Assessing Mould Growth Using the VTT Mould Index Model with Excel-Based Tool

Introduction

Moisture-related problems remain a major concern in buildings because prolonged dampness can support microbial growth, degrade materials and contribute to poor indoor environmental quality. The World Health Organization has emphasised the importance of preventing persistent dampness and microbial growth on interior surfaces and within building structures. However, the presence of elevated relative humidity at a single instant does not by itself describe the likelihood or severity of mould development. The response of a material depends on the combined effects of temperature, relative humidity, exposure time, the susceptibility of the substrate and the environmental history preceding the current condition.

Mould on office ceiling tiles - and simulation of mould growth.

The VTT (Valtion Teknillinen Tutkimuskeskus / Technical Research Centre of Finland) mould-growth approach was developed to represent this time-dependent behaviour numerically. The original mathematical model of Hukka and Viitanen (1999) described mould growth on wooden materials under fluctuating temperature and humidity conditions. Later work extended and recalibrated the approach for a broader range of building materials, including the use of material sensitivity classes and modified decline behaviour during unfavourable periods (Viitanen and Ojanen, 2007; Ojanen et al., 2010). The model expresses the predicted state through a dimensionless Mould Index, M, ranging from 0 to 6.

Although the model is available in scientific publications and is incorporated into specialised hygrothermal software, its equations can also be implemented transparently in a spreadsheet. This provides a practical way to inspect each intermediate variable, modify assumptions and compare alternative operating strategies. The objective of this work was therefore to develop an Excel-based VTT Mould Index tool that calculates the evolution of mould growth potential from hourly surface temperature and relative-humidity data and allows different humidity-control scenarios to be compared within a common modelling framework.

Methodology

VTT Mould Index model

The VTT model represents mould development using the Mould Index M. The index is not a concentration of spores and it is not a direct microbiological measurement. Instead, it is an empirical indicator calibrated from experimental observations of mould development on material surfaces. The scale ranges from M = 0, corresponding to no detected mould growth, to M = 6, corresponding to very extensive mould growth. The updated material-class formulation described by Ojanen et al. (2010) is used as the scientific basis of the present spreadsheet implementation.

Table 1: Interpretation of the VTT Mould Index scale, paraphrased from Ojanen et al. (2010).

Model input parameters and material sensitivity classes

For each calculation time step, the spreadsheet requires the surface temperature, surface relative humidity and time-step duration. In addition, the user specifies the material sensitivity class, the mould-decline coefficient C_eff and the initial mould index. The sensitivity class controls the minimum humidity threshold and the growth parameters used by the model. Ojanen et al. (2010) grouped materials into four sensitivity classes: Very Sensitive, Sensitive, Medium Resistant and Resistant. This classification allows the same mathematical framework to be applied to materials that exhibit substantially different mould-growth responses.

Table 2. Material sensitivity parameters used in the updated VTT mould model (Ojanen et al., 2010).

Critical relative humidity

Equation 1 - Critical relativity humidity equation

Favourable mould-growth conditions require both 0 < T < 50 °C and RH_crit ≤ RH.

If the actual surface relative humidity is below RH_crit, the current environmental condition is treated as unfavourable for mould growth. The time spent under such conditions is tracked because the duration of the unfavourable period affects the decline calculation described later.

Maximum attainable mould index

The model does not allow unlimited growth under every favourable condition. Instead, a maximum attainable mould index, M_max, is calculated from the current relative humidity and the material-specific coefficients A, B and C. M_max represents the level toward which the mould index can develop under the current hygrothermal condition. It should not be interpreted as an instruction to immediately reduce the current mould index whenever environmental conditions become less favourable. In the spreadsheet, M_max is therefore used as a growth-limiting quantity rather than as a direct cap that instantaneously resets M.

Equation 2 - Relative humidity ratio. Equation 3 - Maximum attainable Mould Index

Growth coefficients and mould-growth equation

Two coefficients control the instantaneous growth rate. The first coefficient, k₁, represents the material sensitivity and takes one value while M < 1 and another value when M ≥ 1, as shown in Table 2. The second coefficient, k₂, progressively reduces the growth rate as the current mould index approaches M_max. Consequently, the model predicts faster growth when the material is far from its current maximum attainable state and progressively slower growth as that state is approached.

Equation 4 - Growth-limiting coefficient k_2

Under favourable conditions, the mould-growth rate is calculated as a function of temperature, relative humidity, k₁ and k₂. The exponential-logarithmic form of the VTT equation originates from regression against experimental mould-growth data. The spreadsheet evaluates this rate at each time step and multiplies it by the time-step duration. For the case study presented here, a one-hour time step was used throughout the two-year calculation.

Equation 5 - Mould growth rate under favourable conditions

Unfavourable conditions and mould decline

When the environmental conditions are no longer favourable, growth stops and the model allows the mould index to decline. The original VTT decline formulation for pine distinguishes three periods after the onset of unfavourable conditions: an initial decline during the first six hours, a plateau between six and twenty-four hours, and a slower decline after twenty-four hours. This behaviour is important because short dry periods do not necessarily erase the effect of earlier favourable exposure.

Equation 6 - Reference Mould Index decline under unfavourable conditions

For materials other than the original pine reference, the decline is modified using an effective coefficient C_eff. Ojanen et al. (2010) used relative decline coefficients of 0.50, 0.25 and 0.10 in addition to the reference value of 1.0. A lower C_eff means that the modelled mould index decreases more slowly during unfavourable conditions. Because the material-specific decline database is less extensive than the growth database, C_eff should be regarded as an important modelling assumption and should be reported explicitly whenever the tool is used.

Equation 7 - Material-specific Mould Index decline

Excel implementation and recursive calculation

The VTT equations were implemented directly in Microsoft Excel so that every intermediate calculation remains visible to the user. Each row represents one hourly time step. The main calculation columns are Timestamp, Surface Temperature, Surface Relative Humidity, Δt, Sensitivity Class, C_eff, Previous M, RH_crit, M_max, k₁, k₂, Calculated M and Hours Since Unfavourable Conditions. The material coefficients are stored in a separate parameter table and retrieved according to the selected sensitivity class.

The calculation is recursive. At time step t, the tool first reads the previous mould index M_t−1 and the current surface temperature and relative humidity. RH_crit and M_max are then calculated, followed by k₁ and k₂. If the condition is favourable, the model applies the growth equation; if it is unfavourable, the decline equation is applied according to the accumulated duration of the unfavourable period. The resulting M_t is stored as the Calculated M value and becomes Previous M for the next row. Finally, the result is constrained to the physical model range 0 ≤ M ≤ 6.

Figure 1: Structure of the hourly VTT Mould Index calculation implemented in Excel.

Scenario comparison method

A key function of the spreadsheet is the ability to compare alternative environmental-control strategies while preserving the same mould-model parameters. Separate scenario input profiles can be defined for the baseline and for each dehumidification strategy. The environmental profiles are then passed through the same VTT calculation sequence. This approach isolates the effect of the operating strategy from changes in material sensitivity or initial mould condition.

Where air temperature and air relative humidity are used to define a scenario, the corresponding surface condition must be determined before applying the VTT equations, because the model is driven by the conditions at the material surface. In the present case study, the scenario sheets include a simplified assumption relating air temperature and surface temperature. This temperature offset is an implementation assumption for the case study and is not part of the VTT mould model itself. The surface relative humidity is then recalculated from the moist-air state and the assumed surface temperature using psychrometric relationships.

Monitored-building case study

Environmental monitoring data

The completed tool was demonstrated using environmental measurements obtained during a previous monitoring study in an existing building. The building is intentionally anonymised in this article because the purpose of the case study is to demonstrate the modelling workflow rather than to identify or evaluate a specific client or property. Temperature and relative-humidity measurements were originally recorded at one-minute intervals. Both air and surface-related measurements were available, allowing the hourly profiles required by the model to be established.

Seven complete days of measurements were selected for the demonstration period, from 9 July to 15 July 2026. This produced a full weekly sequence containing daytime, night-time and weekend conditions. The measured data were used as the basis of the baseline scenario and as the reference from which alternative dehumidification schedules were constructed.

Data processing and simulation setup

Because the VTT spreadsheet was configured with an hourly time step, the one-minute measurements were converted to hourly values. For each hour, sixty consecutive measurements were averaged to obtain one representative hourly value. The same procedure was applied to the temperature and relative-humidity variables used by the model. This aggregation reduced the size of the calculation while preserving the daily pattern of the measured environment.

The seven-day dataset produced 168 hourly values. To investigate the long-term behaviour of the model using a controlled and repeatable input pattern, this 168-hour profile was repeated continuously over a two-year simulation period. This is a deliberate scenario assumption rather than a forecast of the actual future building environment. In particular, the repeated-week approach does not represent seasonal changes, weather variability, occupancy changes or long-term operational changes that would occur in buildings in a varied climate with distinct seasons (summer, autumn, winter). For a building in the tropics with no / minimal seasonal variation, it is acceptable to use 1-week measured data to be representative for each week of the year. The two-year result should therefore be interpreted as the model response to repeated exposure to the selected measured week.

Investigated scenarios

Three calculation cases were compared. The Baseline case reproduces the selected measured weekly environmental profile. Dehumidifier 1 represents weekend-only dehumidification, while Dehumidifier 2 combines night-time weekday dehumidification with continuous weekend operation. In both dehumidification scenarios, the air relative-humidity target during operation was 50%. The same sensitivity class, C_eff, initial mould index and hourly time step were maintained across the three cases so that the comparison reflects only the change in environmental exposure.

Table 3. Summary of the environmental scenarios evaluated in the case study.

Results

The Excel tool generated a continuous hourly Mould Index trajectory for each of the three scenarios over the two-year simulation period. Figure 2 compares the three calculated trajectories on the same axes, allowing their long-term behaviour to be compared directly. The vertical axis ranges from M = 0 to M = 6, corresponding to the full range of the VTT Mould Index scale, while the horizontal axis shows the elapsed simulation time from 0 to 24 months.

Figure 2: Predicted evolution of the VTT Mould Index for the baseline and two dehumidification scenarios over the two-year simulation period.

For the baseline case, the Mould Index started from M = 4 and reached a final value of 4.577 after the two-year simulation period. This indicates that, under repeated exposure to the measured reference environmental profile, the predicted mould condition slightly increased over time.

For Dehumidifier 1, the same material properties and initial conditions were maintained, while dehumidification was applied only during the weekend, with the air relative humidity maintained at 50%. During weekdays, the measured/reference profile was retained. The final Mould Index decreased to 2.560, substantially below the baseline value of 4.577. This indicates that weekend-only dehumidification was sufficient to reduce the long-term predicted mould development compared with the reference case, but unable to completely get rid of the mould, as the Mould Index values seems to stabilise between 2 and 3.

For Dehumidifier 2, dehumidification was applied from 6:00 PM to 5:00 AM during weekdays, with the air relative humidity maintained at 50%, while continuous weekend dehumidification was applied at the same target relative humidity. The final Mould Index decreased to 0.984 after the two-year simulation period and continued to show a clear downward trend. Extending the simulation under the same conditions for a further 11 months resulted in the Mould Index reaching 0. At the end of the two-year comparison period, Dehumidifier 2 therefore had the lowest Mould Index among the three scenarios and showed a substantially stronger reduction in predicted mould development than Dehumidifier 1.

Overall, the results show a clear influence of the dehumidification operating schedule on the long-term Mould Index. Compared with the baseline case, weekend-only dehumidification reduced the final Mould Index from 4.577 to 2.560, while the combined night-time weekday and continuous weekend strategy reduced it further to 0.984. Because the material sensitivity class, C_eff, initial Mould Index and time step were identical in all simulations, these differences can be attributed to the different humidity-control strategies applied in each scenario.

Discussion

The results demonstrate that the long-term Mould Index response depends not only on the relative-humidity level, but also on the duration and timing of favourable and unfavourable conditions. This behaviour is important because the VTT model accounts for previous exposure: when conditions become unfavourable, the Mould Index decreases progressively rather than returning immediately to a low value. Conversely, when favourable conditions return, growth continues from the previously calculated state.

The comparison between the three scenarios shows the practical value of the Excel tool for evaluating humidity-control strategies. Since the material sensitivity class, C_eff, initial Mould Index and calculation time step were kept identical, the differences between the trajectories can be attributed to the different dehumidification schedules. In the present case, weekend-only dehumidification reduced the final Mould Index compared with the baseline, while the combination of night-time weekday dehumidification and continuous weekend dehumidification produced the greatest reduction.

The tool should nevertheless be considered a comparative hygrothermal assessment method rather than a direct measurement of mould contamination. The calculated Mould Index represents the modelled response of the selected material class to the imposed temperature and humidity conditions and does not replace inspection or microbiological testing.

Limitations

Several limitations should be considered when interpreting the tool and the case-study results. First, the VTT Mould Index is a modelled indicator rather than a measurement of fungal species, spore concentration or health impact. Second, the result is sensitive to the selected material sensitivity class, initial mould index and Ceff. These parameters should therefore be chosen from appropriate literature or material-specific testing where available and should always be documented alongside the result.

Third, the case-study surface conditions depend on the accuracy of the measured data and, for scenarios constructed from air conditions, on the assumptions used to estimate the corresponding surface temperature and surface relative humidity. A simplified surface-temperature offset may be useful for scenario comparison but does not replace a detailed heat-transfer calculation where surface temperature varies with envelope construction, thermal bridges, solar gains, airflow or external climate.

Fourth, the long-term calculation in this study repeats a single measured 168-hour week for two years. This provides a controlled way to compare operating scenarios but removes real seasonal and inter-annual variability. The resulting curves answer the conditional question of how the model would evolve if the selected week repeated continuously; they should not be described as a weather-based prediction of the actual next two years in the monitored building.

Finally, the implementation has been designed for transparency in Excel rather than for high-resolution coupled hygrothermal simulation. It uses externally supplied surface temperature and relative-humidity profiles and does not itself solve heat and moisture transport through the building envelope. For applications where the surface conditions are not measured or otherwise known, the spreadsheet should be coupled with an appropriate hygrothermal model or validated engineering assumptions.

Conclusion

An Excel-based implementation of the VTT Mould Index model was developed to provide a transparent and accessible method for assessing the time-dependent evolution of mould growth risk under dynamic temperature and humidity conditions. The tool reproduces the principal elements of the updated VTT formulation, including material sensitivity classes, critical relative humidity, maximum attainable mould index, growth coefficients, growth under favourable conditions and material-dependent decline under unfavourable conditions. The recursive hourly structure makes the influence of environmental history explicit and allows each intermediate variable to be inspected directly.

The anonymised monitored-building case study demonstrates how the tool can be used to convert field measurements into an hourly baseline profile and compare alternative dehumidification strategies over an extended calculation period. The final results should be interpreted primarily as a comparison between controlled scenarios rather than as a deterministic forecast of actual future fungal contamination. Within these limitations, the spreadsheet provides a practical screening and decision-support method for exploring how humidity-control schedules can influence the predicted Mould Index in buildings.

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References & Acknowledgements

• Ojanen, T., Viitanen, H., Peuhkuri, R., Lähdesmäki, K., Vinha, J., & Salminen, K. (2010). Mold growth modeling of building structures using sensitivity classes of materials. Proceedings of Buildings XI, ASHRAE.

• World Health Organization Regional Office for Europe. (2009). WHO Guidelines for Indoor Air Quality: Dampness and Mould. WHO Regional Office for Europe.

• Thank you to Gregers Reimann (IEN Consultants) for his conceptual and editorial contribution to this article.