Wound Formation and Correction in the Implexx Sap Flow Sensor.

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A wound is physical damage to living tissue. In the context of sap flow sensors, a wound occurs when a hole is drilled into the xylem (Figure 1). This injury triggers a plant response, including the formation of tyloses—a layer of dead cells that helps prevent infection and seal the damaged tissue. While the wound is superficial to overall plant health and does not hinder growth, it affects sap flow measurements, necessitating a wound correction.

Figure 1. An example of a wound caused by the drilling of holes for the insertion of the Implexx Sap Flow Sensor into xylem. The wound is a region of zero sap flow and includes the drilled hole and the adjacent discoloured ring (tyloses). The wound width is usually the average of the three wounds or the widest width.

Wound response varies across plant species, with some more sensitive than others. Based on Implexx research, plants from drier regions tend to exhibit lower sensitivity compared to those from wetter environments. Citrus species, for example, show strong wound responses, while grapevines and olives are less affected. However, wound response is unpredictable; even individuals of the same species growing in identical conditions may react differently. Consequently, direct measurement of the wound is essential.

Wound size also changes over time. In most species, its impact is negligible within the first 12 months post-drilling, though some species may be more sensitive. To maintain accuracy, sensors should be reinstalled in freshly drilled holes annually. Regardless, measuring the wound is critical for precise sap flow correction.

The wound correction process involves complex mathematical modelling, applying partial differential equations in a two-dimensional framework over discrete time steps. However, Implexx scientists have developed and validated a simplified correction equation, detailed in the following section. Most users only need to input the wound response into the Implexx Sap Flow Workbook, where corrections are automatically applied.

The wound correction model.

The Implexx Sap Flow Sensor is available in two models: the IX-SF30 and IX-SF60. However, only a single wound response correction is required, as both models share identical needle diameters, construction, and materials.

The wound response correction follows the alternating direction implicit (ADI) technique described by Swanson and Whitfield (1981). This numerical method models two-dimensional heat conduction and convection, incorporating thermal properties of both the sensor and xylem. The conduction-convection equation is presented and summarised by Forster (2020, Equations 1 and 2).

The model solves the conduction-convection partial differential equation across spatial and temporal steps, simulating heat transfer under three conditions: (1) an ideal state without a sensor, (2) with a sensor present, and (3) with additional influences, such as a wound. Subsequent statistical analyses (linear or nonlinear regression) determine the correlation between the ideal state and the deviations introduced by the wound.

In the ADI simulation for the Implexx Sap Flow Sensor, the heater and sensor needles have an external diameter of 1.8 mm (accounting for stainless steel sleeves), and material thermal properties are assigned based on material specifications. Wood thermal conductivity is set at 0.0076 W/cm·K in both the x and y directions. The wound is modelled as a region of zero heat velocity spanning the sensor width and the space between sensors.

Temperature profiles are recorded over time at the upstream and downstream sensor needles and the heater needle. Heat pulse velocities are calculated using the time-to-maximum-temperature method (Tmax) and the heat ratio method (HRM), following Kluitenberg’s (2007) modified equations (Forster 2020, Equations 10 and 13).

The HRM was originally referred to as the slow rates of flow method (SRFM) by Marshall (1958). While SRFM was the original nomenclature, modern scientists more commonly refer to it as HRM. Despite our preference to use SRFM, to maintain clarity and consistency, HRM will be used throughout this text.

Does wounding affect the HRM and Tmax methods?

The ADI technique was first applied to determine whether a wound response affected the HRM and Tmax methods. Figure 2 presents simulation results for heat pulse velocities calculated using both methods at imposed velocities ranging from 0 to 98 cm/hr, with wound widths of 0 and 1.6 mm.

Without a wound, calculated values closely match imposed values (Figure 2A). However, when a wound is present, calculated values are significantly lower than imposed values (Figure 2B). These results confirm that a wound correction is essential for accurate sap flow measurements.

Figure 2. Actual and measured heat pulse velocities from HRM (x, blue) and Tmax (+, orange), with 1:1 line in red. (A) The simulation with sensors and no wound. (B) The simulation with a 0.16 cm wound width.

The wound correction for the Implexx Sap Flow Sensor.

The ADI technique successfully corrected the measured heat velocity from the Implexx Sap Flow Sensor. By applying a scaling factor across various wound widths, it was determined that heat pulse velocities calculated using the HRM and Tmax methods closely matched the modelled values.

An example of this relationship, for a wound width of 0.18 cm, is shown in Figure 3. The results indicate that HRM exhibits a strong correlation at slow heat velocities but a poor fit at higher velocities, confirming its suitability for measuring slow flow rates. Conversely, the Tmax method shows no correlation at velocities below approximately 15 cm/hr but demonstrates a strong relationship at higher velocities.

Figure 3. The results of the wound correction for HRM (blue) and Tmax (orange) with a wound width of 0.18 cm.

The complete simulation results for different wound widths are summarised in Table 1. For the Gen 2 Implexx Sap Flow Sensor, the wound correction value is given by:

Wound Correction = 6.5022w + 0.5399

where w is the measured wound width (cm). Users only need to measure the wound width and input this value into the equation. This correction is automatically applied in the Implexx Sap Flow Workbook.

Table 1. A summary of the scaling factor, derived from the ADI technique, for varying wound widths for the Gen 1 and Gen 2 Implexx Sap Flow Sensors.

The dual method approach (DMA) and wound correction.

Previous applications of the ADI technique focused on wound correction for individual sap flow methods, such as HRM, Tmax, or compensation heat pulse (CHP). However, it was unclear whether a single wound correction could be applied across multiple methods. The dual method approach (DMA), proposed by Forster (2020), combines HRM at slow velocities and Tmax at faster velocities, with the transition determined by a theoretically derived threshold. Since DMA integrates two methods, it was uncertain whether a single wound correction would be sufficient or if separate corrections were required.

The ADI technique confirmed that a single wound correction is accurate for the DMA in the Implexx Sap Flow Sensor. Figure 4 presents an example simulation result for a 0.24cm wound widths (other wound widths produced similar results).

The results show a strong overlap between HRM and Tmax in the transition region where heat pulse velocity was approximately 17 to 22 cm/hr, supporting the validity of a single wound correction. At slow velocities, HRM provides accurate measurements, while Tmax is unreliable. Conversely, at faster velocities, HRM becomes increasingly inaccurate, whereas Tmax maintains a strong relationship with imposed values. These findings validate both the DMA and the applied wound correction procedure and support conclusions by Forster (2020.

Figure 4. An example of the simulation results for a 0.24 cm wound width illustrates that a single wound correction is suitable for the DMA. HRM used for the DMA (dark blue) and HRM discarded from the DMA (light blue). Tmax used for the DMA (dark orange) and Tmax discarded from the DMA (light orange). There is a heat pulse velocity around 17 to 22 cm/hr where the HRM and Tmax values overlap, confirming the results from Forster (2020).

Conclusion.

A wound correction for the Implexx Sap Flow Sensor was successfully derived using the ADI technique. For the Gen 2 model, the correction is given by:

Wound Correction = 6.5022w + 0.5399

where w is the measured wound width (cm).

Users can enter the wound width into the Implexx Sap Flow Workbook, where the correction is automatically applied for accurate sap flow measurements.

References.

Forster (2020). doi: 10.1093/treephys/tpaa009

Kluitenberg (2007). doi: 10.2136/sssaj2006.0073N

Marshall (1958). doi: 10.1104/pp.33.6.385

Swanson & Whitfield (1981). doi: 10.1093/jxb/32.1.221