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- tissue engineering, machine learning, modelling
· 10 min read · 9 figures, 7 interactive
Computational tissue engineering and why the field is still experimental
Computers already help design scaffolds and bioreactors, yet tissue engineering still depends on making things and testing them. Why simulation has not replaced the experiment here, and what would have to change.
In brief
- Computation is already good at narrowing the options, from bioreactor flow rates to which formulations to try first.
- It cannot yet guarantee an outcome, because cell behaviour has no agreed governing laws and the inputs vary from batch to batch.
- In my reading of the field, most models are tested on data like their training data; few are tested on new experiments in other labs.
- The field becomes less experimental through shared data, reporting standards and validation, not only through better algorithms.
Contents · 11 sections, 9 figures
In 2024 the Nobel Prize in Chemistry went in part to the people behind AlphaFold, a model that predicts the shape of a protein from its sequence. Weather forecasts have gained about a day of skill per decade: by 2015, a six-day forecast was as good as a five-day forecast had been ten years earlier (Bauer et al., 2015). Engineers test new wings in a computer before they build them.
In tissue engineering, we still make the scaffold, seed the cells and wait to see what happens. Computational tools are everywhere in the field, and I build some of them, but none of them lets us skip the experiment. This post is my attempt to explain why, and what would have to change.
The short answer is not computing power. The fields where simulation is trusted share a few things that tissue engineering does not yet have.
Fig. 1Schematic
Where simulation is already trusted, and why
Yes: in place for routine usePartly: for part of the problemNo: not yet
| Condition | Weather forecasting | Aerodynamics(attached flow) | Protein structure prediction | Tissue engineering |
|---|---|---|---|---|
| Agreed governing equationslaws a model can start from | YesFluid dynamics and thermodynamics of the air. | YesNavier–Stokes; separated flow is still hard to predict (Slotnick et al., 2014). | PartlyThe physics is known, but the best predictions are learned from data (Jumper et al., 2021). | PartlyFor flow, diffusion and mechanics; none for what cells decide. |
| Large, standardised datashared, in one format | YesAbout 10⁷ observations assimilated per day (Bauer et al., 2015). | PartlyRich wind-tunnel and flight data, but scattered and often not public. | Yes261,139 experimental structures in the PDB, in one format (RCSB PDB, October 2026). | NoSmall, assembled by hand from papers, reported inconsistently. |
| Routine testing against realityblind or daily | YesForecasts are checked against observations every day (Bauer et al., 2015). | YesChecked in wind tunnels and flight tests. | YesBlind tests on unpublished structures since 1994 (CASP). | NoNo blind community benchmark that I know of. |
| Inputs that can be measured and controlledknown before the run | PartlyThe starting state is measured, never completely; nothing can be controlled. | YesShape, speed and air properties are set and measured precisely. | YesThe input, an amino-acid sequence, is known exactly. | PartlyDefined materials help, but natural batches and donor cells vary: Matrigel batches at about 400 and 840 Pa (Aisenbrey and Murphy, 2020). |
Weather forecasting
- Agreed governing equations
- YesFluid dynamics and thermodynamics of the air.
- Large, standardised data
- YesAbout 10⁷ observations assimilated per day (Bauer et al., 2015).
- Routine testing against reality
- YesForecasts are checked against observations every day (Bauer et al., 2015).
- Inputs that can be measured and controlled
- PartlyThe starting state is measured, never completely; nothing can be controlled.
Aerodynamics (attached flow)
- Agreed governing equations
- YesNavier–Stokes; separated flow is still hard to predict (Slotnick et al., 2014).
- Large, standardised data
- PartlyRich wind-tunnel and flight data, but scattered and often not public.
- Routine testing against reality
- YesChecked in wind tunnels and flight tests.
- Inputs that can be measured and controlled
- YesShape, speed and air properties are set and measured precisely.
Protein structure prediction
- Agreed governing equations
- PartlyThe physics is known, but the best predictions are learned from data (Jumper et al., 2021).
- Large, standardised data
- Yes261,139 experimental structures in the PDB, in one format (RCSB PDB, October 2026).
- Routine testing against reality
- YesBlind tests on unpublished structures since 1994 (CASP).
- Inputs that can be measured and controlled
- YesThe input, an amino-acid sequence, is known exactly.
Tissue engineering
- Agreed governing equations
- PartlyFor flow, diffusion and mechanics; none for what cells decide.
- Large, standardised data
- NoSmall, assembled by hand from papers, reported inconsistently.
- Routine testing against reality
- NoNo blind community benchmark that I know of.
- Inputs that can be measured and controlled
- PartlyDefined materials help, but natural batches and donor cells vary: Matrigel batches at about 400 and 840 Pa (Aisenbrey and Murphy, 2020).
Tissue engineering is missing more than equations. My assessment, not a survey; sources for the facts behind each mark are linked.
Even those fields are less settled than they look from outside. A review of aerospace simulation commissioned by NASA found that reliable use was “confined to a small but important region of the operating design space”, because flows that separate from a surface are still hard to predict (Slotnick et al., 2014). A trusted simulation is always trusted for a particular use, and checked against reality for that use.
What the term covers
“Computational tissue engineering” is not one method. I find it useful to think of three layers.
The physics layer uses equations that are well established elsewhere: elasticity for how a scaffold deforms, the Navier–Stokes equations for how medium flows through it, diffusion for how oxygen and nutrients reach the cells. Finite element and computational fluid dynamics models live here.
The biology layer describes what cells do: whether they divide, migrate, die or turn into bone or cartilage. Models here, such as mechano-regulation rules and agent-based simulations of individual cells, are built from observed patterns rather than from first principles.
The data layer skips mechanisms and learns from examples: machine learning models trained on experiments, and optimisation methods that decide which experiment to run next.
These layers have to cover an enormous range. Physiology spans about nine orders of magnitude in space and fifteen in time, from molecules to organs and from microseconds to a lifetime, which is why it needs a hierarchy of models rather than one model of everything (Hunter, 2004).
Fig. 2SchematicInteractive
The toolbox, by scale
Choose a method to see what it predicts and what it needs.
- Physics layer
- Biology layer
- Data layer, outside the map
- Scales few models connect
Time, log scale
Length, log scale
For scale
Finite element models of scaffold mechanics
- Predicts
- How a scaffold deforms, and where stress and strain concentrate under load.
- Needs as input
- The geometry, from the design file or a micro-CT scan, and the material’s properties.
- Usually checked by
- Compression and tensile tests on printed samples.
- Hardest to validate
- The local strain that cells feel inside the printed, degrading scaffold.
- Molecular dynamics
Predicts: How polymer chains, peptides and proteins move, fold and bind, for example a peptide on a material surface.
Needs as input: Atomic structures and a force field.
Usually checked by: Known structures and binding measurements on small, purified systems.
Hardest to validate: Whether nanosecond behaviour carries over to the material a cell actually meets.
- Signalling and metabolic networks (ODE models)
Predicts: How a cell’s signalling or metabolism changes over time in response to growth factors, oxygen or load.
Needs as input: A reaction network and its rate constants, many of them fitted rather than measured.
Usually checked by: Time courses of protein or gene expression in culture.
Hardest to validate: Rate constants measured in other cell types; many parameter sets fit the same curves.
- Agent-based and cellular Potts models
Predicts: Where individual cells move, divide, differentiate and die inside a scaffold.
Needs as input: A rule for each cell behaviour, with parameters that are often tuned rather than measured.
Usually checked by: Cell counts and images of where the cells are, at a few time points.
Hardest to validate: Rules that reproduce the observations may still be the wrong rules.
- Finite element models of scaffold mechanics
Predicts: How a scaffold deforms, and where stress and strain concentrate under load.
Needs as input: The geometry, from the design file or a micro-CT scan, and the material’s properties.
Usually checked by: Compression and tensile tests on printed samples.
Hardest to validate: The local strain that cells feel inside the printed, degrading scaffold.
- Fluid dynamics and reaction–diffusion: flow, oxygen and nutrients
Predicts: Flow and shear stress through a scaffold or bioreactor, and how far oxygen and nutrients reach.
Needs as input: The geometry, the flow rate, diffusion coefficients and how fast the cells consume oxygen.
Usually checked by: Pressure drop, oxygen probes and where the cells survive.
Hardest to validate: Shear stress at the cell surface, which cannot be measured directly.
- Growth and remodelling models
Predicts: How new tissue forms while the scaffold degrades, and how the construct’s stiffness changes as they do.
Needs as input: Mechano-regulation rules, degradation rates and the starting geometry.
Usually checked by: Histology, micro-CT and mechanical tests at a few end points.
Hardest to validate: Different rules reproduce the same healing, so a good fit does not single out the right one.
- Machine learning on literature data
Predicts: An outcome, such as printability or cell viability, from a recipe of material, concentration and settings.
Needs as input: Many comparable examples, usually gathered by hand from papers.
Usually checked by: Held-out rows, ideally from other papers and other labs.
Hardest to validate: Materials and labs unlike those in the training data.
No single model spans the scales a tissue lives on. Approximate orders of magnitude; my map of the field, not a survey.
Show the numbers
| Method | Length | Time |
|---|---|---|
| 1. Molecular dynamicsPhysics layer | ≈1–20 nm | 1 ns–1 µs |
| 2. Signalling and metabolic networks (ODE models)Biology layer | ≈1–30 µm, one cell | minutes to days |
| 3. Agent-based and cellular Potts modelsBiology layer | ≈10 µm–1 mm | minutes to weeks |
| 4. Finite element models of scaffold mechanicsPhysics layer | ≈100 µm–5 cm | quasi-static, drawn at seconds |
| 5. Fluid dynamics and reaction–diffusion: flow, oxygen and nutrientsPhysics layer | ≈100 µm–5 cm | seconds to days |
| 6. Growth and remodelling modelsBiology layer | ≈1 mm–10 cm | days to months |
| 7. Machine learning on literature dataData layer | none | none |
Where computation already earns its place
It would be wrong to say that models do not help. They help most where the physics dominates and the question is narrow.
Perfusion bioreactors are a good example. The shear stress that flowing medium puts on cells inside a scaffold cannot be measured directly, but it can be computed from the scaffold’s geometry, and that calculation was being done on micro-CT images of real scaffolds twenty years ago (Porter et al., 2005). Combining such simulations with a rule for how bone cells respond to shear lets researchers choose a flow rate for a given scaffold without a series of trial-and-error cultures; in one study the best rates depended mainly on scaffold geometry and ranged from 0.5 to 5 mL per minute (Zhao et al., 2018).
Models also make search cheaper. A simplified model of tissue growth in a bioreactor ran about 100,000 times faster than the full three-dimensional one, fast enough to optimise feeding schedules on the computer (Mehrian et al., 2018). In bioprinting, Bayesian optimisation found good printing settings for gelatin-based inks in between 4 and 47 experiments per ink, from a search space of thousands of combinations (Ruberu et al., 2021).
What these successes have in common is that the computer narrows the options and the experiment still decides. That is valuable. It is not the same as prediction you can rely on without checking.
The physics depends on the scaffold you actually made
Even the physics layer is less solid than it looks, because the model describes the scaffold that was designed, not the one that came out of the printer.
Fig. 3Data
The scaffold you designed is not the one you made
How far apart, as a ratio (1× = perfect agreement, log scale)
Fluid flow in extruded polymer scaffoldsCampos Marin and Lacroix, 2015. Five samples of a commercial polycaprolactone scaffold, scanned by micro-CT.
Local flow speed and shear stressSimulation on the scans against simulation on the design file
up to 5×
Same place, sample against sampleSame simulation on scans of different samples: printed copies of one design differed from each other
up to 2×
Fluid flow in a printed scaffold unit cellDe Boodt et al., 2010. Patterned model of one unit cell of a printed bone scaffold; the authors put the gap down to the printed geometry and unsteady flow.
Average flow speedSimulation on the design against micro-PIV measurement: 19% apart
1.19×
Wall shear stressSimulation on the design against micro-PIV measurement: 27% apart
1.27×
Stiffness of laser-melted titanium scaffoldsKhalil et al., 2024. Six sheet-based lattice designs in pure titanium, made by selective laser melting and compression-tested.
Stiffness, design modelFinite element model of the design against compression tests: 11% apart on average
1.11×
Stiffness, model of the scanSimulation on micro-CT scans against compression tests: 54% too stiff; the authors suggest the scans missed small voids and cracks
1.54×
Even the physics is only as good as the geometry it is given. Different studies, measures and materials; each row compares a model of the scaffold with measurements or with a model of the real part, except the second, which compares printed copies of the same design. Values marked ‘up to’ are the largest local differences, not averages.
Source: Campos Marin and Lacroix, 2015 (abstract); De Boodt et al., 2010 (abstract); Khalil et al., 2024 (abstract and conclusions). Differences reported without a direction are shown as ratios above 1.
Show the numbers
| Study | Measure | Comparison | As reported | Ratio |
|---|---|---|---|---|
| Campos Marin and Lacroix, 2015 | Local flow speed and shear stress | Scan-based against design-based simulation | Up to five times higher in the scanned samples | up to 5× |
| Campos Marin and Lacroix, 2015 | Same place, sample against sample | Scan of one sample against scan of another | Up to two times higher from sample to sample | up to 2× |
| De Boodt et al., 2010 | Average flow speed | Design-based simulation against micro-PIV | 19% difference | 1.19× |
| De Boodt et al., 2010 | Wall shear stress | Design-based simulation against micro-PIV | 27% difference | 1.27× |
| Khalil et al., 2024 | Stiffness, design model | Design-based finite element model against compression tests | Average deviation of 11% | 1.11× |
| Khalil et al., 2024 | Stiffness, model of the scan | Scan-based simulation against compression tests | Overestimated by 54% | 1.54× |
Printed strands sag, fuse and vary in width; struts in laser-melted metal come out rough, with cracks and trapped voids (Khalil et al., 2024). In five samples of one commercial scaffold with a nominally regular design, simulations based on micro-CT scans of each sample gave local fluid velocities and shear stresses up to five times higher than the design file predicted, and the same location differed by up to two-fold from one sample to the next (Campos Marin and Lacroix, 2015). Hydrogels add swelling, slow creep and degradation on top of that, so their geometry keeps changing after printing.
Easy maths, hard numbers
Some of the most useful calculations in the field are simple. How far into a block of cells can oxygen reach before the cells in the middle run out? With a few textbook assumptions, the answer is one short formula, and every student who designs a thick construct should try it.
Fig. 4ModelInteractive
How deep does oxygen reach?
Change the cell density and how much oxygen each cell uses.
Diffusion coefficient: 2.7 × 10⁻⁹ m²/s
Oxygen at the open face: 0.18 mM, as in medium under air at 37 °C (fixed).
Depth = √(2 × diffusion coefficient × oxygen at the face ÷ uptake per millilitre)
Oxygen reaches about1.0 mm
Cells deeper than that get none: that is 51% of the 2 mm slab drawn below.
Depth against cell density
| Cells per millilitre | 1 amol per cell per second | 400 amol per cell per second |
|---|---|---|
| 1 × 10⁶ | 31 mm | 1.6 mm |
| 1 × 10⁷ | 9.9 mm | 490 µm |
| 1 × 10⁸ | 3.1 mm | 160 µm |
| 1 × 10⁹ | 1.0 mm | 49 µm |
At 10⁸ cells per millilitre, the same formula puts the limit anywhere from about 3 mm to 160 µm, depending on which published uptake per cell you use. Simplified textbook model: constant consumption, one dimension, no vessels, no cell death or migration.
Source: Oxygen in air-saturated medium at 37 °C (0.18 mM) and its diffusion coefficient in medium (2.7 × 10⁻⁹ m²/s): Place, Domann and Case, 2017. Uptake per cell: Wagner, Venkataraman and Buettner, 2011 (below 1 to above 350 amol per cell per second) and Place et al. (200–400 for liver cells). Dense gels, up to 40% slower diffusion: Colom et al., 2014. Capillary distance: Lovett et al., 2009.
Show the numbers
| Cells per millilitre | Oxygen each cell uses (amol per second) | |||
|---|---|---|---|---|
| 1 | 10 | 100 | 400 | |
| In culture medium (diffusion coefficient 2.7 × 10⁻⁹ m²/s) | ||||
| 1 × 10⁶ | 31 mm | 9.9 mm | 3.1 mm | 1.6 mm |
| 1 × 10⁷ | 9.9 mm | 3.1 mm | 1.0 mm | 490 µm |
| 1 × 10⁸ | 3.1 mm | 1.0 mm | 310 µm | 160 µm |
| 1 × 10⁹ | 1.0 mm | 310 µm | 99 µm | 49 µm |
| In a dense gel (diffusion coefficient 1.7 × 10⁻⁹ m²/s) | ||||
| 1 × 10⁶ | 25 mm | 7.9 mm | 2.5 mm | 1.2 mm |
| 1 × 10⁷ | 7.9 mm | 2.5 mm | 790 µm | 390 µm |
| 1 × 10⁸ | 2.5 mm | 790 µm | 250 µm | 120 µm |
| 1 × 10⁹ | 790 µm | 250 µm | 79 µm | 39 µm |
The difficulty is not the equation. It is the inputs. How much oxygen a cell consumes depends on the cell type, its state and its surroundings, and published values for cells in culture range from below 1 to more than 350 attomoles per cell per second (Wagner et al., 2011). Because the depth depends on the square root of the inputs, a tenfold uncertainty in one of them still moves the answer about threefold, which is the difference between a construct that survives and one with a dead core. The formula is not the weak point; we just do not know the numbers to put into it precisely enough.
Cells do not follow an equation we know
The physics layer at least has agreed equations. The biology layer does not. There are no accepted first-principles laws for when a stem cell becomes bone, cartilage or scar tissue, so models of those decisions are built from rules that fit observations.
That makes them hard to test. In bone, for example, the links between mechanical loading, cell proliferation, blood supply and nutrient transport are still poorly understood, and every extra rule added to a model makes it harder to prove wrong (Giorgi et al., 2016). When several published mechano-regulation rules were run in the same fracture-healing model, all of them reproduced normal healing (Isaksson et al., 2006). A model that fits the data is not yet a model that explains it.
Agent-based models, which simulate cells one by one, face the same problem from another direction. A recent model of muscle regeneration needed 52 parameters that could not be related to any known physiological measurement and had to be tuned against a few time courses of tissue-level data (Haase et al., 2024).
And the system does not stand still. A scaffold is designed to disappear.
Fig. 5SchematicInteractive
The scaffold you model is not the tissue you get
Switch between day 1, week 2 and week 6.
- strand (degrading)
- cells
- new matrix
- strand on day 1
Day 1: the strands are at full size with sharp edges. A few cells sit on their surfaces, and the pores are empty.
- strand (degrading)
- cells
- new matrix
- strand on day 1
Day 1
Day 1: the strands are at full size with sharp edges. A few cells sit on their surfaces, and the pores are empty.
Week 2
Week 2: the strands are thinner and softer as the material degrades. Cells multiply along their surfaces, and new matrix begins to line the pores.
Week 6
Week 6: little of the printed strands is left. Cells fill the pores, and new matrix takes up most of the space that was empty on day 1.
Schematic; shape only, no data. How fast this happens depends on the material: a soft, fast-degrading gel can change this much in weeks, a polycaprolactone scaffold over years. Either way, a model built on the day-1 geometry soon describes a structure that no longer exists.
The data are small, uneven and optimistic
If the rules are unknown, the obvious alternative is to learn them from data. This is where I work, and it is where the limits are clearest to me.
First, the datasets are small. AlphaFold was trained on structures from the Protein Data Bank, which now holds more than 260,000 experimentally determined structures, all described in a standard format (RCSB PDB, October 2026). A large tissue-engineering dataset has a few thousand rows assembled by hand from papers; the MLATE dataset has 2,646.
Second, the inputs are not what they seem. Natural materials vary: two batches of Matrigel measured in one study had a stiffness of about 400 Pa and a third had about 840 Pa (Aisenbrey and Murphy, 2020). Cells vary too: the age and sex of the donor change how mesenchymal stromal cells grow and behave (Siegel et al., 2013), and these cells change gradually with every passage rather than only at the end (Wagner et al., 2008). A row in a dataset that says “alginate, 2%, mesenchymal stem cells” hides all of this. Part of the variability is a choice, though: a carefully controlled synthesis of gelatin methacryloyl gave batches that were almost identical (Zhu et al., 2019).
Third, the record is optimistic. Failed formulations are rarely published. We have no direct measurement of this for tissue engineering, but other preclinical fields show its size: in animal studies of stroke, about one experiment in seven was never published, and the missing studies made treatments look nearly a third more effective than they were (Sena et al., 2010).
Fourth, reporting is not standardised. Bio-nano research has proposed a minimum reporting checklist (Faria et al., 2018). Bioprinting has a standard guide for bioinks, ASTM F3659-24, but it does not yet give quantitative criteria for judging printability (Martín Compaired et al., 2025).
All of this affects how models are tested. When the test data come from the same papers as the training data, a model can score well by recognising the lab rather than understanding the material.
Fig. 6Illustration: invented numbersInteractive
A model that recognises the study
Switch between a random split and a split by study.
- Training sample
- Test sample
Study A
5 training, 1 test6 training, 0 test
Study B
5 training, 1 test6 training, 0 test
Study C
5 training, 1 test6 training, 0 test
Study D
5 training, 1 test6 training, 0 test
Study E
5 training, 1 test0 training, 6 test
Study F
5 training, 1 test0 training, 6 test
Random split. About 1 sample in 6 is drawn for testing, from every study. Each test sample has five siblings from its own study in training.
Split by study. Studies E and F, 12 samples, are held out whole. No test sample has a sibling in training.
What a test sample shares with the training data
- Lab protocol
- SharedNot shared
- Material batch
- SharedNot shared
- Measurement method
- SharedNot shared
Part of the score comes from recognising the study, so it overestimates how the model will do in a new lab.
The score is usually lower, and closer to what to expect from a new lab, because only what the model learned about materials carries over.
- Training sample
- Test sample
Random split
Study A
5 training, 1 test
Study B
5 training, 1 test
Study C
5 training, 1 test
Study D
5 training, 1 test
Study E
5 training, 1 test
Study F
5 training, 1 test
About 1 sample in 6 is drawn for testing, from every study. Each test sample has five siblings from its own study in training.
Lab protocol, material batch and measurement method: shared with the training data. Part of the score comes from recognising the study, so it overestimates how the model will do in a new lab.
Split by study
Study A
6 training, 0 test
Study B
6 training, 0 test
Study C
6 training, 0 test
Study D
6 training, 0 test
Study E
0 training, 6 test
Study F
0 training, 6 test
Studies E and F, 12 samples, are held out whole. No test sample has a sibling in training.
Lab protocol, material batch and measurement method: not shared with the training data. The score is usually lower, and closer to what to expect from a new lab, because only what the model learned about materials carries over.
Invented example. Splitting by study is the stricter test: no test sample has a sibling from its own study in training.
Where the field’s attention is
I wanted to know how much of the field’s work is computational, so I counted papers in PubMed.
Fig. 7DataInteractive
Machine learning is a small, fast-growing share of the field
Switch views; on the chart, point, tap or use the arrow keys to read each year.
Tissue-engineering papers first published in 2025, by type
Machine learning 238 papers
68% reviews (161)32% other (77)
Modelling 202 papers
21% reviews (42)79% other (160)
All tissue engineering, for comparison 7,186 papers
32% reviews (2,288)68% other (4,898)
Machine learning passed modelling in 2025, but mostly in reviews. About two thirds of the 2025 machine-learning papers are indexed as reviews, against about a fifth of the modelling papers and a third of all tissue-engineering papers.
How these were counted
One PubMed search per year and topic, run through the NCBI E-utilities on 25 October 2026 with a script in the site’s repository. Each paper is counted once, in the year it was first published (online or in print): (query AND 2025[dp]) NOT 1800:2024[dp]. Shares divide by the tissue-engineering count for the same year; the comparison line divides by every PubMed record of that year.
- Tissue engineering
("tissue engineering"[mh] OR "tissue engineering"[tiab] OR "tissue engineered"[tiab] OR "tissue scaffolds"[mh] OR "bioprinting"[mh] OR bioprint*[tiab] OR biofabricat*[tiab])- Machine learning
- tissue engineering AND
("machine learning"[tiab] OR "deep learning"[tiab] OR "artificial intelligence"[tiab] OR "artificial neural network*"[tiab] OR "convolutional neural network*"[tiab] OR "deep neural network*"[tiab] OR "graph neural network*"[tiab] OR "recurrent neural network*"[tiab] OR "back propagation neural network*"[tiab] OR "random forest*"[tiab] OR "support vector machine*"[tiab] OR "machine learning"[mh] OR "neural networks, computer"[mh]) - Modelling
- tissue engineering AND
("finite element"[tiab] OR "finite element analysis"[mh] OR "computational fluid dynamics"[tiab] OR "agent-based"[tiab] OR "in silico"[tiab] OR "computational model*"[tiab] OR "mathematical model*"[tiab] OR "multiscale model*"[tiab]) - Reviews
- the same search AND
review[pt] - All of PubMed
- every record of the year; machine learning uses the terms above without the tissue-engineering ones
Caveats
- Keyword matching: [tiab] searches titles, abstracts and author keywords; [mh] searches MeSH headings. Papers that use machine learning without naming it there (for example only “Bayesian optimisation” or “Gaussian process”) are missed, and papers that mention artificial intelligence in passing, mostly reviews, are included.
- Bare “neural network*” is left out of the machine-learning terms because in tissue engineering it mostly matches biological neural networks; named computational architectures are searched instead.
- “in silico” also matches some bioinformatics and docking studies.
- Each record is counted once, in its first publication year. A plain <year>[dp] search on the PubMed website counts a record in both years when its electronic and print dates differ, so its yearly totals are higher.
- Recent years can still rise: PubMed keeps adding records, and MeSH headings for them, after the year ends.
- MeSH headings changed over time (Tissue Scaffolds from 2008, Bioprinting from 2013, Machine Learning from 2016); the free-text terms cover the years before each heading existed.
- PubMed under-covers engineering, computational and materials-science journals, so both the machine-learning and the modelling counts are probably lower than in Scopus or Web of Science.
- Before about 2018 the machine-learning counts are in single digits, so their shares are noisy.
Source: PubMed via NCBI E-utilities, retrieved 25 October 2026; keyword queries under “How these were counted”. Download the data (CSV)
Show the numbers
| Year | Tissue-engineering papers | All of PubMed | ||||
|---|---|---|---|---|---|---|
| All | Machine learning | Share | Modelling | Share | Machine learning share | |
| 2005 | 1,830 | 4 | 0.22% | 33 | 1.8% | 0.25% |
| 2006 | 2,086 | 1 | 0.05% | 37 | 1.8% | 0.25% |
| 2007 | 2,269 | 1 | 0.04% | 44 | 1.9% | 0.26% |
| 2008 | 2,587 | 1 | 0.04% | 49 | 1.9% | 0.28% |
| 2009 | 3,043 | 3 | 0.10% | 54 | 1.8% | 0.29% |
| 2010 | 3,683 | 1 | 0.03% | 71 | 1.9% | 0.27% |
| 2011 | 3,736 | 0 | 0% | 86 | 2.3% | 0.28% |
| 2012 | 4,097 | 5 | 0.12% | 89 | 2.2% | 0.28% |
| 2013 | 4,581 | 1 | 0.02% | 78 | 1.7% | 0.33% |
| 2014 | 4,730 | 3 | 0.06% | 85 | 1.8% | 0.35% |
| 2015 | 4,831 | 5 | 0.10% | 81 | 1.7% | 0.43% |
| 2016 | 5,063 | 2 | 0.04% | 85 | 1.7% | 0.49% |
| 2017 | 5,346 | 8 | 0.15% | 100 | 1.9% | 0.64% |
| 2018 | 5,591 | 10 | 0.18% | 109 | 1.9% | 0.98% |
| 2019 | 5,820 | 17 | 0.29% | 126 | 2.2% | 1.4% |
| 2020 | 6,230 | 29 | 0.47% | 120 | 1.9% | 1.8% |
| 2021 | 6,604 | 41 | 0.62% | 148 | 2.2% | 2.5% |
| 2022 | 6,094 | 52 | 0.85% | 142 | 2.3% | 3.2% |
| 2023 | 6,026 | 75 | 1.2% | 153 | 2.5% | 3.7% |
| 2024 | 6,531 | 112 | 1.7% | 154 | 2.4% | 4.4% |
| 2025 | 7,186 | 238 | 3.3% | 202 | 2.8% | 5.6% |
Two things stand out. Computational modelling has stayed a small share of tissue-engineering papers for twenty years, between about 1.7% and 2.8%, creeping up since 2016. Machine learning was almost absent until about 2018 and has grown quickly since, passing modelling for the first time in 2025, but much of that growth is in reviews rather than new models. The field is talking about machine learning faster than it is testing it.
What “credible” would mean
Other fields have worked out how to decide when a model can be trusted, and their answers are instructive. The ASME V&V 40 standard (2018), which the US Food and Drug Administration recognised in 2019, does not ask whether a model is good in general. It asks how much a decision relies on the model and how bad a wrong decision would be, and it scales the evidence required to match (ASME). The FDA’s guidance on computational modelling in medical device submissions, final since November 2023, builds on the same idea, but it covers physics-based and mechanistic models, including mechanistic models of physiology, and explicitly leaves out standalone machine learning (FDA, 2023).
There are precedents for simulation standing in for experiments. A simulator of type 1 diabetes was accepted by the FDA as a substitute for animal trials in preclinical testing of insulin-control algorithms (Kovatchev et al., 2009), and an entirely computer-simulated imaging trial reached the same conclusion as a clinical trial for detecting breast masses (Badano et al., 2018). Both rest on well-characterised physics or physiology and large amounts of data. Since December 2022, US drug law also counts computer modelling among the “nonclinical tests” that can support an application, alongside cell-based assays and animal tests (Public Law 117-328, Sec. 3209). I have not found a documented case of a regulator accepting in silico evidence in place of experiments for a tissue-engineered product.
So when I ask how credible a tissue-engineering model is, I think of a ladder.
Fig. 8SchematicInteractive
How a model earns trust
Open a rung to see what it takes.
A regulator accepts the model’s results in place of some experiments, as the FDA did for a type 1 diabetes simulator in preclinical testing of control algorithms (Kovatchev et al., 2009). ASME V&V 40 and the FDA's 2023 guidance set out how such credibility is judged; for a tissue-engineered product, none is documented that I could find.
People act on the model’s output, and someone keeps count of how often it was right. Weather forecasts are checked against observations every day, which is how we know they gain about a day of skill per decade (Bauer et al., 2015).
The predictions hold when other labs, materials and equipment produce the data, ideally in a blind test. Protein structure prediction has had such a test since 1994 (CASP); tissue engineering has none that I know of.
The model predicts an experiment before it is run, and the same lab then runs it. Bayesian optimisation works at this rung: in bioprinting it found good printing settings in 4 to 47 experiments per ink (Ruberu et al., 2021).
The model predicts results it was not trained on, but from the same papers or labs. In my reading, most machine-learning studies stop here, and a model can pass by recognising the lab rather than the material.
The model reproduces the data it was built from. Almost every published model gets this far, and it proves little: when several published mechano-regulation rules were run in one fracture-healing model, all of them reproduced normal healing (Isaksson et al., 2006).
Where I think most tissue-engineering models are today: rungs 1 and 2.
- Rung 6: Accepted as evidence for a regulatory decision. Checked by a regulator
A regulator accepts the model’s results in place of some experiments, as the FDA did for a type 1 diabetes simulator in preclinical testing of control algorithms (Kovatchev et al., 2009). ASME V&V 40 and the FDA's 2023 guidance set out how such credibility is judged; for a tissue-engineered product, none is documented that I could find.
- Rung 5: Changes decisions, and its record is tracked. Checked in use
People act on the model’s output, and someone keeps count of how often it was right. Weather forecasts are checked against observations every day, which is how we know they gain about a day of skill per decade (Bauer et al., 2015).
- Rung 4: Predicts new experiments across labs and materials. Checked across labs
The predictions hold when other labs, materials and equipment produce the data, ideally in a blind test. Protein structure prediction has had such a test since 1994 (CASP); tissue engineering has none that I know of.
- Rung 3: Predicts new experiments in the same lab. Checked in the lab
The model predicts an experiment before it is run, and the same lab then runs it. Bayesian optimisation works at this rung: in bioprinting it found good printing settings in 4 to 47 experiments per ink (Ruberu et al., 2021).
- Rung 2: Predicts held-out data from the same sources. Checked on the computer
The model predicts results it was not trained on, but from the same papers or labs. In my reading, most machine-learning studies stop here, and a model can pass by recognising the lab rather than the material.
- Rung 1: Fits past data. Checked on the computer
The model reproduces the data it was built from. Almost every published model gets this far, and it proves little: when several published mechano-regulation rules were run in one fracture-healing model, all of them reproduced normal healing (Isaksson et al., 2006).
Where I think most tissue-engineering models are today: rungs 1 and 2.
Most of the climb happens outside the computer. My framing, drawing on ASME V&V 40 and the FDA’s 2023 guidance.
Source: ASME V&V 40-2018 and FDA guidance of 17 November 2023 for the frameworks; the example in each rung links to its own source.
What would make it less experimental
None of this means the field should model less. It means computation and experiment have to be joined more tightly, so that every experiment also improves the model.
That is already happening. A robotic system that used Bayesian optimisation to improve how stem cells are turned into retinal pigment epithelium tested 143 conditions, out of about 200 million possible combinations, in 111 days, and improved the pigmentation score by 88% over the starting protocol (Kanda et al., 2022). Digital twins of bioreactors, mechanistic models that run alongside a culture and are updated from its measurements, are an active idea, although still mostly at the stage of concepts and prototypes (Möller and Pörtner, 2021).
Fig. 9SchematicInteractive
Design, build, test, learn
Switch between today and a better-connected loop.
Design
Computer: proposes which formulations to try next.
Lab: knows what can really be made, and with which cells.
Then Build.
Build
Computer: drives printers and pipetting robots.
Lab: prepares the cells and materials.
Mostly by hand Automated labs
Then Test.
Test
Computer: reads the images and measurements.
Lab: days to weeks of culture that cannot be skipped.
Mostly by hand Automated labs
Then Learn.
Learn
Computer: updates the model with every result.
Lab: records each result, failures included.
Tested on data like its training data Shared benchmarks
Back to Design, through a weak link: unpublished failures, missing metadataBack to Design: shared data with failures, minimum reporting standards
Today most experiments are run and recorded by hand, and the next design starts from what was published.Automated labs already exist, such as the robotic culture system described above (Kanda et al., 2022).
Today
Design
Then Build.
Build
Mostly by hand
Then Test.
Test
Mostly by hand
Then Learn.
Learn
Tested on data like its training data
Back to Design, through a weak link: unpublished failures, missing metadata
Today most experiments are run and recorded by hand, and the next design starts from what was published.
With shared data and standards
Design
Then Build.
Build
Automated labs
Then Test.
Test
Automated labs
Then Learn.
Learn
Shared benchmarks
Back to Design: shared data with failures, minimum reporting standards
Automated labs already exist, such as the robotic culture system described above (Kanda et al., 2022).
- Design
- Computer: proposes which formulations to try next. Lab: knows what can really be made, and with which cells.
- Build
- Computer: drives printers and pipetting robots. Lab: prepares the cells and materials.
- Test
- Computer: reads the images and measurements. Lab: days to weeks of culture that cannot be skipped.
- Learn
- Computer: updates the model with every result. Lab: records each result, failures included.
The loop only learns if what happens in the lab comes back to the model. Today much of it is lost: failed experiments are rarely published, and published ones often leave out details a model needs.
Source: Example of an automated lab: Kanda et al., 2022. The two states are my sketch.
What would move the field further, in my view:
- defined materials and scaffolds characterised as built, not only as designed;
- a minimum reporting standard for biofabrication studies, in the spirit of the bio-nano checklist;
- shared datasets that follow the FAIR principles (Wilkinson et al., 2016) and include formulations that failed;
- blind community benchmarks, like the CASP experiment that has tested protein structure prediction on unpublished structures since 1994 (CASP);
- models that report their uncertainty, and credibility frameworks that cover data-driven models as well as physics-based ones.
Tissue engineering is still experimental because living tissue is more variable, less described and less measured than air over a wing. Computation will not remove the experiment. It will, more and more, choose which experiment to run.
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