Negative porosity issue in the Heckel analysis: A possible solution

A parameterization of compaction simulator generated dynamic compression profile with a few grams of powder provides important information about the material deformation and compact elasticity. The Heckel equation is by far the most popular choice among pharmaceutical scientists for such parametrization. A general approach of Heckel analysis uses pycnometric powder density (ρP0) for relative density calculation. However, as ‘in-die’ tablet bulk density at applied compression pressure (ρBP) becomes greater than or equal to the measured ρP0, the general approach typically poses a negative porosity challenge at high compression pressure regions. It is only theoretically possible to have a tablet with zero or negative porosity. Negative porosity may be detected during ‘in-die’ compression analysis, but it will not exist after ejection of the tablet in practical aspect.


  • Pycnometric tablet density can resolve Heckel negative porosity issue.
  • New approach allows efficient use of full Heckel plot without negative porosity.
  • New approach can overcome the limitations of modified Heckel equation approach.

Thus, the present work proposes a new approach to using pycnometric tablet density (ρPP) in the relative density calculations of Heckel analysis. This ρPP may be a better representation of actual tablet particle volume, as it is composed of non-accessible intra-particulate pores, which are broken under applied compression pressure. A new approach showed its immunity for Heckel high-pressure negative porosity. It enables the utilization of the compression and decompression phases of dynamic compression profiles to evaluate macroscopic compaction performance. The proposed approach was validated with a reported modified Heckel approach. The Heckel parameters computed with both methodologies for microcrystalline cellulose and lactose were not statistically different. However, a modified Heckel approach was unable to compute Heckel parameters of poorly compacting starch unlike the new approach. A modified Heckel approach became invalid during starch compaction at low compression pressures (below 400 MPa), where starch was forming weaker but still intact tablets. Certainly, a complete Heckel profiling with a new approach could save time and costs in an early development stage for designing and screening scientifically based lead prototype formulations.

Read more

Devang Patel, Vivek D. Patel, Robert Sedlock, Rahul V. Haware, Negative porosity issue in the Heckel analysis: A possible solution, International Journal of Pharmaceutics, Volume 627, 2022, 122205, ISSN 0378-5173,

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