SimBiology.Scenarios
Simulation scenarios
Description
SimBiology.Scenarios
is an object that lets you generate
different simulation scenarios based on different sample values of model quantities. You can
combine these quantities with different doses or variants and simulate various scenarios to
explore model behaviors under different experimental conditions and dosing
regimens.
Creation
Syntax
Description
returns a sObj
= SimBiology.Scenarios(name
,content
)Scenarios
object sObj
with one entry.
name
is the name of a model quantity or the name of a group of
variants or doses for scenario generation. content
contains the
corresponding numeric values for the model quantity or a vector of variant objects or
vector of dose objects.
specifies to generate the sample values for one or more model quantities
sObj
= SimBiology.Scenarios(quantityNames
,probDist
,Name,Value
)quantityNames
from the joint probability distribution
probDist
. Specify additional options for the probability
distributions and sampling method using one or more name-value pair arguments. To specify
the probability distributions, you must have Statistics and Machine Learning Toolbox™.
Input Arguments
name
— Entry name
character vector | string
Entry name, specified as a character vector or string.
You can set the entry name to the name of a model quantity (species, parameter, or compartment). Alternatively, you can define a name for a group of doses or variants to be included in the sample (scenarios) generation.
Example: "k1"
Data Types: char
| string
content
— Model quantity values or vector of doses or variants
numeric vector | vector of RepeatDose
or
ScheduleDose
objects | vector of variant objects
Model quantity values, or a vector of doses or variants, specified as
a numeric vector, vector of RepeatDose
or
ScheduleDose
objects, or vector of
variant
objects.
If you specify a quantity name for the name
input
argument, set content
to a numeric
vector.
If you specify a name for a group of doses or variants, set
content
to a vector of dose
objects or vector of variant objects.
Example: [0.5,1,1.5]
quantityNames
— Names of model quantities
character vector | string | string vector | cell array of character vectors
Names of model quantities for the sample (scenario) generation, specified as a character vector, string, string vector, or cell array of character vectors.
Example: ["k12","k21"]
Data Types: char
| string
| cell
probDist
— Probability distributions
vector of probability distribution objects | character vector | string | string vector | cell array of character vectors
Probability distributions to generate sample values for model quantities, specified as a vector of probability distribution objects, character vector, string, string vector, or cell array of character vectors containing the names of supported probability distributions. To specify the probability distributions, you must have Statistics and Machine Learning Toolbox.
Use the makedist
(Statistics and Machine Learning Toolbox) function to create distribution
objects. For a list of supported distributions, see distname (Statistics and Machine Learning Toolbox).
Example: [pd1,pd2]
Specify optional
comma-separated pairs of Name,Value
arguments.
Name
is the argument name and Value
is the
corresponding value. Name
must appear inside quotes. You can specify
several name and value pair arguments in any order as
Name1,Value1,...,NameN,ValueN
.
Example: 'Number',10
specifies to generate 10
samples.
Number
— Number of samples
[]
(default) | positive scalar
Number of samples to draw from probability distributions, specified as the comma-separated
pair consisting of 'Number'
and a positive scalar. The default value
[]
means that the function infers the number of samples from
other entries. If the number cannot be inferred, the number is set to
2
.
Example: 'Number',5
RankCorrelation
— Rank correlation matrix
[]
(default) | numeric matrix
Rank correlation matrix for the joint probability distribution, specified as the
comma-separated pair consisting of 'RankCorrelation'
and a numeric
matrix. The default behavior is that when both 'RankCorrelation'
and
'Covariance'
are set to []
,
SimBiology.Scenarios
draws uncorrelated samples from the joint
probability distribution.
You cannot specify 'RankCorrelation'
if 'Covariance'
is
set. The number of columns in the matrix must
match the number of specified distributions. The
matrix must be symmetric with diagonal values of
1. All of its eigenvalues must also be
positive.
Example: 'RankCorrelation',[1 0.3;0.3 1]
Mean
— Mean values
numeric vector
Mean values of quantities, specified as the comma-separated pair consisting of
'Mean'
and a numeric vector.
You can specify mean values for normal distributions only. The number of mean values must equal the number of specified probability distributions.
Example: 'Mean',[0.5,1.5]
Covariance
— Covariance matrix
[]
(default) | numeric matrix
Covariance matrix for the joint probability distribution, specified as the comma-separated
pair consisting of 'Covariance'
and a numeric
matrix. The default behavior is that if both
'RankCorrelation'
and
'Covariance'
are set to
[]
,
SimBiology.Scenarios
draws
uncorrelated samples from the joint probability distribution.
You cannot specify 'Covariance'
if you
specify 'RankCorrelation'
.
You can specify the covariance matrix for normal distributions only. The number of columns in the matrix must match the number of specified distributions. All of its eigenvalues must also be nonnegative.
Example: 'Covariance',[0.25 0.15;0.15 0.25]
SamplingMethod
— Sampling method
'random'
(default) | 'lhs'
| 'copula'
| 'sobol'
| 'halton'
Sampling method, specified as the comma-separated pair consisting of
'SamplingMethod'
and a character vector or string. Depending on
whether probability distributions with 'RankCorrelation'
or normal
distributions with 'Covariance'
are specified, the sampling
techniques differ.
If an entry contains a (joint) normal distribution with Covariance
specified, the sampling methods are:
'random'
– Draw random samples from the specified normal distribution usingmvnrnd
(Statistics and Machine Learning Toolbox).'lhs'
– Draw Latin hypercube samples from the specified normal distributions usinglhsnorm
(Statistics and Machine Learning Toolbox). For details, see Generating Quasi-Random Numbers (Statistics and Machine Learning Toolbox).
If an entry contains a (joint) distribution with no Covariance
specified,
the sampling methods are:
'random'
– Draw random samples from the specified probability distributions usingrandom
(Statistics and Machine Learning Toolbox).'lhs'
– Draw Latin hypercube samples from the specified probability distributions using an algorithm similar tolhsdesign
(Statistics and Machine Learning Toolbox). This approach is a more systematic space-filling approach than random sampling. For details, see Generating Quasi-Random Numbers (Statistics and Machine Learning Toolbox).'copula'
– Draw random samples using a copula (Statistics and Machine Learning Toolbox). Use this option to impose correlations between samples using copulas.'sobol'
– Use the sobol sequence (sobolset
(Statistics and Machine Learning Toolbox)) which is transformed using the inverse cumulative distribution function (icdf
(Statistics and Machine Learning Toolbox)) of the specified probability distributions. Use this method for highly systematic space-filling. For details, see Generating Quasi-Random Numbers (Statistics and Machine Learning Toolbox).'halton'
– Use the halton sequence (haltonset
(Statistics and Machine Learning Toolbox)) which is transformed using the inverse cumulative distribution function (icdf
(Statistics and Machine Learning Toolbox)) of the specified probability distributions. For details, see Generating Quasi-Random Numbers (Statistics and Machine Learning Toolbox).
If no Covariance
is specified,
SimBiology.Scenarios
essentially performs two steps. The first
step is to generate samples using one of the above sampling methods. For
lhs
, sobol
, and halton
methods, the generated uniform samples are transformed to samples from the specified
distribution using the inverse cumulative distribution function icdf
(Statistics and Machine Learning Toolbox). Then, as the second step, the samples are correlated using the
Iman-Conover algorithm if RankCorrelation
is specified. For
random
, the samples are drawn directly from the specified
distributions and the samples are then correlated using the Iman-Conover
algorithm.
Example: 'SamplingMethod','lhs'
SamplingOptions
— Options for sampling method
struct
Options for the sampling method, specified as a scalar struct. The options differ depending on
the sampling method: sobol
, halton
, or
lhs
.
For sobol
and halton
, specify each field name and value
of the structure according to each name-value argument of the sobolset
(Statistics and Machine Learning Toolbox) or haltonset
(Statistics and Machine Learning Toolbox) function. SimBiology uses the
default value of 1
for the Skip
argument for both
methods. For all other name-value arguments, the software uses the same default values of
sobolset
or haltonset
. For instance, set up a
structure for the Leap
and Skip
options with
nondefault values as
follows.
s1.Leap = 50; s1.Skip = 0;
For lhs
, there are three samplers that support different sampling options.
If you specify a covariance matrix, SimBiology uses
lhsnorm
(Statistics and Machine Learning Toolbox) for sampling.SamplingOptions
argument is not allowed.Otherwise, use the field name
UseLhsdesign
to select a sampler.If the value is
true
, SimBiology useslhsdesign
(Statistics and Machine Learning Toolbox). You can use the name-value arguments oflhsdesign
to specify the field names and values.If the value is
false
(default), SimBiology uses a nonconfigurable Latin hypercube sampler that is different fromlhsdesign
. This sampler does not require Statistics and Machine Learning Toolbox.SamplingOptions
cannot contain any other options, exceptUseLhsdesign
.
For instance, set up a structure to use lhsdesign
with the Criterion
and Iterations
options.
s2.UseLhsdesign = true;
s2.Criterion = "correlation";
s2.Iterations = 10;
You cannot specify sampling options for the random
and
copula
methods.
Data Types: struct
Properties
Expression
— Combination expression
character vector
This property is read-only.
Combination expression summarizing the combination of entries in the object,
specified as a character vector. The plus +
sign indicates the
elementwise combination, and the cross x
sign
indicates the cartesian combination. For details, see Combine Simulation Scenarios in SimBiology.
Example:
'(k1 + k2 + k3) x doses'
Data Types: char
NumberOfEntries
— Number of entries
positive integer
Number of entries in the scenarios object, specified as a positive integer.
Example:
4
Data Types: double
RandomSeed
— Seed or state for random number generation
[]
(default) | nonnegative integer smaller than
232
| structure returned by rng
Seed for random number generation to obtain reproducible scenarios, specified as a
nonnegative integer smaller than 232
or
structure returned by rng
that defines the random state. The
default value []
means that the generated scenarios will be different
every time the generate
function is called unless you set the
random seed before calling the function or use reproducible sequences such as Sobol or
Halton.
Example:
10
Data Types: double
| struct
Object Functions
add | Add quantity values, doses, or variants to SimBiology.Scenarios
object |
getEntry | Get entry contents from SimBiology.Scenarios object |
updateEntry | Update entry contents from SimBiology.Scenarios
object |
rename | Rename entry from SimBiology.Scenarios object |
remove | Remove entries from SimBiology.Scenarios object |
verify | Verify SimBiology.Scenarios object |
generate | Generate scenarios from SimBiology.Scenarios object and return
table |
getNumberScenarios | Return number of scenarios from SimBiology.Scenarios
object |
Examples
Generate Different Simulation Scenarios for Glucose-Insulin Response
Load the model of glucose-insulin response. For details about the model, see the Background section in Simulate the Glucose-Insulin Response.
sbioloadproject('insulindemo','m1');
The model contains different parameter values and initial conditions that represents different insulin impairments (such as Type 2 diabetes, low insulin sensitivity, and so on) stored in five variants.
variants = getvariant(m1)
variants = SimBiology Variant Array Index: Name: Active: 1 Type 2 diabetic false 2 Low insulin se... false 3 High beta cell... false 4 Low beta cell ... false 5 High insulin s... false
Suppress an informational warning that is issued during simulations.
warnSettings = warning('off','SimBiology:DimAnalysisNotDone_MatlabFcn_Dimensionless');
Select a dose that represents a single meal of 78 grams of glucose.
singleMeal = sbioselect(m1,'Name','Single Meal');
Create a Scenarios
object to represent different initial conditions combined with the dose. That is, create a scenario
object where each variant is paired (or combined) with the dose, for a total of five simulation scenarios.
sObj = SimBiology.Scenarios; add(sObj,'cartesian','variants',variants); add(sObj,'cartesian','dose',singleMeal)
ans = Scenarios (5 scenarios) Name Content Number ________ ___________________ ______ Entry 1 variants SimBiology variants 5 x Entry 2 dose SimBiology dose 1 See also Expression property.
sObj
contains two entries. Use the generate
function to combine the entries and generate five scenarios. The function returns a scenarios table, where each row represents a scenario and each column represents an entry of the Scenarios
object.
scenariosTbl = generate(sObj)
scenariosTbl=5×2 table
variants dose
______________________ _________________________
1x1 SimBiology.Variant 1x1 SimBiology.RepeatDose
1x1 SimBiology.Variant 1x1 SimBiology.RepeatDose
1x1 SimBiology.Variant 1x1 SimBiology.RepeatDose
1x1 SimBiology.Variant 1x1 SimBiology.RepeatDose
1x1 SimBiology.Variant 1x1 SimBiology.RepeatDose
Change the entry name of the first entry.
rename(sObj,1,'Insulin Impairements')
ans = Scenarios (5 scenarios) Name Content Number ____________________ ___________________ ______ Entry 1 Insulin Impairements SimBiology variants 5 x Entry 2 dose SimBiology dose 1 See also Expression property.
Create a SimFunction
object to simulate the generated scenarios. Use the Scenarios
object as the input and specify the plasma glucose and insulin concentrations as responses (outputs of the function to be plotted). Specify []
for the dose input argument since the Scenarios
object already has the dosing information.
f = createSimFunction(m1,sObj,{'[Plasma Glu Conc]','[Plasma Ins Conc]'},[])
f = SimFunction Parameters: Name Value Type Units ___________________________ ______ _____________ ___________________________________________ {'[Plasma Volume (Glu)]' } 1.88 {'parameter'} {'deciliter' } {'k1' } 0.065 {'parameter'} {'1/minute' } {'k2' } 0.079 {'parameter'} {'1/minute' } {'[Plasma Volume (Ins)]' } 0.05 {'parameter'} {'liter' } {'m1' } 0.19 {'parameter'} {'1/minute' } {'m2' } 0.484 {'parameter'} {'1/minute' } {'m4' } 0.1936 {'parameter'} {'1/minute' } {'m5' } 0.0304 {'parameter'} {'minute/picomole' } {'m6' } 0.6469 {'parameter'} {'dimensionless' } {'[Hepatic Extraction]' } 0.6 {'parameter'} {'dimensionless' } {'kmax' } 0.0558 {'parameter'} {'1/minute' } {'kmin' } 0.008 {'parameter'} {'1/minute' } {'kabs' } 0.0568 {'parameter'} {'1/minute' } {'kgri' } 0 {'parameter'} {'1/minute' } {'f' } 0.9 {'parameter'} {'dimensionless' } {'a' } 0 {'parameter'} {'1/milligram' } {'b' } 0.82 {'parameter'} {'dimensionless' } {'c' } 0 {'parameter'} {'1/milligram' } {'d' } 0.01 {'parameter'} {'dimensionless' } {'kp1' } 2.7 {'parameter'} {'milligram/minute' } {'kp2' } 0.0021 {'parameter'} {'1/minute' } {'kp3' } 0.009 {'parameter'} {'(milligram/minute)/(picomole/liter)' } {'kp4' } 0.0618 {'parameter'} {'(milligram/minute)/picomole' } {'ki' } 0.0079 {'parameter'} {'1/minute' } {'[Ins Ind Glu Util]' } 1 {'parameter'} {'milligram/minute' } {'Vm0' } 2.5129 {'parameter'} {'milligram/minute' } {'Vmx' } 0.047 {'parameter'} {'(milligram/minute)/(picomole/liter)' } {'Km' } 225.59 {'parameter'} {'milligram' } {'p2U' } 0.0331 {'parameter'} {'1/minute' } {'K' } 2.28 {'parameter'} {'picomole/(milligram/deciliter)' } {'alpha' } 0.05 {'parameter'} {'1/minute' } {'beta' } 0.11 {'parameter'} {'(picomole/minute)/(milligram/deciliter)'} {'gamma' } 0.5 {'parameter'} {'1/minute' } {'ke1' } 0.0005 {'parameter'} {'1/minute' } {'ke2' } 339 {'parameter'} {'milligram' } {'[Basal Plasma Glu Conc]'} 91.76 {'parameter'} {'milligram/deciliter' } {'[Basal Plasma Ins Conc]'} 25.49 {'parameter'} {'picomole/liter' } Observables: Name Type Units _____________________ ___________ _______________________ {'[Plasma Glu Conc]'} {'species'} {'milligram/deciliter'} {'[Plasma Ins Conc]'} {'species'} {'picomole/liter' } Dosed: TargetName TargetDimension __________ _____________________ {'Dose'} {'Mass (e.g., gram)'} TimeUnits: hour
Simulate the model for 24 hours and plot the simulation data. The data contains five runs, where each run represents a scenario in the Scenarios object.
sd = f(sObj,24); sbioplot(sd)
ans = Axes (SbioPlot) with properties: XLim: [0 30] YLim: [0 450] XScale: 'linear' YScale: 'linear' GridLineStyle: '-' Position: [0.0956 0.1100 0.2509 0.8150] Units: 'normalized' Use GET to show all properties
If you have Statistics and Machine Learning Toolbox™, you can also draw sample values for model quantities from various probability distributions. For instance, suppose that the parameters Vmx
and kp3
, which are known for the low and high insulin sensitivity, follow the lognormal distribution. You can generate sample values for these parameters from such a distribution, and perform a scan to explore model behavior.
Define the lognormal probability distribution object for Vmx
.
pd_Vmx = makedist('lognormal')
pd_Vmx = LognormalDistribution Lognormal distribution mu = 0 sigma = 1
By definition, the parameter mu
is the mean of logarithmic values. To vary the parameter value around the base (model) value of the parameter, set mu
to log(
model_value
)
. Set the standard deviation (sigma) to 0.2. For a small sigma value, the mean of a lognormal distribution is approximately equal to log(
model_value
)
. For details, see Lognormal Distribution (Statistics and Machine Learning Toolbox).
Vmx = sbioselect(m1,'Name','Vmx'); pd_Vmx.mu = log(Vmx.Value); pd_Vmx.sigma = 0.2
pd_Vmx = LognormalDistribution Lognormal distribution mu = -3.05761 sigma = 0.2
Similarly define the probability distribution for kp3.
pd_kp3 = makedist('lognormal'); kp3 = sbioselect(m1,'Name','kp3'); pd_kp3.mu = log(kp3.Value); pd_kp3.sigma = 0.2
pd_kp3 = LognormalDistribution Lognormal distribution mu = -4.71053 sigma = 0.2
Now define a joint probability distribution to draw sample values for Vmx and kp3, with a rank correlation to specify some correlation between these two parameters. Note that this correlation assumption is for the illustration purposes of this example only and may not be biologically relevant.
First remove the variants entry (entry 1) from sObj
.
remove(sObj,1)
ans = Scenarios (1 scenarios) Name Content Number ____ _______________ ______ Entry 1 dose SimBiology dose 1 See also Expression property.
Add an entry that defines the joint probability distribution with a rank correlation matrix.
add(sObj,'cartesian',["Vmx","kp3"],[pd_Vmx, pd_kp3],'RankCorrelation',[1,0.5;0.5,1])
ans = Scenarios (2 scenarios) Name Content Number ____ ______________________ ___________ Entry 1 dose SimBiology dose 1 x (Entry 2.1 Vmx Lognormal distribution 2 (default) + Entry 2.2) kp3 Lognormal distribution 2 (default) See also Expression property.
By default, the number of samples to draw from the joint distribution is set to 2. Increase the number of samples.
updateEntry(sObj,2,'Number',50)
ans = Scenarios (50 scenarios) Name Content Number ____ ______________________ ______ Entry 1 dose SimBiology dose 1 x (Entry 2.1 Vmx Lognormal distribution 50 + Entry 2.2) kp3 Lognormal distribution 50 See also Expression property.
Verify that the Scenarios
object can be simulated with the model. The verify
function throws an error if any entry does not resolve uniquely to an object in the model or the entry contents have inconsistent lengths (sample sizes). The function throws a warning if multiple entries resolve to the same object in the model.
verify(sObj,m1)
Generate the simulation scenarios. Plot the sample values using plotmatrix
. You can see the value of Vmx
is varied around its model value 0.047 and that of kp3
around 0.009.
sTbl = generate(sObj); [s,ax,bigax,h,hax] = plotmatrix([sTbl.Vmx,sTbl.kp3]); ax(1,1).YLabel.String = "Vmx"; ax(2,1).YLabel.String = "kp3"; ax(2,1).XLabel.String = "Vmx"; ax(2,2).XLabel.String = "kp3";
Simulate the scenarios using the same SimFunction you created previously. You do not need to create a new SimFunction object even though the Scenarios object has been updated.
sd2 = f(sObj,24); sbioplot(sd2);
By default, SimBiology uses the random sampling method. You can change it to the Latin hypercube sampling (or sobol or halton) for a more systematic space-filling approach.
entry2struct = getEntry(sObj,2)
entry2struct = struct with fields:
Name: {'Vmx' 'kp3'}
Content: [2x1 prob.LognormalDistribution]
Number: 50
RankCorrelation: [2x2 double]
Covariance: []
SamplingMethod: 'random'
SamplingOptions: [0x0 struct]
entry2struct.SamplingMethod = 'lhs'
entry2struct = struct with fields:
Name: {'Vmx' 'kp3'}
Content: [2x1 prob.LognormalDistribution]
Number: 50
RankCorrelation: [2x2 double]
Covariance: []
SamplingMethod: 'lhs'
SamplingOptions: [0x0 struct]
You can now use the updated structure to modify entry 2.
updateEntry(sObj,2,entry2struct)
ans = Scenarios (50 scenarios) Name Content Number ____ ______________________ ______ Entry 1 dose SimBiology dose 1 x (Entry 2.1 Vmx Lognormal distribution 50 + Entry 2.2) kp3 Lognormal distribution 50 See also Expression property.
Visualize the sample values.
sTbl2 = generate(sObj); [s,ax,bigax,h,hax] = plotmatrix([sTbl2.Vmx,sTbl2.kp3]); ax(1,1).YLabel.String = "Vmx"; ax(2,1).YLabel.String = "kp3"; ax(2,1).XLabel.String = "Vmx"; ax(2,2).XLabel.String = "kp3";
Simulate the scenarios.
sd3 = f(sObj,24); sbioplot(sd3);
Restore warning settings.
warning(warnSettings);
More About
SimBiology.Scenarios
Terminology
This section annotates the command line display of the
SimBiology.Scenarios
object and explains the terms shown in the output.
Specifically, it explains these terminologies: Scenarios
,
Entry
, Subentry
, Name
,
Content
, Number
, Expression
,
inconsistent
and Diagnosis
.
A consistent
Scenarios
object has entries that have the correct number of samples so
that entries can be combined without error. An example of a consistent
Scenarios
object is shown next.
An inconsistent Scenarios object has one or more entries with incorrect number of samples. You need to correct these entries before you can use the object for simulation. An example of an inconsistent object is shown next.
The Diagnosis
column suggests which entries to fix to have the
correct number of samples. Use updateEntry
,
rename
, and
remove
to edit
the entries.
References
[1] Iman, R., and W.J. Conover. 1982. A distribution-free approach to inducing rank correlation among input variables. Communications in Statistics - Simulation and Computation. 11(3):311–334.
Version History
Introduced in R2019b
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