MICROLEAKAGE

INTRODUCTION One of the requisite of a restorative material is

to adapt itself to cavity walls The gap left between cavity walls and the

restorative materials plays important role in the prognosis of the restorative treatments .

Bacterial leakage is a greater threat to pulp than the toxicity of restorative materials.

Definition :

Microleakage is defined as “The clinically undetectable passage of  bacteria and bacterial products, fluids, molecules or ions from the oral environment along the various gaps present in the cavity restoration interface”.

Nanoleakage

Specific type of leakage within the dentine margins of restorations, with fluid transport through bonding layers

Detectable only by electron microscopy techniques

Leakage occurs within nanometrisized spaces around collagen fibrils within hybrid layer that have not infiltered by resin (Sano et al)

Paths of transport are related to

hydrolytic degradation

acid etching procedure, by allowing the penetration of pulpal and oral fluids into porosities within or adjacent to the hybrid layer

The amount of penetration depends on the type of bonding agent used hydrophilic nature of monomers within the

adhesive different parameters of the application technique

such as dentine moisture and etching time.

Possible Routes of Microleakage :1)Within/via the smear layer.

2)Between the smear layer and cavity varnish/cement.

3)Between the cavity varnish/cement and the restoration

Min of 1µm space is left at tooth restoration interface even after employing the adhesive liners and materials

Clinical implications

Post-operative sensitivity Secondary Caries/Recurrent Caries Pulpal pathology Marginal discolouration Dissolution of the certain materials like

cements Partial or total loss of restoration

Post-operative sensitivity

Due to direct communication between oral fluids and pulp

Leads to change in local ionic concentrations.

Leakage of acids/basic materials and other substances produce movement of fluids in tubules

Lead to pain in pulp

More pronounced in proximal & cervical cavities

More common in resin restorations due to polymerization shrinkage

Secondary Caries/Recurrent Caries :

Carious lesions exist along walls of a restored cavity microleakage at tooth restoration interface

Bacteria with diameter > 1.0µm - penetrate the gaps.

Gap width 50µm - can house nutrients for the bacteria recurrent caries.

Pulpal pathology :

Marginal gaps allow growth of bacteria.

Produce a number of inflammatory components

Penetrate unprotected dentinal tubules

Pulpal diseases

Marginal discolouration :

Evident in esthetic restorations

Accumulation of subsurface interfacial staining

Dissolution of the certain materials like cements

Causes of microleakage

Dimensional changes of materials due to polymerisation shrinkage

Thermal contraction Absorption of water Mechanical stress Dimensional changes in tooth structure

Factors that Influence Microleakage

Properties of restorative materials

Operators care in placing material

Properties of restorative materials

Major • Coefficient of thermal expansion • Plymerization shrinkage• Adhesion.

Minor

CreepElasticityResistance to fatigue failuresSolubility

Coefficient of thermal expansion (CTE) :

change in length per with length of a material per degree change in temperature.

With increase in temperature expansion

With decrease in temperature contraction

Ideally rest material should closely matches to tooth

The coefficient of thermal expansion of composite resin (25 to 60 ppm°C-1) is

several times larger than that of enamel (11,4 ppm°C-1) and

dentin ( 8 ppm°C-1) 28. This physical property is also reported to be

responsible of microleakage in resin-based

restorations

Polymerization Shrinkage :

Occurs with polymeric materials

Monomer chains are polymerized polymer chain

Decrease in volume and increase in density

Pulls material away from cavity walls.

Intermediate adhesive resin high contraction stresses break in adhesive bond microleakage

Modern composite resins undergo volumetric contractions ranging between 2.6% to 4.8 % 19.

Even when modern dentine bonding agents exhibit bond

strengths to dentine higher than 20 MPa20, exceeding the

contraction stress generated by polymerisation stress (13-17 MPa),

the total contraction forces may be higher than the

adhesive strength, leading to open margins.

The shape of the cavity can also challenge the adaptation of

the restorative material to the margins. Indeed, the C-factor of

cavities is closely related to the occurrence of microleakage,

especially when restored with a composite resin and dental

adhesive

Adhesion :

Adhesion is the attraction of molecules of two different substances to each other when they are brought in close contact.

Lack of adhesion microleakage

Adhesion influenced by – 

Wetting capabilities Surface energy Presence of water & smear layer  Composition of enamel and dentin Surface roughness

Influence by operator :o Improper isolationo Poor packing , condensation & insertiono Poor cavity designs increased diamensional

change early dissolution poor marginal fito Poor burnishing of margins of cast inlay

exposing thin cemental line to oral cavity

Surface contamination inadequate bond microleakage

Role of smear layer in microleakage :

Subsequent to instrumentation of the tooth, the natural deposits composed of microcrystalline cutting debris embedded within the denatured collagen is formed on the cut surfaces known as “smear layer”.•It is 1-2µm thick •Consists of blood, saliva, bacteria, enamel and dentin particles

Initial cutting debris – may be pushed into tubulesby 1-5µm smear plugs

Divergence in opinion role of smear layer

One opinion – leave smear layer intact to act as barrier

Smear layer is acid labile at pH 6.0- 6.8 &less

When pH level drops – it dissolves

2nd opinion – remove smear layer 

SL contain bacteria & prevent diffusion of bacteria but not bacterial products

Removal good adaptation of adhesive material.

Best way – remove natural SL but not smear plugs 

Replace with sterile, inert and non toxic synthetic SL

Factors controlling bacterial penetration : Size and nature of the gap :

Varies with different rest materials – 10-50µms

But 10µm is enough for lactobacillus entry.

Self sealing capability of rest materials reduce bacterial penetration

Self sealing occur because of 

o Deposition of mineral salts of low solutility

o Accumulation of corrosion products

o Calcification of plaque like debris around margins

Host defence factors :

Sclerotic dentin/reparative dentine decrease ML

Hydrostatic pressure of pulp more than outside pressure of oral cavitymoves dentinal fluid outside opposes inward movement of bacteria & products

Plasma proteins in dentinal fluid – act as antimicrobial agents

Large molecular weight proteins like fibrinogen make dentin less permeable to bacteria

•Presence of smear plugs – increase M.L.

•Alteration of chemical structure of dentin byleaching of tin/Mercury ions from amalgam &leaching of fluoride from GIC and silicate cement checks bacterial diffusion

Restorations

Alters dentin permeability 

GIC, silicates, compomers release fluoride into gaps- antimicrobial effect

Silver, tin, mercury – decrease ML 

Microleakage around amalgam restoration

Fresh condensed amalgam – does not adapt closely to walls of prepared cavity(10-15µm gap)

Adaptation improves with time self sealing restoration due to corrosive products

In low copper –Corrosive products like oxides & chlorides of tin

In high copper – greater resistance to corrosion & slower rate of formation of corrosive products microleakage for longer period

ML due to dimensional changes :•Quite minimal•During setting – small contraction initially (when mercury is consumed)•Followed by small expansion (as crystal matrix is formed)

High Cu alloys – dimensional change very little (±0.2% by volume)•According to ADA No. 1 – dimentional change of 20µm/cm is allowable for set amalgam.•Coefficient of thermal expansion of amalagm not much different from tooth Moderate leakage

Measures to reduce microleakage :

Types of alloys :Different types have different leakage•Spherical alloy – more leakage & postoperative sensitivity.

Because not closely adapted more shrinkage after it sets

•So lateral condensation done•Better to select lathe cut/admixed alloys

Condensation of amalgam :

o Condense immediately as time lapse loss of plasticity & increase in internal voids & layering

o Incremental insertion – for proper condensation & adaptation of each increment

o Adequate condensation pressure – 10 pounds with 2 mm condenser tip( varies with alloy particle)

Condensation from center to periphery (stepping process)

Removes air spaces & pushes material against cavity walls decreases microleakage

Mechanical condensation better

Burnishing :

•Adapt material to margins decrease microleakage

Enhance homogenity

Varies with particle shape of amalgam

•Spherical alloys – no reduction in micreleakage.Because during condensation particles may be pushed aside

Alloys with lesser creep values :

• Less creep – less M.L.

• According to ADA no.1 creep > 3% is acceptable

Low copper alloys – 0.8 –8%

High copper alloys – 0.1 – 1% (decrease ML)

Sealing the cavity wall with varnish

•Prevents microleakage (until corrosion products form)

•Benefit does not exist as long as life of restoration solubility in oral environment

. Limited to six months (enough for corrosion products to fill gaps)

Application of varnish under high copper amalgam do not reduce ML

Use of GIC liners – decrease microleakage

Sealed amalgam restorations

A coating of unfilled resin is placed over rest margins and adjacent enamel after etching enamel surface

Resin may wear away But covers until corrosion products fills gap

Offer fewest marginal deficiency &best survival rate compared to traditional amalgam &composite resin

Bonded amalgamsHave shown to overcome microleakage

Use of gallium alloys

It has high wetting ability

Microleakage around GIC :

Adheres to tooth with chemical bond between carboxyl groups of cement and Ca+ of tooth

Hydrophilic so can bond even in wet surfaces•C.T.E – closely match tooth•Fluoride releasing property

Has ability to renew broken ionic bonds

•Highly technique sensitive •first 30 min –isolation from moisture – ions are leached out interfere with tooth restoration interface•first 24 hours – more solubility results in chalky,crazed or cracked surface ML

coat surface with varnish/unfilled resins protect from dehydration

Using of sharp hand instruments for finishing before material has completely setharms marginal integrity

Prevention

1)Proper manipulation •Liquid/powder ratio-if lower – increase solubility•Placed only after proper cleaning of the surfaces

2) Use rotary instruments over manual cutting while finishing tear material at margins marginal ditching done after 24 hrs

Prior conditioning – increase bonding – decrease ML ( tannic acid, poly acrylic acid citric acid )

RMGI Rapid initial setting – decrease moisture contamination decrease ML

Increased ML compared to chemically cured bcoz resin component causes it to shrink during polymerization & setting

Chemically cured GIC permit stress relief RMGI more rapid setting contraction through light polymerization

RMGI –less water &less carboxylic content decreases wetting increase ML

Protection from moistureDuring fInishing – apply Vaseline /petroleum jelly•Final protection – 2 coats of varnish/unfilled resin

Varnish semipermeable Unfilled resin-more resistant water  But varnish preferred –as at adheres closely

Microleakage around composite restorations :

Unable to bond on their own to tooth Marked polymerization shrinkage Thermal expansion/contraction-predispose to ML Prior treatment of tooth acid etching , priming /

conditioning use of enamel &dentin bonding agents necessary•If insufficient enamel thickness – increase M.L.

It bonds dentin but not protect dentin restorative interface completely

vitality of dentin

due to difference in physical &chemical composition of dentin

presence of dentinal fluids smear layer etc

Development of internal stresses from polymerization shrinkage and thermal effects detrimental

Factors contribute to marginal leakage of composite Technique sensitive Polymerization shrinkage, masticatory forces,

water sorption, thermal changes formation of marginal gap

Volumetric polymerization shrinkage- range 1.67 – 5.68% less for light activated

DB agents - bonds composite to tooth structure shrinkage development of tensile/shear stresses

Within limits adhesive bond withstand stress

Once the stresses exceed bond strength and the plastic/elastic deformation of combined system Separation of interface ->ML

Functional stresses due to masticatory forces ML due to repeated plastic/elastic deformation of rest

Difference in CTE of resin& tooth detrimental C.T.E of composite 22-55 × 10-6 C-Higher than tooth - debonding microleakage

Water absorbtion

Absorb water from environment cause rest to expand

Able to compensate poly. Shrinkage – but mechanical prop impaired

o Technique sensitive : in class II :

.Placement in gingival areas difficult•Entrapment of air •Difficult during condensation (sticky)•Inadequate bonding to gingival wall – polymerization shrinkage

Measures to Reduce Marginal Leakage

1-Choice of materialMicrofilled :Better marginal adaptation due to .greater flexibility decreases contraction forces .more water absorption counteract shrinkage

2-Cavity design :size of cavity

.conservativeto overcome PS & wear under occlusal stress

.Modified cavity design

.Placement of bevel

.Reduced depth

.Rounded internal angle reduce leakage

Shape of cavity

Decreasing ratio of volume/areareduction in ML Role of bevel in cavosurface margin-controversial

recommended on accessible facial &lingual margins beveling gingival margin –not indicated

3– Acid etch tech &bonding Acid etch –removes surface contaminants

raises surface energy

increase reactivity of enamel

increase surface area for bonding Polymer tag –provide micromechanical

interlocking reduces ML

Effectiveness is compromised by Position Surface structure of enamel

Negligible ML score on occlusal cavosurface margin but significant ML on gingival margin

Reduced degree of nanoleakage with self etching priming system than with system use acidic conditioner as separate step

Long term performance of DB agents under stress &continued exposure to oral fluid -questionable

Glass ionomer bonding agents

Eg scotch bond multipurpose,Pertac universal bond attatch composite to GIC

Diluted version of RMGI (Fuji Bond ll LC)- replace conventional bonding agents under composite reduce ML

Cavity filling tech Thick /bulk material high PSS ML Small multiple increment control PSS Thickness of increment 1.0-1.5mm recommended

To minimize PSS improving placement techniques improving material and composite formulation curing methods

Different placement tech &issues The incremental technique Direct shrinkage Bulk technique

The incremental technique polymerizing with resin-based composite layers

less than 2-millimeters thick achieve good marginal quality prevent distortion of the cavity wall ensure complete polymerization of the resin-

based composite

Horizontal technique› occlusogingival layering › generally used for small restorations› increases the C-factor

Three-site technique› clear matrix and reflective wedges› guide the polymerization vectors toward

the gingival margin.

Oblique technique› wedge-shaped composite increments

› prevent distortion of cavity walls and reduce the C-factor

› polymerization first through the cavity walls and then from the occlusal surface

› direct vectors of polymerization toward the adhesive surface (indirect polymerization technique)

Successive cusp buildup technique

› the first composite increment is applied to a single dentin surface without contacting the opposing cavity walls

› Then wedge-shaped composite increments

› Each cusp then is built up separately

› to minimize the C-factor in 3-D cavity preparations

Schematic representation of wedge-shaped composite increments(1-6) used to build up the enamel proximal surface. F: Facial aspect. L: Lingual aspect

Decreasing resin filler ratio control PS Introduction of beta quartz glass inserts as mega

fillers no PS & water sorption Inserts are made of lithium aluminosilicate glass C.T.E close to dentin Pre polymerized composite ball substitute for glass

insert Soft start polymerisation –reduce marginal gap

&improve marginal integrity

5 Direction of light source While curing proximal restoration –gingival

increment shrink occlusally Curing aids –light curing wedges ,flexible light

guides ,focussing tip better curing &invert shrinkagetowards gingival floor vectors

Three sited light curing tech better adaptation

6 sealing the marginal gap

Application of unfilled low viscosity resin to marginafter polishing

7 Delaying finishing process

delay 24 hrs until polymerisation complete

Dry finishing tech increased ML

Light intermittent stroke with generous air coolant

Use of Soflex disks best marginal quality

8 Use of cavity liners and bases

Calcium hydroxide & GIC – commonly used

Adv : protect pulp

reduces bulk of composite resin –PS Bond of GIC to dentin –stronger Bond bet etched GIC & composite –stronger CTE close to tooth Fluoride reservoir Kind to pulp Bilayered restoration /sandwitch restoration Light cure GIC –better performance

9 use of composite inlay restoration

Chemically cure/dual cure

bulk of contraction occur prior to cementation- PS

vulnerable part- luting cements

Hybrid luting resin more susceptible to wear than microfilled

Fails to bond chemically with inlay- 60% failure after 6mos

Light curing luting agents – not preferred lead to high conversion rate of inlay

reduces availability of remaining un converted monomers for co-polymerization with the luting resin

Fails to bond chemically with inlay

Chemically cured preferred than light cured inlay may be 2 mm/more thick

How to Improve bond bet composite & resin cement

Use of solvents (ethyl acetate)-soften cavity side prior to cementation

sand blasting cavity surface with aluminium oxide –increase bonding

Etching with 10%hydrofluoric acid

10 expanding matrix resins for composites

Expand while polymerization

Compensate polymerization shrinkage

Spiro-orthocarbonates are used

Used with epoxy resin

Microleakage around direct gold restoration

Factors contribute for decreased microleakage

High malleability &ductility –burnishing

Short bevel on cavosurface margin

Complete insolubility in oral fluids

Elastic compression of underlying dentin while condensation-strong adaptation

Good adaptibility of gold to cavity walls

decreased microleakage

Improper compaction air spaces/voids Type of gold selected Non-uniform method of stepping Improper lines of force Inadequate condensation pressure

Measures to reduce leakage Mat/powdered gold –

more porous

improper cavity seal

used for internal bulk of restorarion & cohesive gold used as veneer

prevents leakage

Uniform stepping of condensor tip in individual steps as well as lines of steps

Stepping from centre to periphery Lines of force directed

90° to pulpal floor in centre

45° to cavity walls at periphery Average force of 10 pounds applied with 1.0mm

condensor point – optimal Building of restoration done in convex form Surface procedures like burnishing, finishing,

polishing – improve marginal seal

Microleakage around cast restoration

Gap ranging from 10-160 µm reported in cast restoration

Intermediate layer of luting cement –necessary for retention

Adhesive luting cement –added chemical retention

Excessive taper of underlying preparationpromote leakage

low viscous luting agent preferred

↓

 It penetrate into irregularities of both tooth and rest

↓

micromechanical retention

 Now – adhesive luting agents available with addedchemical retention

intermediate cement layer-promote leakage

↓   Highly solubile cements(zinc phosphate, silicate,

silicophosphate)burnishing delayed for 24 hrs

margins are not adequately beveled and burnished

cement line may be exposed to oral environment

Eg ging areas in class II inlays

↓ when harder gold is used for crowns-not easy to

burnish

Measures to reduce microleakage : Adhesive luting agents should be preferred

↓

chemical bonding

In case of gold –  Bevels placed properly Burnishing margins (malleable and ductile)

↓

If rest have close fit within 20µms

↓ degradation of cement is resisted

↓ increase life of restoration

Microleakage around porcelain restoration

Resin cement for luting dual cure Treating surface of inlay mechanically &chemically Acid etching using hydrofluoric acid for fired

porcelain Ammonium bifluoride for milled & cast ceramic Etched surface is silanated –to promote wetting Most vulnerable site - wear of cement lute &

interface zone

Microleakage around porcelain restorations :

Dental porcelain is a brittle material

low tensile strength

if strain exceeds 0.1%

fracture

so bonded properly

Later weakened by hydrolysis

↓

decrease bond strength after 1 year 

↓

wear of cement lute at interfaces with inlay and tooth

Interfacial gapsVaries with diff. systems because of technique sensitivity

Difficult to prepare ceramic inlays that precisely fit cavity.

Fired ceramic inlays – depend on operator skill

Ceramic inlays gaps wider than composite inlay

Measure to reduce microleae  • Operator skill and patience. Advances in adhesive technology Resin luting cements better than luting cements as bond

degrates with time ceramic inlay surface treated both mechanically and chemicallyfirstst – acid etching done-Hydrofluoric acid – for fired porcelain-Ammonium bifluoride – for milled / cast ceramics

↓give micromechanical retention↓etched surface than silanated to increase wetting and so

improveschemical retention.Resin luting cements should not be applied with one prior tooth

bonding procedures.Closure fit of restoration Closure fit of restorationOperators skill and patience Glass ceramic restorations (dicor) – excellent marginaladaptation

Method to detect microleakage :

Invitro tests tries to simulate oral environment by thermocycling

Dynamic nature of pulpodentinal complex and its defence mechanisms cannot be easily simulated

Accumulation of plaque and other agents might vary the microleakage results in vivo.

The various methods are described, however none of these method is considered perfect till now

Methods

1) Dyes

2) Chemical tracers

3) Radioactive isotopes

4) Neutron activation analysis

5) Scanning electron microscopy

6) Bacterial studies

7) Electrochemical studies

8) Air pressure

9) Artificial caries

10) Pain perception

11) Reverse diffusion method

Dyes : Coloured agents like organic dyes used Have contrasting colour 

Agents used Methylene blue India ink  Crystal violet Fluoroscein Rhodamine B eosin Basic fuschin Erythrosine

Requirements : Should not bond to tooth / restoration

Should be color stable under all conditions of investigation

Availability : Solution Particle suspensions of different particle sizes

Technique Immersion of restored/extracted tooth in dye

solution for predetermined period Tooth removed, washed and sectioned Examined under microscope for extent of

penetration of dye Results quantified by assigning numbers to the

defined depth of penetration

Limitations : Diff. conc of two dyes vary penetrations times

from 5min-1 hr. Dyes may bind to tooth / restorations

Eg : basic fuschin bonds to carious dentin and mistaken for large gap.

Some dyes may be not colour stable

Eg : aniline blue – colourless in alkaline conditions such as in presence of Ca(OH)2

Figure 9-10: To evaluate microleakage after immersion in a dye solution,each tooth is embedded in acrylic resin and longitudinally sectioned atthree different levels in the mesio-distal direction.

2) Chemical tracers :

Rely on reaction b/w one and more chemicals used

Chemical used : 50% silver nitrate solution / 1% silver chloride benzene 1,4-diol (hydroquinone) – photographic developer 

Technique

Two colourless chemicals react – produce an opaque ppt (usuallysilver salt)

Immerse extracted/ filled tooth in 50% silver nitrate solutions which reacts with photographic developer (benzene 1,4 diol)& opaque silver salt produced

Limitations : Similar to dye penetration methods

3) Radioactive isotopes : 45Ca,131I, 32P, 14C, 35S, 86Rb etc used similar to

dyes-to asses microleakae Technique Specimens are immersed in isotope solutions Removed, washed, sectioned autoradiographed to

detect tracer 

Advantages :

They can detect minute amount of microleakage

Because of their small size – 40nm whereas dye smallest size is – 120nm

Limitations :

a)Subjective assessment of results (with using steriomicroscope – subjectivity can be minimized

b)High energy isotopes produce scatter on film – mistaken for increased leakage

Isotopes of low energies preferred for resolution

c)isotopes of 45Ca – have affinity to tooth / rest material – may mislead the results

d)Expensive and technique sensitive

 4) Neutron activation analysis :

Both invivo &invitro

Technique : Restored tooth soaked in an aqueous solution of

non-radioactive manganese salt

Then tooth placed in core of nuclear reactor 

Bombardment with neutrons activates 55Mn - 56 Mn Radiation emitted by tooth is measured to quantify

the volume of tracer  present.

Limitations :

Inability to identify the points where rest. has leaked 

Heavy experimental costs

Combined effort of nuclear engineers and dentists required

Manganese may be absorbed by tooth / rest material

5) Scanning electron microscope :

It is direct visual observation of rest adaptation to cavity margins because of high magnification and depth.

Used in both invivo and invitro.

Earlier – used replicas of tooth

Recently – low vacuum SEM evaluates rubber base impressions directly

↓ Reduces number of steps Inaccuracy is decreased

Limitations : Potential to induce artifacts during specimen

preparation

6) Bacterial studies : Test the possibility of bacteria penetrating

through or around rest.material

Technique : Restored teeth is immersed in the cultured broths Filling is removed Dentin sharing from the base of cavity cultured.

Limitations :

Results are qualitative and not quantitative

Marginal gaps of 0.5-1µm or larger – allow bacterial penetration

Smaller than this gap cannot be detected- allow penetration of harmful toxins

7) Electrochemical studies :

Technique : Insertion of electrode into extracted tooth in a

way that it contacts base of rest Once restored, teeth is sealed to prevent any

electrical leakage through natural tooth structure. Then immersed in a electrolytic bath Potential is applied between tooth and the bath Leakage assessed by measuring current flow

across as serial resistor

 

Drawback :

Unsuitable for metallic rest

Inability in invivo situations

8) Air pressure

Compressed air was used to test the marginal seal

Technique : Compressed air is introduced through the root

canal and pulp chamber  loss of pressure is measured within static system microscopic examination of air bubbles at

margins is noticed – subjective view.

Disadvantages : Inability to use invivo Drying effect of compressed air  Some air may leak before it enters tooth

Advantage : Tooth need not be destroyed and result can be

quantified

9) Artificial caries

Produced invitro using bacterial cultures / chemical system-acidified gelatin gel tech

Histological appearance on polarized light –two parts

Outer lesion features of primary attack

Cavity wall formed by ML of ions from caries inducing medium into tooth restoration interface

Advantage

ML directly related to develop of artificial lesion

Depth of lesion measurable parameter

10) Pain perception

Suspected margins painted with calcium chloride

After few min pain perceived open communication(30-60sec)

Disadvantage Subjectivity reg pain perception of patient

11) Reverse diffusion method Place tracers/calcium hydroxide on cavity floor

prior to insertion of restorative material Immerse tooth in definite volume of medium Measure amount of tracers leak into medium pH of Ca(OH)2 seen when litmus paper is

placed at interface

Advantage Measure time dependent leakage

Limitations

Minimum amount of tracer necessary at a given time

How to quantify ML with the number of tracers