating conditions to the computational fluid dynamics model of the present disclosure. Information about freeze-thaw operating conditions can include temperature, convection pattern, adjacent airflow, density, and proximity of containers to each other.

[0096] The computational fluid dynamics model of the present disclosure can be modeled, for example, using the fluid simulation software ANSYS Fluent (ANSYS, Inc., Cannonsburg, Pennsylvania). For a comprehensive overview of the modeling options available in ANSYS Fluent that are compatible with the computational fluid dynamics model of the present disclosure, see ANSYS Fluent Theory Guide, Release 2021R1, January 2021, ANSYS, Inc., the entire teaching of which is incorporated herein, and ANSYS Fluent User's Guide, Release 2021R1, January 2021, ANSYS, Inc., the entire teaching of which is incorporated herein. The set of equations that govern the computational fluid dynamics model of the present disclosure can, for example, model mass transfer and heat transfer. The equations included in the control group can, for example, include the Navier-Stokes equations, the mass conservation equation, the momentum conservation equation, the energy conservation equation, the energy equation, the turbulence equation, the species equation, the back diffusion equation, and equations for modeling thermal buoyancy and solute buoyancy. Shell conduction methods can be used, for example, to model the material of the boundary imposed by the container to account for the effects of the container material without having to solve for the material structure. The mushy zone approximation method can be used, for example, to model the freezing front within the container to spatially advance the freezing of the liquid based on the modeled freezing operating conditions. Multiphase flow simulation can be used, for example, to model stagnant air between the solution filling level and the upper boundary of the container. The volume of fluid method can be used, for example, to model the air-liquid interface. The interfacial anti-diffusion surface model can be used, for example, to account for the significant difference in viscosity between air and solution.

[0097] The computational fluid dynamics model of the present embodiment can use information about material inputs and freeze-thaw operating conditions to determine a solution to a selected set of equations. The solution to the governing set of equations can provide a physical measure of the freeze-thaw process within a container subjected to freeze-thaw operating conditions. However, it can be difficult to determine an analytical solution to the selected set of equations. In contrast, the computational fluid dynamics model of the present disclosure can use spatial and temporal discretization to determine a numerical solution that estimates the analytical solution to the selected set of equations.

[0098] Spatial discretization divides the spatial domain within the container into discrete volumes at a point when the container is subjected to freeze-thaw operating conditions. Figure 3 The spatial domain of a scaled container is shown as being partitioned into discrete volumes after spatial discretization at a point while the container is subjected to freezing operating conditions, according to an exemplary embodiment. The computational fluid dynamics model of the present disclosure can determine a numerical solution (e.g., location-specific) that estimates (e.g., predicts) the average value of the analytical solution within each discrete volume of the discretized spatial domain within the container. For example, Figure 4 1 shows the predicted thermodynamic temperature of a scaled-scale solution at one point in a scaled-scale vessel when the scaled-scale vessel is subjected to refrigerated operating conditions, according to an exemplary embodiment. Figure 5 The predicted velocity at a point within a scale-scale container partially filled with a scale-scale solution while the scale-scale container is subjected to freezing operating conditions, according to an exemplary embodiment, is shown. Thus, the computational fluid dynamics model of the present disclosure can predict physical metrics of the freeze-thaw process across the entire spatial domain within a container subjected to freeze-thaw operating conditions, across scales and geometries.

[0099] Time discretization is performed periodically while the container is subjected to freeze-thaw operating conditions. The computational fluid dynamics model can use interpolation to estimate the analytical solution at the time points between consecutive spatial discretization operations. For example, Figure 6 The predicted thermodynamic temperatures at two points within a scale-scale solution in a scale-scale container when the scale-scale container is subjected to freezing operating conditions are shown according to an exemplary embodiment. Thus, the computational fluid dynamics model of the present disclosure can estimate (e.g., predict) physical metrics of the freeze-thaw process within a container subjected to freeze-thaw operating conditions over the entire spatiotemporal domain.

[0100] The numerical solution determined by the computational fluid dynamics model of the present disclosure can predict the thermodynamic temperature of a solution in a container subjected to freeze-thaw operating conditions. For example, Figure 4-Figure 6 : The thermodynamic temperature of a solution predicted by the computational fluid dynamics model of the present disclosure if subjected to modeled freezing operating conditions according to an exemplary embodiment is shown. The thermodynamic temperature of a solution subjected to freezing and thawing operating conditions can be used to determine the total freezing and thawing time, the first freezing point, the first melting point, the last freezing point and the last melting point, the time to central freezing, the time to central melting, and the temperature profile of the solution edge. For example, Figure 7 It shows that the computational fluid dynamics model of the present disclosure can predict whether 48 hours is sufficient freezing operating conditions to freeze 3.5 L of high concentration or low concentration API / free API solution in a 5 L polycarbonate bottle. The user input can be Figure 7 The computational fluid dynamics model shown provides information about the material input and freezing operating conditions, including the position of a 5 L polycarbonate bottle relative to other bottles under freezing operating conditions. Figure 7The computational fluid dynamics model shown can make conservative predictions by modeling the last theoretical freezing point of the solution (i.e., the center of the solution). Figure 8 The last freezing point (e.g., red sphere) in a scaled-down solution subjected to freezing operating conditions, as predicted by the computational fluid dynamics model of the present disclosure, is shown according to an exemplary embodiment. The numerical solution determined by the computational fluid dynamics model of the present disclosure can also estimate the freeze-thaw rate of a solution subjected to freeze-thaw operating conditions.

[0101] Spatially weighting and interpolating the predicted physical metrics of a solution subjected to freeze-thaw operating conditions can provide the average physical metrics of the solution when subjected to freeze-thaw operating conditions. For example, Figure 9 According to an exemplary embodiment, the computational fluid dynamics model of the present disclosure can use weighted averaging to predict the average representation of a scaled solution subjected to freeze-thaw operating conditions, including the average temperature. In addition, the weighted averaging enables the computational fluid dynamics model of the present disclosure to model the freeze-thaw process of solutions across scales and geometries. For example, Figure 2 A representation of a full-scale solution in a full-scale container having a cuboid geometry and a scaled-scale solution in a scaled-scale container having an expansion bag geometry within a computational fluid dynamics model of the present disclosure according to an exemplary embodiment is shown. Additionally, Figure 5-Figure 7 1 shows the physical measurements of a scale solution in a scale container having a longitudinal cuboid geometry as predicted by the computational fluid dynamics model of the present disclosure, according to an exemplary embodiment. Figure 4 and Figure 8 Shown are physical metrics of a scale-scale solution in a scale-scale container having an expanded bag geometry, as predicted by the computational fluid dynamics model of the present disclosure, according to an exemplary embodiment.

[0102] In some embodiments, the average physical metric of a solution subjected to freeze-thaw operating conditions can be a freeze-thaw curve. In some embodiments, a freeze-thaw curve can include a predicted average temperature and total freeze-thaw time of a solution subjected to freeze-thaw operating conditions. Figure 9 It is also indicated that by developing a set temperature sequence, the computational fluid dynamics model of the present disclosure can represent the average volume of the full-scale solution subjected to freeze-thaw operating conditions in the scaled-scale solution. In some embodiments, the scaled-scale solution subjected to the set temperature sequence developed by the computational fluid dynamics model reproduces the predicted average temperature profile (e.g., predicted freeze-thaw curve) of the full-scale solution in the scaled-scale solution.

[0103] In some embodiments, a computational fluid dynamics model can develop a set temperature sequence by first fitting an equation to a predicted freeze-thaw curve for a scaled-up solution. Figure 10Presented are exponential equations fitted to the average thermodynamic temperature of the freezing curve of a scaled-scale solution by a computational fluid dynamics model of the present disclosure, according to exemplary embodiments. In some embodiments, when predicting a set temperature sequence and the freeze-thaw curve of a scaled-scale solution subjected to the set temperature sequence, the computational fluid dynamics model can then set the equation as a transient temperature boundary condition. In one aspect, the computational fluid dynamics model of the present disclosure can improve the set temperature sequence prediction until the predicted total freeze-thaw time of the scaled-scale solution differs by no more than about 10% from the predicted total freeze-thaw time of the scaled-scale solution. In another aspect, the computational fluid dynamics model of the present disclosure can improve the set temperature sequence prediction until the predicted average temperature of the scaled-scale solution differs by no more than about 10% from the predicted average temperature at any point of the scaled-scale solution during the freeze-thaw process.

[0104] In some embodiments, the scaled-down solution can be subjected to a set temperature sequence that is predicted to reproduce the freeze-thaw curve of the full-scale solution. In one aspect, a computational fluid dynamics model can operate the temperature regulation system to generate the set temperature sequence. Figure 11 In the exemplary embodiment depicted, the computational fluid dynamics model may operate S3 benchtop freezing platform (Sartorius Stedim Biotech GmbH, In one embodiment, the freeze-thaw curve of the isomeric scale solution in the scaled-scale solution of 1L or 5L polycarbonate bottle (Thermo Fisher Scientific, Waltham, Massachusetts) is reproduced in the scaled-scale solution in the 30mL bag. In one aspect, the temperature of at least one point of interest in the scaled-scale solution can be measured during the freeze-thaw process. On the other hand, the measured temperature of at least one point of interest in the scaled-scale solution can be measured when the scaled-scale solution is subjected to a set temperature sequence. In another aspect, the measured temperature of at least one point of interest in the scaled-scale solution subjected to a set temperature sequence can be used to determine the average temperature of the scaled-scale solution when subjected to a set temperature sequence. In yet another aspect, the average temperature of the scaled-scale solution subjected to a set temperature sequence can be used to determine the total freeze-thaw time, and the actual freeze-thaw curve of the scaled-scale solution can include total freeze-thaw time and the average temperature of the scaled-scale solution subjected to a set temperature sequence.

[0105] In one aspect, when measuring the temperature of at least one point of interest, the geometric scale solution by the computational fluid dynamics modeling can be subjected to the freeze-thaw operating condition of modeling. In yet another aspect, the measured temperature of at least one point of interest in the geometric scale solution that stands one group of freeze-thaw operating condition can be used for determining the mean temperature of geometric scale solution. In yet another aspect, the mean temperature of geometric scale solution during the freeze-thaw process can be used for determining the total freeze-thaw time of solution, and the actual freeze-thaw curve of geometric scale solution can comprise total freeze-thaw time and the mean temperature of the geometric scale solution that stands one group of freeze-thaw operating condition.

[0106] In one aspect, the total freeze-thaw time of the geometric ratio scale freeze-thaw curve actual and predicted and the scaled-down scale freeze-thaw curve differs from each other by no more than about 10%.In yet another aspect, the mean temperature of the geometric ratio scale freeze-thaw curve actual and predicted and the scaled-down scale freeze-thaw curve at one point during the freeze-thaw process differs from each other by no more than about 10%. Figure 2 An exemplary embodiment is presented in which the actual and predicted total freeze-thaw times for a full-scale solution in a 5 L polycarbonate bottle and a scaled-scale solution in a 100 mL bag can differ by less than about 6.67%.

[0107] The present disclosure provides the benefit of determining the impact of proportional scale freeze-thaw rates on the quality attributes of freeze-thaw sensitive materials without carrying out proportional scale experiments. Therefore, in one aspect, at least one quality attribute of the reduced scale volume can be determined after the freeze-thaw process. The quality attributes of the present disclosure can be physical, chemical, biological or microbiological properties or characteristics, and these properties or characteristics should be within appropriate limits, scope or distribution to ensure the desired product quality.

[0108] For example, in one aspect, the solution can comprise a medicament, a pharmaceutical product, a drug, a chemical compound, a nucleic acid, a toxin, a peptide, a protein, a fusion protein, an antibody, an antibody fragment, a Fab region of an antibody, an antibody-drug conjugate, a biopharmaceutical, a pharmaceutical protein product, or an antibody. Thus, the method of the present disclosure provides a robust and cost-effective method for optimizing the freeze-thaw process of pharmaceuticals at a scaled scale to ensure the quality, safety, and efficacy of pharmaceuticals for patients.

[0109] External conduction

[0110] In some embodiments, the shell conduction method can model the material of the boundary imposed by the container to account for the effects of the container material without solving for the material structure. The shell conduction method can account for thermal mass in transient thermal analysis problems. The shell conduction method can also allow heat conduction through multiple joints. The shell conduction method can be applied to boundaries and internal walls. Using fluid simulation software, such as ANSYS Fluent (ANSYS, Inc., Cannonsburg, Pennsylvania), the shell conduction method can model heat conduction in the plane and normal directions of the boundary imposed by the wall. The shell conduction method can model thin plates without the need to mesh the wall thickness in the preprocessor. When utilizing the shell conduction method, the user can turn conjugate heat transfer on or off for any wall. Specifying the thickness, material properties of the wall boundary and enabling the shell conduction method in ANSYS Fluent causes ANSYS Fluent to generate a layer of prismatic elements or hexagonal elements for the wall, depending on the type of face mesh utilized. Without the shell conduction method and without specifying thicknesses for the boundaries imposed by the container, modeling the boundaries imposed by the wall allows the container's material to present no thermal resistance to heat transfer in the model. Alternatively, without the shell conduction method, specifying thicknesses for the boundaries imposed by the container can result in appropriate thermal resistance only on the boundaries imposed in the normal direction of the container.

[0111] Proportional scale container

[0112] In some aspects, the computational fluid dynamics model can predict location-specific physical quantities for a freeze-thaw process across the entire spatial domain within a geometrically shaped full-scale container having a volume of about 1 L to about 20 L. In some aspects, the computational fluid dynamics model can predict location-specific physical quantities for a freeze-thaw process across a geometrically shaped full-scale solution having a volume of about 0.75 L to about 15 L.

[0113] Exemplary, non-restrictive geometric scale container comprises 1L polycarbonate bottle, 2L polycarbonate bottle, 5L polycarbonate bottle, 10L polycarbonate bottle, 20L polycarbonate bottle, 1L bag, 2L bag, 8.3L bag and 16.6L bag, for these geometric scale containers, computational fluid dynamics model can predict the position-specific physical quantity of the freeze-thaw process of whole spatial domain in the container.Exemplary, non-restrictive geometric scale container geometry, for these geometric scale container geometry, computational fluid dynamics model can predict the position-specific physical quantity of the freeze-thaw process of whole spatial domain in the container.In one aspect, geometric scale container is square container and in one aspect, scaled-down container is bag-shaped container, and wherein the solution in the bag causes expansion.

[0114] Scaled container

[0115] In some aspects, the computational fluid dynamics model can predict location-specific physical quantities for a freeze-thaw process across the entire spatial domain within a scaled-scale container having a volume of about 30 mL to about 100 mL across a geometry. In some aspects, the computational fluid dynamics model can predict location-specific physical quantities for a freeze-thaw process across a scaled-scale solution having a volume of about 20 mL to about 100 mL across a geometry.

[0116] Exemplary, non-limiting scaled-scale containers, for which the computational fluid dynamics model can predict the location-specific physical quantities of the freeze-thaw process over the entire spatial domain within the container, include 30 mL bags and 100 mL bags. Exemplary, non-limiting scaled-scale container geometries include bag geometries (wherein the solution within the bag causes expansion), for which the computational fluid dynamics model can predict the location-specific physical quantities of the freeze-thaw process over the entire spatial domain within the container.

[0117] The present invention will be more fully understood by reference to the following examples. However, the following examples should not be construed as limiting the scope of the present invention.

[0118] Example 1

[0119] In whole freeze-thaw process, temperature probe monitors the temperature of isometric scale volume solution at multiple points of interest to determine freezing rate.Information about freeze-thaw rate is that the computational fluid dynamics (CFD) model of freeze-thaw system provides information.CFD model is designed for providing the position-specific prediction of the freeze-thaw rate of each position solution in the container across scale and geometry.CFD model is also designed for control temperature regulating system, so that the scaled freeze-thaw rate simulation isometric scale freeze-thaw rate of solution.

[0120] like Figure 12 As seen in part by comparing the 5L Nalgene TM Polycarbonate Biotainer TM Total freezing time of the isoscale solution in the bottle compared to the 5L Nalgene predicted by the CFD model TM Polycarbonate Biotainer TM The total freezing time of the isoscale solution in the bottle (e.g., the "predicted isoscale freezing curve") was used to validate the CFD model. Figure 12 As seen in the 3D model, the predicted total freezing time (e.g., 6.75 hours) and the actual total freezing time (e.g., 7 hours) for a scaled volume of solution differ by 3.57% (e.g., "Scaled Experiment"). The CFD model then fits the equation to the predicted average thermodynamic temperature from the scaled freezing curve and sets the equation as the transient temperature boundary condition. Next, the CFD model simultaneously predicts the temperature of 100 mL of a solution subjected to a set-set temperature sequence. The freezing curve of the scaled-scale solution in the Pak (e.g., the "predicted scaled-scale freezing curve") and the development of a set-set temperature sequence such that the predicted scaled-scale freezing curve mimics the predicted scaled-scale freezing curve. Figure 11 As seen in the CFD model, the model then generates scaled-down inputs that can be manipulated according to the developed temperature progression scheme. The temperature of the S3 benchtop freezer platform was then manipulated using input from a scaled-down scale. S3 benchtop freezing platform will 100mL The CFD model was further validated by freezing the scaled-scale solution in a Pak and comparing the predicted total freezing time and the actual total freezing time of the scaled-scale solution with the actual total freezing time of the full-scale solution. Figure 12 As seen in Figure 3, the predicted total freezing time (e.g., 6.83 hours) and actual total freezing time (e.g., 7.2 hours) for the scaled-down volume solution differed from the actual total freezing time for the equal-scale volume solution by 2.43% and 2.86%, respectively.

[0121] like Figure 1 As seen in the , the CFD model consists of a set of governing equations with simplifying assumptions that mathematically describe the underlying physics of the refrigeration system. This set of equations models the mass transfer, heat transfer, and material properties within the refrigeration system. Figure 1 As seen in , user input provides information about material inputs and operating conditions to the CFD model equations. Information about the material includes the geometry of the vessel and the mechanical and thermal properties of the material inputs, such as Figure 1 As seen in Figure 1 As seen in , information about operating conditions includes temperature, convection patterns, adjacent airflow mechanisms, and the proximity of the container to other containers under freezing operating conditions. Figure 1 As seen in , the numerical solution estimates the continuous solutions of the differential equations in the system of equations governing the CFD model using a spatial discretization according to a time-marching scheme. Figure 1 As can be seen in , the spatial discretization spatially averages the regions within the container over the entire spatial domain at discrete times during the simulation of the freezing process. Figure 1 As seen in , the spatially averaged region provides an approximation to the continuous solution of the differential equation in discrete time.

[0122] like Figure 1 As seen in , time spatialization performs a sequential spatial discretization technique for the span of the time domain of the freezing process simulation. Thus, after receiving information about the freezing system from user input, the CFD model can provide location-specific approximations of physical quantities of the freezing process (including freeze-thaw rates) at any point within the container. Figure 9As seen in the figure, weighted spatial averaging within the freezing domain allows the CFD model to TM Polycarbonate Biotainer TM The total volume of the bottle is represented on a scaled basis to 100 mL. Pak. Therefore, 100mL Pak is 5LNalgene TM Polycarbonate Biotainer TM Average representation of the total volume of the bottles.

[0123] Shell conduction method for 5L Nalgene TM Polycarbonate Biotainer TM Bottle material and 100mL Pak material modeling to take into account the effects of bottle material without the need for costly material structure solutions. The Pak model reflects the expansion that occurs due to the solution, as well as a gentle convective heat transfer gradient through the sides and bottom to simulate a 5L Nalgene TM Polycarbonate Biotainer TM The heat transfer rate of the bottle. The shell conduction method can account for thermal mass in transient thermal analysis problems. The shell conduction method also allows heat conduction through multiple joints. The shell conduction method can be applied to boundary walls and internal walls. Using the fluid simulation software ANSYS FLUENT, the shell conduction method can model heat conduction in both the plane and normal directions of the boundaries imposed by the wall. The shell conduction method can model thin plates without requiring preprocessor meshing for wall thickness. When using the shell conduction method, the user can turn conjugate heat transfer on or off for any wall. Specifying the thickness and material properties of the wall boundary and enabling the shell conduction method in ANSYS FLUENT causes ANSYS FLUENT to generate a layer of prismatic or hexagonal elements for the wall, depending on the face mesh type used. Without the shell conduction method and without specifying a thickness for the container-imposed boundaries, modeling the wall-imposed boundaries results in the container material presenting no thermal resistance to heat transfer. Alternatively, without the shell conduction method, specifying a thickness for the container-imposed boundaries results in appropriate thermal resistance only for the container-imposed boundaries in the normal direction.

[0124] ANSYS Fluent uses the mushy zone approximation available within ANSYS Fluent to model the freezing front, allowing the liquid freezing to advance spatially based on the freezing operating conditions. TM Polycarbonate Biotainer TMThe air between the bottle's solution fill level and the cap is modeled. The air-liquid interface is modeled using the volume of fluid method, and the interfacial anti-diffusion surface model accounts for the significant difference in viscosity between air and liquid.

[0125] Example 2

[0126] like Figure 7 As seen in the CFD model, the 5L Nalgene TM Polycarbonate Biotainer TM Can a 3.5L bottle of solution containing high or low concentrations of drug substance or free drug substance (e.g., specified by the user) be frozen within 48 hours? The user provides information about the material input to the CFD model (e.g., 5L Nalgene TM Polycarbonate Biotainer TM The user provides the CFD model with information about the freezing operating conditions, including the geometry of the bottle and the mechanical and thermal properties of the material input. TM Polycarbonate Biotainer TM The position of the bottle relative to the other bottles. The CFD model uses a conservative approach to determine whether 48 hours is sufficient time for the center of the solution (i.e., the last theoretical freezing point) to freeze. Taking into account the information provided by the user about the material inputs and the freezing operating conditions (which are not specified), the computational fluid dynamics model estimates that the solution will freeze within 48 hours.

Claims

1. A method for freezing a solution, the method comprising: (a) using a computational fluid dynamics model to predict a first freezing curve for a scaled volume of the solution subjected to a first freezing operating condition, wherein the first freezing curve includes a predicted average temperature of the solution during freezing and a total freezing time; (b) fitting a transient temperature boundary equation to the first freezing curve using the computational fluid dynamics model; (c) using the computational fluid dynamics model to predict a set temperature sequence that produces a predicted second freezing curve for a scaled volume of the solution, wherein: (i) the transient temperature boundary equation is used to predict the conditions of the set temperature sequence; and (ii) the second freezing curve includes a predicted average temperature of the solution during freezing and a total freezing time; and (d) freezing the scaled volume of the solution using the set temperature sequence.

2. The method of claim 1 , further comprising determining at least one quality attribute of the solution in the scaled volume after freezing.

3. The method of claim 2, wherein the solution comprises a pharmaceutical agent, a pharmaceutical product, a drug, a chemical compound, a nucleic acid, a toxin, a peptide, a protein, a fusion protein, an antibody, an antibody fragment, a Fab region of an antibody, an antibody-drug conjugate, a biopharmaceutical, a pharmaceutical protein product, or an antibody.

4. The method of claim 3 further comprising operating a temperature regulation system using the computational fluid dynamics model to generate the set temperature sequence for freezing the scaled volume.

5. The method of claim 4, further comprising measuring the temperature of at least one point of interest in the scaled volume throughout the freezing process.

6. The method of claim 5, wherein the isomeric volume is from about 0.2 L to about 20 L.

7. The method of claim 6, wherein the scaled volume is from about 20 mL to about 100 mL.

8. The method of claim 5, wherein the isoscale volume is in an isoscale container having a volume of about 1 L to about 20 L.

9. The method of claim 8, wherein the scaled volume is in a scaled container having a volume of about 30 mL to about 100 mL.

10. The method of claim 9, wherein the scale-up container is selected from the group consisting of 1 L polycarbonate bottles, 2 L polycarbonate bottles, 5 L polycarbonate bottles, 10 L polycarbonate bottles, 20 L polycarbonate bottles, 1 L bags, 2 L bags, 8.3 L bags, and 16.6 L bags.

11. The method of claim 10, wherein the scale-down container is selected from the group consisting of a 30 mL bag and a 100 mL bag.

12. A method for melting a solution, the method comprising: (a) using a computational fluid dynamics model to predict a first melt curve for a scaled volume of the solution subjected to a first melt operating condition, wherein the first melt curve includes a predicted average temperature of the solution during the melt and a total melt time; (b) fitting a transient temperature boundary equation to the first melt curve using the computational fluid dynamics model; (c) using the computational fluid dynamics model to predict a set temperature sequence that produces a predicted second melt curve for the scaled volume of the solution, wherein: (i) the transient temperature boundary equation is used to predict the conditions of the set temperature sequence; and (ii) the second melt curve includes a predicted average temperature of the solution during melting and a total melting time; and (d) melting the scaled volume of the solution using the set temperature sequence.

13. The method of claim 12, further comprising determining at least one quality attribute of the solution in the scaled volume after thawing.

14. The method of claim 13, wherein the solution comprises a pharmaceutical agent, a pharmaceutical product, a drug, a chemical compound, a nucleic acid, a toxin, a peptide, a protein, a fusion protein, an antibody, an antibody fragment, a Fab region of an antibody, an antibody-drug conjugate, a biopharmaceutical, a pharmaceutical protein product, or an antibody.

15. The method of claim 14, further comprising operating a temperature regulation system using the computational fluid dynamics model to generate the set temperature sequence for melting the scaled volume.

16. The method of claim 15, further comprising measuring the temperature of at least one point of interest in the scaled volume throughout the melting process.

17. The method of claim 16, wherein the isomeric volume is from about 0.75 L to about 15 L.

18. The method of claim 17, wherein the scaled volume is from about 20 mL to about 100 mL.

19. The method of claim 16, wherein the isoscale volume is in an isoscale container having a volume of about 1 L to about 20 L.

20. The method of claim 19, wherein the scaled volume is in a scaled container having a volume of about 30 mL to about 100 mL.

21. The method of claim 20, wherein the scale-up container is selected from the group consisting of 1 L polycarbonate bottles, 2 L polycarbonate bottles, 5 L polycarbonate bottles, 10 L polycarbonate bottles, 20 L polycarbonate bottles, 1 L bags, 2 L bags, 8.3 L bags, and 16.6 L bags.

22. The method of claim 21, wherein the scale-down container is selected from the group consisting of a 30 mL bag and a 100 mL bag.

23. The method of claim 1, wherein the computational fluid dynamics model takes environmental factors into account.

24. The method of claim 23, wherein the environmental factor is selected from the group consisting of air flow, proximity to other surfaces of different temperatures, relative humidity, pressure, and any combination thereof.

25. A method for freezing a solution, the method comprising: (a) Using computational fluid dynamics models to predict freezing curves for scale-scale solutions subjected to freezing operating conditions; (b) ensuring that freezing will occur within the necessary time period; and (c) freezing the isomeric volume of the solution using the freezing operating conditions.

26. A method for melting a solution, the method comprising: (a) using a computational fluid dynamics model to predict a melting curve of the isomeric solution subjected to a first melting operating condition; (b) ensuring that melting will occur within the necessary time period; as well as (c) melting the isomeric volume of the solution using the melting operating conditions.

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